diff -Nru eclib-20220621/configure.ac eclib-20221012/configure.ac
--- eclib-20220621/configure.ac	2022-06-21 14:25:26.000000000 +0000
+++ eclib-20221012/configure.ac	2022-10-12 11:04:09.000000000 +0000
@@ -7,7 +7,7 @@
 # The version is the concatenation of 'v' and the year, month, date: vyyyymmdd
 # To access this as a string or integer triple, see libsrc/eclib/version.h
 
-AC_INIT([eclib], [20220621], [john.cremona@gmail.com])
+AC_INIT([eclib], [20221012], [john.cremona@gmail.com])
 
 AM_INIT_AUTOMAKE([-Wall])
 AC_MSG_NOTICE([Configuring eclib...])
@@ -40,9 +40,9 @@
 #
 # NB The suffix of the library name (libec.so here) is (c-a).a.r
 
-LT_CURRENT=10
+LT_CURRENT=11
 LT_REVISION=0
-LT_AGE=0
+LT_AGE=1
 AC_SUBST(LT_CURRENT)
 AC_SUBST(LT_REVISION)
 AC_SUBST(LT_AGE)
diff -Nru eclib-20220621/debian/changelog eclib-20221012/debian/changelog
--- eclib-20220621/debian/changelog	2022-06-22 07:03:59.000000000 +0000
+++ eclib-20221012/debian/changelog	2022-10-18 05:06:17.000000000 +0000
@@ -1,3 +1,15 @@
+eclib (20221012-1) unstable; urgency=medium
+
+  * New upstream release.
+
+ -- Julien Puydt <jpuydt@debian.org>  Tue, 18 Oct 2022 07:06:17 +0200
+
+eclib (20220621-2) unstable; urgency=medium
+
+  * Fix d/watch.
+
+ -- Julien Puydt <jpuydt@debian.org>  Sun, 02 Oct 2022 21:48:28 +0200
+
 eclib (20220621-1) unstable; urgency=medium
 
   * New upstream release.
diff -Nru eclib-20220621/debian/watch eclib-20221012/debian/watch
--- eclib-20220621/debian/watch	2022-06-22 07:03:59.000000000 +0000
+++ eclib-20221012/debian/watch	2022-10-18 05:06:17.000000000 +0000
@@ -1,2 +1,2 @@
 version=4
-https://github.com/JohnCremona/eclib/releases .*/v?(\d\S*)\.tar\.gz
+https://github.com/JohnCremona/eclib/tags .*/v?(\d\S*)\.tar\.gz
diff -Nru eclib-20220621/doc/sage_packaging.txt eclib-20221012/doc/sage_packaging.txt
--- eclib-20220621/doc/sage_packaging.txt	1970-01-01 00:00:00.000000000 +0000
+++ eclib-20221012/doc/sage_packaging.txt	2022-10-12 11:04:09.000000000 +0000
@@ -0,0 +1,35 @@
+Notes on how to package a new version of eclib for Sage
+
+After making a new eclib release VERSION:
+
+1. make dist-bzip2
+   This creates the file eclib-<VERSION>.tar.bz2
+   Copy it to ~/sage/upstream
+
+2. In ~/sage, checkout the development branch, update it from trac and
+   run "make".
+
+3. Make a new sage branch, say
+   git checkout -b eclib-<VERSION>
+
+4. In ~/sage/build/pkgs/eclib, update the version number in
+   package-version.txt and spkg-configure.m4
+
+5. Run (using this sage)
+   sage --package fix-checksum eclib
+
+6. Build this new eclib in sage, with checks:
+   sage -i -c eclib
+
+   [Doing 'make eclib' is also OK, bu does not run eclib's checks.]
+
+7. Test sage to see if any doctests need changing.  Start with:
+   sage -t --long src/sage/libs/eclib
+   sage -t --long src/sage/schemes/elliptic_curves
+
+8. Make a github release and upload eclib-<VERSION>.tar.bz2 to it.
+
+9. Commit the changes to sage, upload the branch to the trac ticket
+   and call for review.
+
+
diff -Nru eclib-20220621/libsrc/cubic.cc eclib-20221012/libsrc/cubic.cc
--- eclib-20220621/libsrc/cubic.cc	2022-06-21 14:25:26.000000000 +0000
+++ eclib-20221012/libsrc/cubic.cc	2022-10-12 11:04:09.000000000 +0000
@@ -28,31 +28,182 @@
 #include <eclib/polys.h>
 #include <cassert>
 
-void cubic::init()
-{
-  coeffs = new bigint[4];
-}
+bigint zero(0), one(1);
 
-cubic::~cubic()
+// comparison operator for sorting
+int operator<(const cubic& F1, const cubic& F2)
 {
-  delete [] coeffs;
+  return std::lexicographical_compare(F1.coeffs.begin(), F1.coeffs.end(), F2.coeffs.begin(), F2.coeffs.end());
 }
 
-void cubic::transform(const unimod& m)
+vector<bigint> transform_helper(const bigint& a, const bigint& b, const bigint& c, const bigint& d,
+                                const unimod& m)
 {
   bigint m112=sqr(m(1,1)); bigint m113=m112*m(1,1);
   bigint m212=sqr(m(2,1)); bigint m213=m212*m(2,1);
   bigint m222=sqr(m(2,2)); bigint m223=m222*m(2,2);
   bigint m122=sqr(m(1,2)); bigint m123=m122*m(1,2);
 
-  bigint A = m113*a() + m(2,1)*m112*b() + m212*m(1,1)*c() + m213*d();
-  bigint B = 3*m(1,2)*m112*a() + (m(2,2)*m112 + 2*m(2,1)*m(1,2)*m(1,1))*b()
-    + (2*m(2,2)*m(2,1)*m(1,1) + m212*m(1,2))*c() + 3*m(2,2)*m212*d();
-  bigint C = 3*m122*m(1,1)*a() + (2*m(2,2)*m(1,2)*m(1,1) + m(2,1)*m122)*b()
-    + (m222*m(1,1) + 2*m(2,2)*m(2,1)*m(1,2))*c() + 3*m222*m(2,1)*d();
-  bigint D = m123*a() + m(2,2)*m122*b() + m222*m(1,2)*c() + m223*d();
-  set(A,B,C,D);
-  }
+  bigint A = m113*a + m(2,1)*m112*b + m212*m(1,1)*c + m213*d;
+  bigint B = 3*m(1,2)*m112*a + (m(2,2)*m112 + 2*m(2,1)*m(1,2)*m(1,1))*b
+    + (2*m(2,2)*m(2,1)*m(1,1) + m212*m(1,2))*c + 3*m(2,2)*m212*d;
+  bigint C = 3*m122*m(1,1)*a + (2*m(2,2)*m(1,2)*m(1,1) + m(2,1)*m122)*b
+    + (m222*m(1,1) + 2*m(2,2)*m(2,1)*m(1,2))*c + 3*m222*m(2,1)*d;
+  bigint D = m123*a + m(2,2)*m122*b + m222*m(1,2)*c + m223*d;
+
+  return {A,B,C,D};
+}
+
+vector<bigint> transform_helper(const vector<bigint>& abcd, const unimod& m)
+{
+  return transform_helper(abcd[0],abcd[1],abcd[2],abcd[3],m);
+}
+
+void cubic::transform(const unimod& m)
+{
+  coeffs = transform_helper(coeffs, m);
+}
+
+cubic transform(const cubic& F, const unimod& m)
+{
+  return cubic(transform_helper(F.coeffs, m));
+}
+
+void cubic::sl2_reduce(unimod& m)
+{
+  if (disc()<0)
+    jc_reduce(m);
+  else
+    hess_reduce(m);
+}
+
+//#define DEBUG_NORMALISE
+
+// - for an sl2-reduced cubic, normalise w.r.t. <-I> (default) or <S> or <TS>
+// - updates m by multiplying by normalising transformation
+void cubic::normalise(unimod& m)
+{
+  int nautos = 2;
+
+#ifdef DEBUG_NORMALISE
+  cout<<"Normalising "<<(*this)<<endl;
+#endif
+
+  if (disc()<zero)
+    {
+      // Coeffs of covariant are [h0,h1,h2].  We have extra autos if
+      // h0=h2, i.e. C1=0.  The covariant is const*(X^2+Y^2) if also
+      // h1=0, i.e. C4=0, or const*(X^2+XY+Y^2) if also h1=h0,
+      // i.e. C2=0.
+      bigint C1=j_c1(), C2=j_c2(), C4=j_c4();
+      nautos = (C1==0? (C4==0? 4: (C2==0? 6: 2)): 2);
+#ifdef DEBUG_NORMALISE
+      cout<<"Covariant quantities are C1="<<C1<<", C2="<<C2<<", C3="<<j_c3()<<", C4="<<C4<<endl;
+#endif
+    }
+  else
+    {
+      // Coeffs of covariant are [P,Q,R].  We have extra autos if P=R.
+      // The covariant is const*(X^2+Y^2) if also Q=0, or
+      // const*(X^2+XY+Y^2) if also Q=R.
+      bigint P=p_semi(), Q=q_semi(), R=r_semi();
+      nautos = (P==R? (Q==0? 4: (Q==R? 6: 2)): 2);
+#ifdef DEBUG_NORMALISE
+      cout<<"Hessian coefficients are P="<<P<<", Q="<<Q<<", R="<<R<<endl;
+      cout<<"Hessian root is "<<hess_root()<<endl;
+#endif
+    }
+
+#ifdef DEBUG_NORMALISE
+      cout<<"Number of automorphisms = "<<nautos<<endl;
+#endif
+
+  vector<cubic> Flist; // will hold the candidates
+  vector<unimod> transforms; // will hold the transformations taking original cubic to candidates
+  cubic F1 = *this;
+  Flist.push_back(F1);
+  unimod autpower; // initialised to identity
+  transforms.push_back(autpower);
+  unimod auto2(-one,zero,zero,-one), auto4(zero,-one,one,zero), auto6(one,one,-one,zero);
+  unimod aut = (nautos==4? auto4: (nautos==6? auto6: auto2));
+  for(int i=1; i<nautos; i++)
+    {
+      F1.transform(aut);
+      Flist.push_back(F1);
+      autpower*=aut;
+      transforms.push_back(autpower);
+    }
+
+#ifdef DEBUG_NORMALISE
+  cout<<"Comparing "<<Flist.size()<<" candidates for the reduced representative of "<<(*this)<<": "<<Flist<<endl;
+#endif
+  auto biggest = std::max_element(Flist.begin(),Flist.end());
+  coeffs = biggest->coeffs;
+  autpower = *(transforms.begin() + (biggest-Flist.begin()));
+#ifdef DEBUG_NORMALISE
+  cout<<"Largest one after sorting is "<<(*this)<<", the transform by "<<autpower<<endl;
+#endif
+  m *= autpower;
+  return;
+}
+
+// Tests for sl2/gl2-equivalence:
+int cubic::sl2_equivalent(const cubic& G) const
+{
+  unimod m; // not used but the reduction functions need one
+  cubic F1(*this), G1(G);
+  if (F1==G1)
+    return 1;
+  F1.negate(m);
+  if (F1==G1)
+    return 1;
+  if (F1.disc()!=G1.disc())
+    return 0;
+  F1.sl2_reduce(m);
+  G1.sl2_reduce(m);
+  return F1==G1;
+}
+
+int cubic::gl2_equivalent(const cubic& G) const
+{
+  unimod m(-one,zero,zero,one);
+  return (sl2_equivalent(G) || sl2_equivalent(::transform(G,m)));
+}
+
+// Test for sl2/gl2-equivalence to one in a list:
+int cubic::sl2_equivalent_in_list(const vector<cubic>& Glist) const
+{
+  for (auto Gi=Glist.begin(); Gi!=Glist.end(); ++Gi)
+    if (sl2_equivalent(*Gi))
+      return 1;
+  return 0;
+}
+
+int cubic::gl2_equivalent_in_list(const vector<cubic>& Glist) const
+{
+  for (auto Gi=Glist.begin(); Gi!=Glist.end(); ++Gi)
+    if (gl2_equivalent(*Gi))
+      return 1;
+  return 0;
+}
+
+// affine roots of F mod q.
+// NB rootsmod requires a non-constant polynomial
+
+// affine roots of F mod q, assuming leading coefficient a() is nonzero:
+vector<bigint> cubic::roots_mod(const bigint& q) const
+{
+  bigint aq(a()%q), bq(b()%q), cq(c()%q), dq(d()%q);
+  if (is_zero(aq) && is_zero(bq) && is_zero(cq))
+    return {};
+  return rootsmod({dq,cq,bq,aq}, q);
+}
+
+// Return 1 iff F has a projective root mod q:
+int cubic::has_roots_mod(const bigint& q) const
+{
+  return div(q,a()) || (roots_mod(q).size() > 0);
+}
 
 void cubic::x_shift(const bigint& e, unimod& m)
 {
@@ -96,61 +247,63 @@
 
 bigint cubic::j_c1() const
 {
-  bigint b2=sqr(b());
-  bigint b3=b()*b2;
-  bigint b4=b()*b3;
-  bigint b5=b()*b4;
-  bigint b6=b()*b5;
-  bigint a2=sqr(a());
-  bigint a3=a()*a2;
-  bigint a4=a()*a3;
-  bigint c2=sqr(c());
-  bigint c3=c()*c2;
-  bigint c4=c()*c3;
-  bigint c5=c()*c4;
-  bigint c6=c()*c5;
-  bigint d2=sqr(d());
-  bigint d3=d()*d2;
-  bigint d4=d()*d3;
-  bigint ac=a()*c(), bd=b()*d();
-  return - 108*b3*a2*d() - 3*b4*c2 + 54*a2*c4 + 18*b5*d() + 243*a2*d2*b2 -
-    54*b3*ac*d() - 162*bd*c2*a2 - 54*a3*c3 + 486*a3*bd*c() + 3*c4*b2 -
-      18*c5*a() + 54*c3*a()*bd - 243*d2*a2*c2 + 162*d2*ac*b2 + 2*c6 -
+  bigint a = coeffs[0], b=coeffs[1], c=coeffs[2], d=coeffs[3];
+  bigint b2=sqr(b);
+  bigint b3=b*b2;
+  bigint b4=b*b3;
+  bigint b5=b*b4;
+  bigint b6=b*b5;
+  bigint a2=sqr(a);
+  bigint a3=a*a2;
+  bigint a4=a*a3;
+  bigint c2=sqr(c);
+  bigint c3=c*c2;
+  bigint c4=c*c3;
+  bigint c5=c*c4;
+  bigint c6=c*c5;
+  bigint d2=sqr(d);
+  bigint d3=d*d2;
+  bigint d4=d*d3;
+  bigint ac=a*c, bd=b*d;
+  return - 108*b3*a2*d - 3*b4*c2 + 54*a2*c4 + 18*b5*d + 243*a2*d2*b2 -
+    54*b3*ac*d - 162*bd*c2*a2 - 54*a3*c3 + 486*a3*bd*c + 3*c4*b2 -
+      18*c5*a + 54*c3*a*bd - 243*d2*a2*c2 + 162*d2*ac*b2 + 2*c6 -
 	729*a4*d2 - 2*b6 + 18*b4*ac - 27*a2*b2*c2 + 729*d4*a2 + 54*b3*d3 +
-	  108*c3*d2*a() - 18*c4*bd + 27*d2*c2*b2 - 486*d3*ac*b() - 54*d2*b4;
+	  108*c3*d2*a - 18*c4*bd + 27*d2*c2*b2 - 486*d3*ac*b - 54*d2*b4;
 
 }
 
-// MINUS the quantity called C_2 in the paper, = -Norm(h0-h1) and should be
-// NON-POSITIVE for a reduced form:
+// The quantity called C_2 in the paper, = Norm(h0-h1) and should be
+// NON-NEGATIVE for a reduced form:
 
 bigint cubic::j_c2() const
 {
-  bigint b2=sqr(b());
-  bigint b3=b()*b2;
-  bigint b4=b()*b3;
-  bigint b5=b()*b4;
-  bigint b6=b()*b5;
-  bigint a2=sqr(a());
-  bigint a3=a()*a2;
-  bigint a4=a()*a3;
-  bigint c2=sqr(c());
-  bigint c3=c()*c2;
-  bigint c4=c()*c3;
-  bigint c5=c()*c4;
-  bigint c6=c()*c5;
-  bigint d2=sqr(d());
-  bigint d3=d()*d2;
-  bigint d4=d()*d3;
-  bigint ac=a()*c(), bd=b()*d();
-
-  return - 108*b3*a2*d() + 12*b4*c2 - 216*a2*c4 - 72*b5*d() - 486*a3*c2*d()
-    + 270*a2*c3*b() - 90*b3*c2*a() - 972*a2*d2*b2 + 216*b3*ac*d() +
-      648*bd*c2*a2 - 54*a3*c3 + 486*a3*bd*c() - 16*c3*b3 + 216*d2*b3*a() +
-	72*d()*b4*c() + 72*c4*b()*a() + 216*d()*c3*a2 - 432*d()*b2*a()*c2 
-    - 729*a4*d2 - 2*b6
-	  + 18*b4*ac - 27*a2*b2*c2 + 6*b5*c() - 648*b2*c()*a2*d() 
-    + 162*a()*d()*b4 +  1458*a3*d2*b();
+  bigint a = coeffs[0], b=coeffs[1], c=coeffs[2], d=coeffs[3];
+  bigint b2=sqr(b);
+  bigint b3=b*b2;
+  bigint b4=b*b3;
+  bigint b5=b*b4;
+  bigint b6=b*b5;
+  bigint a2=sqr(a);
+  bigint a3=a*a2;
+  bigint a4=a*a3;
+  bigint c2=sqr(c);
+  bigint c3=c*c2;
+  bigint c4=c*c3;
+  bigint c5=c*c4;
+  bigint c6=c*c5;
+  bigint d2=sqr(d);
+  bigint d3=d*d2;
+  bigint d4=d*d3;
+  bigint ac=a*c, bd=b*d;
+
+  return 108*b3*a2*d - 12*b4*c2 + 216*a2*c4 + 72*b5*d + 486*a3*c2*d
+    - 270*a2*c3*b + 90*b3*c2*a + 972*a2*d2*b2 - 216*b3*ac*d -
+      648*bd*c2*a2 + 54*a3*c3 - 486*a3*bd*c + 16*c3*b3 - 216*d2*b3*a -
+	72*d*b4*c - 72*c4*b*a - 216*d*c3*a2 + 432*d*b2*a*c2 
+    + 729*a4*d2 + 2*b6
+	  - 18*b4*ac + 27*a2*b2*c2 - 6*b5*c + 648*b2*c*a2*d 
+    - 162*a*d*b4 -  1458*a3*d2*b;
 }
 
 // The quantity called C_3 in the paper, = Norm(h0+h1) and should be
@@ -201,7 +354,7 @@
   return 27*d*c3*a2 + (27*d2*b3 - 54*d*c2*b2 + 9*c4*b)*a + 9*d*c*b4 - 2*c3*b3;
 }
 
-//#define DEBUG
+//#define DEBUG_REDUCE
 
 bigcomplex cubic::hess_root() const
 {
@@ -218,13 +371,17 @@
   return gamma;
 }
 
-int cubic::is_hessian_reduced() // for positive discriminant only
+int cubic::is_hessian_reduced()
+// for positive discriminant only
+// The condition is -P < Q <= P < R or 0 <= Q <= P=R.
 {
   bigint P = p_semi();
   bigint R = r_semi();
   if (P>R) return 0;
+  // now P<=R
   bigint Q = q_semi();
   if (Q>P) return 0;
+  // now Q<=P<=R
   if (P==R) return (Q>=0);
   return (Q>-P);
 }
@@ -233,7 +390,7 @@
 {
   int s=1;  bigint k;
   m.reset();
-#ifdef DEBUG
+#ifdef DEBUG_REDUCE
   cout<<"Using hess_reduce() on "<<(*this)<<endl;
 #endif
   while(s)
@@ -245,27 +402,27 @@
       if(!is_zero(k))
 	{
 	  s=1;	  x_shift(k,m);
-#ifdef DEBUG
+#ifdef DEBUG_REDUCE
 	  cout << "Shift by " << k << ": " << (*this) << endl;
 #endif
 	}
       if(p_semi()>r_semi())
 	{
 	  s=1;	  invert(m);
-#ifdef DEBUG
+#ifdef DEBUG_REDUCE
 	  cout << "invert: " << (*this) << endl;
 #endif
 	}
     }
   // Now we have -P <= Q < P <= R and test for boundary condition
-  if((p_semi()==r_semi()) && (q_semi()<0))
+  if ((p_semi()==r_semi()) && (q_semi()<0))
     {
       invert(m);
-#ifdef DEBUG
+#ifdef DEBUG_REDUCE
       cout << "Final inversion: " << (*this) << endl;
 #endif
     }
-  if(a()<0) negate(m);
+  normalise(m);
 }
 
 void cubic::mathews_reduce(unimod& m)
@@ -278,7 +435,7 @@
       if(mat_c1()<0)
 	{
 	  s=1; invert(m);
-#ifdef DEBUG
+#ifdef DEBUG_REDUCE
 	  cout << "invert: " << (*this) << endl;
 #endif
 	}
@@ -288,7 +445,7 @@
         {
           s=1;
           x_shift(k,m);
-#ifdef DEBUG
+#ifdef DEBUG_REDUCE
       cout << "Shift by "<<k<<": "<<(*this)<<endl;
 #endif
         }
@@ -296,14 +453,14 @@
       while(mat_c2()>0)
 	{
 	  s=1; x_shift(plus1,m);
-#ifdef DEBUG
+#ifdef DEBUG_REDUCE
 	  cout << "Shift by +1: "<<(*this)<<endl;
 #endif
 	}
       while(mat_c3()<0)
 	{
 	  s=1; x_shift(minus1,m);
-#ifdef DEBUG
+#ifdef DEBUG_REDUCE
 	  cout << "Shift by -1: "<<(*this)<<endl;
 #endif
 	}
@@ -313,27 +470,40 @@
 
 int cubic::is_jc_reduced() // for negative discriminant only
 {
+  if (is_zero(a())) // we want the quadratic form (b,c,d) to be reduced
+    {
+      bigint b(coeffs[1]), c(coeffs[2]), d(coeffs[3]);
+      if (b==d)
+        return ((0<=c) && (c<=b));
+      else
+        return ((-b<c) && (c<=b) && (b<d));
+    }
   bigint C1 =  j_c1();
   if (C1<0) return 0;
-  bigint C2 = -j_c2(); // NB sign change from JCM paper
+  // now C1>=0, i.e. h0<=h2
+  bigint C2 = j_c2();
   if (C2<0) return 0;
-  bigint C4 =  j_c4(); // = N(h1)/8, not in JCM paper
-  if (C1==0) return (C4>=0);
+  // now C1, C2 >=0, i.e. h1<=h0<=h2
+  if (is_zero(C1)) // i.e. h0=h2
+    {
+      bigint C4 =  j_c4(); // = N(h1)/8, not in JCM paper
+      return (C4>=0); // i.e. h1 >= 0
+    }
   bigint C3 =  j_c3();
-  return (C3>0);
+  return (C3>0); // i.e. h1 > -h0
 }
 
 void cubic::jc_reduce(unimod& m)
 {
   int s=1;   bigint k, jc2, jc3;
-  bigint plus1, minus1;  plus1=1; minus1=-1;
+  bigint plus1(one), minus1(-one);
 
   bigfloat alpha, ra, rb, rc, rd, h0, h1, h2;
 
   m.reset();
-#ifdef DEBUG
+#ifdef DEBUG_REDUCE
       cout << "\nJC-reducing " << (*this) << "...\n";
-      cout<<"C1="<<j_c1()<<", C2="<<-j_c2()<<", C3="<<j_c3()<<", C4="<<j_c4()<<endl;
+      cout<<"C1="<<j_c1()<<", C2="<<j_c2()<<", C3="<<j_c3()<<", C4="<<j_c4()<<endl;
       alpha = real_root();
       cout<<"alpha = "<<alpha<<endl;
       ra = I2bigfloat(a());
@@ -346,7 +516,7 @@
       cout << "(h0,h1,h2) = ("<<h0<<", " << h1 << ", "<<h2<<")"<<endl;
 #endif
 
-  if (a()==0)
+      if (is_zero(a()))
     {
       bigint bb=b(), cc=c(), q,r;
       if (bb<0)
@@ -356,27 +526,35 @@
           m.negate();
         }
       ::divides(-cc,2*bb,q,r);
-      x_shift(r,m);
-#ifdef DEBUG
-      cout << "shift by "<<r<< " to get " << (*this) << endl;
+      if (r>=bb)
+        q+=1;
+#ifdef DEBUG_REDUCE
+      cout << "[a=0] shift "<< (*this);
+#endif
+      x_shift(q,m);
+#ifdef DEBUG_REDUCE
+      cout << " by "<<q<< " to get " << (*this) << endl;
+      cout<<"b="<<b()<<", c="<<c()<<", d="<<d()<<endl;
 #endif
+      // assert (is_jc_reduced());
+      normalise(m);
       return;
     }
 
   while(s)
     {
       s=0;
-      if (a()==0)
+      if (is_zero(a()))
         {
           jc_reduce(m);
           return;
         }
-      if(j_c1()<0)
+      if(j_c1()<0) // then h0 <= h2 fails, so invert:
 	{
 	  s=1;  invert(m);
-#ifdef DEBUG
+#ifdef DEBUG_REDUCE
 	  cout << "inverting --> " << (*this) << endl;
-          cout<<"C1="<<j_c1()<<", C2="<<-j_c2()<<", C3="<<j_c3()<<", C4="<<j_c4()<<endl;
+          cout<<"C1="<<j_c1()<<", C2="<<j_c2()<<", C3="<<j_c3()<<", C4="<<j_c4()<<endl;
           alpha = real_root();
           cout<<"alpha = "<<alpha<<endl;
           ra = I2bigfloat(a());
@@ -389,11 +567,11 @@
           cout << "(h0,h1,h2) = ("<<h0<<", " << h1 << ", "<<h2<<")"<<endl;
 #endif
 	}
-      if ((j_c2()>0) || (j_c3()<0))
+      if ((j_c2()<0) || (j_c3()<=0)) // then -h0 < h1 <= h0 fails, so shift:
         {
           s=1;
           alpha = real_root();
-#ifdef DEBUG
+#ifdef DEBUG_REDUCE
           cout<<"alpha = "<<alpha<<endl;
 #endif
           ra = I2bigfloat(a());
@@ -402,13 +580,13 @@
           h0 = (9*ra*ra*alpha + 6*ra*rb)*alpha  + 6*ra*rc-rb*rb;
           h1 = 6*(ra*rb*alpha + (rb*rb-ra*rc))*alpha + 2*rb*rc;
           h2 = 3*(ra*rc*alpha + rb*rc-3*ra*rd)*alpha + 2*rc*rc - 3*rb*rd;
-          k = Iround(-h1/(2*h0));
+          k = Iround(-h1/(2*h0)); // this is the amount to shift by
           if (k!=0)
             {
               x_shift(k,m);
-#ifdef DEBUG
+#ifdef DEBUG_REDUCE
               cout << "Shift by "<<k<<"--> "<<(*this)<<endl;
-              cout<<"C1="<<j_c1()<<", C2="<<-j_c2()<<", C3="<<j_c3()<<", C4="<<j_c4()<<endl;
+              cout<<"C1="<<j_c1()<<", C2="<<j_c2()<<", C3="<<j_c3()<<", C4="<<j_c4()<<endl;
               alpha = real_root();
               cout<<"alpha = "<<alpha<<endl;
               ra = I2bigfloat(a());
@@ -422,27 +600,27 @@
 #endif
             }
           // Two loops to guard against rounding error in computing k:
-          while(j_c2()>0)
+          while(j_c2()<0) // h1>h0 so shift by -1
             {
               x_shift(minus1,m);
-#ifdef DEBUG
+#ifdef DEBUG_REDUCE
               cout << "Shift by -1 --> "<<(*this)<<endl;
 #endif
             }
-          while(j_c3()<0)
+          while(j_c3()<=0) // h1<=-h0 so shift by +1
             {
               x_shift(plus1,m);
-#ifdef DEBUG
+#ifdef DEBUG_REDUCE
               cout << "Shift by +1--> "<<(*this)<<endl;
 #endif
             }
         }
-      if ((j_c1()==0) && (j_c4()<0))
+      if (is_zero(j_c1()) && (j_c4()<0)) // h0=h2 and h1<0, so invert
         {
           s=1;  invert(m);
-#ifdef DEBUG
+#ifdef DEBUG_REDUCE
           cout << "final inversion--> " << (*this) << endl;
-          cout<<"C1="<<j_c1()<<", C2="<<-j_c2()<<", C3="<<j_c3()<<", C4="<<j_c4()<<endl;
+          cout<<"C1="<<j_c1()<<", C2="<<j_c2()<<", C3="<<j_c3()<<", C4="<<j_c4()<<endl;
           alpha = real_root();
           cout<<"alpha = "<<alpha<<endl;
           ra = I2bigfloat(a());
@@ -455,8 +633,8 @@
           cout << "(h0,h1,h2) = ("<<h0<<", " << h1 << ", "<<h2<<")"<<endl;
 #endif
         }
-#ifdef DEBUG
-      cout<<"C1="<<j_c1()<<", C2="<<-j_c2()<<", C3="<<j_c3()<<", C4="<<j_c4()<<endl;
+#ifdef DEBUG_REDUCE
+      cout<<"C1="<<j_c1()<<", C2="<<j_c2()<<", C3="<<j_c3()<<", C4="<<j_c4()<<endl;
       alpha = real_root();
       cout<<"alpha = "<<alpha<<endl;
       ra = I2bigfloat(a());
@@ -469,7 +647,8 @@
       cout << "(h0,h1,h2) = ("<<h0<<", " << h1 << ", "<<h2<<")"<<endl;
 #endif
     }
-  if(a()<0) negate(m);
+  normalise(m);
+  assert (is_jc_reduced());
 }
 
   // Just shifts x:
@@ -533,8 +712,7 @@
 
 vector<bigrational> cubic::rational_roots() const
 {
-  vector<bigint> co(coeffs, coeffs+4);
-  return roots(co);
+  return roots(coeffs);
 }
 
 
@@ -546,10 +724,7 @@
   int sU;
   bigfloat i3a, a23, ra2, rb2, D, D2, D3, D32, D4, Pmax, Pmin;
 
-  int sl2_equiv, gl2_equiv;
-  bigint ZERO(0), ONE(1);
   unimod m;
-  const unimod m1(ONE,ZERO,ZERO,-ONE);
 
   bigfloat third = 1/to_bigfloat(3);
   bigfloat const1 = 2 / sqrt(to_bigfloat(27));
@@ -591,6 +766,7 @@
                       if ((verbose>1) && glist.size()==0) cout<<disc<<" :\n";
                       cubic g(a,b,c,d);
                       assert(g.disc()==disc);
+                      g.sl2_reduce(m);
                       glist.push_back(g);
                       if(verbose>1)
                         {
@@ -641,6 +817,7 @@
                           if (verbose>1 && glist.size()==0) cout<<disc<<" :\n";
                           cubic g(a,b,c,d);
                           assert(g.disc()==disc);
+                          g.sl2_reduce(m);
                           if(verbose>1) cout<<"found "<<g;
                           int irred = g.is_irreducible();
                           if (verbose>1)
@@ -666,9 +843,9 @@
       cout<<endl;
     }
 
-  for (vector<cubic>::const_iterator gi=glist.begin(); gi!=glist.end(); gi++)
+  for (auto gi=glist.begin(); gi!=glist.end(); gi++)
     {
-      cubic g = *gi, gneg;
+      cubic g = *gi;
       if(verbose) cout<<g;
       if (neg)
         {
@@ -697,34 +874,22 @@
               if(verbose) cout<<g;
             }
         }
+
       // Check to see if this reduced cubic is already in the list:
-      sl2_equiv = find(reduced_glist.begin(),reduced_glist.end(),g) != reduced_glist.end();
-      // ...if not but we are using GL(2,Z)-equivalence check that its
-      // seminegation is there:
-      if (!sl2_equiv && gl2)
-        {
-          if (reduced_glist.size()==0)
-            gl2_equiv=0;
-          else
-            {
-              gneg=g;
-              gneg.transform(m1);
-              if (neg)
-                gneg.jc_reduce(m);
-              else
-                gneg.hess_reduce(m);
-              gl2_equiv = find(reduced_glist.begin(),reduced_glist.end(),gneg) != reduced_glist.end();
-            }
-        }
-      if (sl2_equiv || (gl2&&gl2_equiv))
+      int equiv;
+      if (gl2)
+        equiv = g.gl2_equivalent_in_list(reduced_glist);
+      else
+        equiv = g.sl2_equivalent_in_list(reduced_glist);
+      if (equiv)
         {
           if(verbose)
             {
               cout<<" -REPEAT";
-              if(sl2_equiv)
-                cout<<" (SL(2,Z)-equivalent)";
-              else
+              if(gl2)
                 cout<<" (GL(2,Z)-equivalent)";
+              else
+                cout<<" (SL(2,Z)-equivalent)";
             }
         }
       else
diff -Nru eclib-20220621/libsrc/eclib/cubic.h eclib-20221012/libsrc/eclib/cubic.h
--- eclib-20220621/libsrc/eclib/cubic.h	2022-06-21 14:25:26.000000000 +0000
+++ eclib-20221012/libsrc/eclib/cubic.h	2022-10-12 11:04:09.000000000 +0000
@@ -37,35 +37,33 @@
 
 class cubic {
   friend class unimod;
-private: 
-  bigint * coeffs;  // will always have length 4
-  // init just allocates memory
-  void init();
+private:
+  vector<bigint> coeffs;  // will always have length 4
 public:
-  void set(long a, long b, long c, long d) 
-    {coeffs[0]=a; coeffs[1]=b; coeffs[2]=c; coeffs[3]=d;}
-  void set(const  bigint& a, const bigint& b, const bigint& c, const bigint& d) 
-    {coeffs[0]=a; coeffs[1]=b; coeffs[2]=c; coeffs[3]=d;}
-  void set(const  cubic& q)
-    {coeffs[0]=q.coeffs[0]; coeffs[1]=q.coeffs[1]; 
-     coeffs[2]=q.coeffs[2]; coeffs[3]=q.coeffs[3];}
-  cubic() 
-    {init(); set(0,0,0,0);}
-  ~cubic();
+  // void set(long a, long b, long c, long d)
+  // {coeffs = {BIGINT(a),BIGINT(b),BIGINT(c),BIGINT(d)};}
+  // void set(const  bigint& a, const bigint& b, const bigint& c, const bigint& d)
+  // {coeffs = {a,b,c,d};}
+  // void set(const vector<bigint>& abcd)
+  // {std::copy(abcd.begin(), abcd.end(), coeffs.begin());}
+  // void set(const  cubic& q)
+  // {std::copy(q.coeffs.begin(), q.coeffs.end(), coeffs.begin());}
+  cubic()
+  {coeffs.resize(4, BIGINT(0));}
   cubic(const  bigint& a, const bigint& b, const bigint& c, const bigint& d) 
-    {init(); set(a,b,c,d);}
+  {coeffs = {a,b,c,d};}
   cubic(long a, long b, long c, long d) 
-    {init(); set(a,b,c,d);}
-  cubic(const  cubic& q)  
-    {init(); set(q);}
-  void operator=(const cubic& g) {set(g);}
-  int operator==(const cubic& g)
-  {return ((coeffs[0]==g.coeffs[0]) && (coeffs[1]==g.coeffs[1]) &&
-           (coeffs[2]==g.coeffs[2]) && (coeffs[3]==g.coeffs[3]));}
-  inline bigint coeff(int i) 
-    {if((i>=0)&&(i<=3)) return coeffs[i]; else return coeffs[0];}
+  {coeffs = {BIGINT(a),BIGINT(b),BIGINT(c),BIGINT(d)};}
+  cubic(const vector<bigint>& abcd)
+  {coeffs = abcd;}
+  cubic(const  cubic& q)
+  {coeffs = q.coeffs;}
+  int operator==(const cubic& g) const
+  {return (coeffs==g.coeffs);}
+  inline bigint coeff(int i)
+  {if((i>=0)&&(i<=3)) return coeffs[i]; else return coeffs[0];}
   inline bigint operator[](int i) const
-    {if((i>=0)&&(i<=3)) return coeffs[i]; else return coeffs[0];}
+  {if((i>=0)&&(i<=3)) return coeffs[i]; else return coeffs[0];}
   inline bigint a(void) const {return coeffs[0];}
   inline bigint b(void) const {return coeffs[1];}
   inline bigint c(void) const {return coeffs[2];}
@@ -87,22 +85,55 @@
       os<<"["<<a()<<","<<b()<<","<<c()<<","<<d()<<"]";
     }
   friend inline ostream& operator<<(ostream& os, const cubic& g);
+  friend int operator<(const cubic&, const cubic&);
+
+  // transform self by m in place
   void transform(const unimod& m);
+  // return transform of F by m
+  friend cubic transform(const cubic& F, const unimod& m);
+
   // In the next 4 functions, m already holds a unimod and is updated:
   void x_shift(const bigint& e, unimod& m);
   void y_shift(const bigint& e, unimod& m);
   void invert(unimod& m); // apply [0,-1;1,0]
   void negate(unimod& m); // apply [-1,0;0,-1]
   void seminegate(unimod& m); // apply [1,0;0,-1] (det=-1)
-  void reduce(unimod& m);
 
-// Mathews quantities for use when disc<0:
+  // Reduce with respect to SL(2,Z): the covariant point z will be in
+  // the strict fundamental region, i.e. -1/2 < Re(z) <= +1/2 and
+  // |z|>1, or 0 < Re(z) <= +1/2 and |z|=1. Note that -I always fixes
+  // z, so does [0,-1;1,0] (of order 4) if z=i (covariant a multiple
+  // of (X^2+Y^2)), and [1,1;-1,0] (of order 6) if z=(1+sqrt(-3))/2
+  // (covariant a multiple of (X^2+XY+Y^2).
+  void sl2_reduce(unimod& m);
+
+  // for an sl2-reduced cubic, normalise w.r.t. <-I> (default) or <S>
+  // or <TS>.  Two reduced and normalised forms are SL(2,Z)-equivalent
+  // iff they are equal
+  void normalise(unimod& m);
+
+  // Test for sl2/gl2-equivalence:
+  int sl2_equivalent(const cubic& G) const;
+  int gl2_equivalent(const cubic& G) const;
+  // Test for sl2/gl2-equivalence to one in a list:
+  int sl2_equivalent_in_list(const vector<cubic>& Glist) const;
+  int gl2_equivalent_in_list(const vector<cubic>& Glist) const;
+
+  // affine roots of F mod q, assuming leading coefficient a() is nonzero:
+  vector<bigint> roots_mod(const bigint& q) const;
+
+  // Return 1 iff F has a projective root mod q:
+  int has_roots_mod(const bigint& q) const;
+
+  // Mathews quantities for use when disc<0:
   bigint mat_c1() const
     { return d()*(d()-b())+a()*(c()-a());}
   bigint mat_c2() const
     {  return a()*d() - (a()+b())*(a()+b()+c());}
   bigint mat_c3() const
     {  return a()*d() + (a()-b())*(a()-b()+c());}
+
+  // P, Q, R: coefficients of the Hessian, used for reduction when disc>0
   bigint p_semi() const
     {  return sqr(b())-3*a()*c(); }
   bigint q_semi() const
@@ -111,9 +142,22 @@
     {  return sqr(c())-3*b()*d(); }
   bigint u_semi() const
     {  return 2*b()*sqr(b()) + 27*sqr(a())*d() - 9*a()*b()*c();}
+
+  // jc_reduce uses the algebraic real quadratic covariant with coeffs
+  // [h0,h1,h2]. A form is reduced if -h0<h1<=h0<h2 or 0<=h1<=h0=h2,
+  // i.e. C1>=0, C2>=0, C3>0 and C4>=0 if C1=0.
+
+  // jc_c1() is the quantity denoted C1=N(h2-h0) in the paper, its
+  // sign is sign(h2-h0) so is >=0 for a reduced form:
   bigint j_c1() const;
+  // jc_c2() is the quantity denoted C2=N(h0-h1) in the paper, its
+  // sign is sign(h0-h1) so is >=0 for a reduced form:
   bigint j_c2() const;
+  // jc_c3() is the quantity denoted C3=N(h0+h1) in the paper, its
+  // sign is sign(h1+h0) so is >0 for a reduced form:
   bigint j_c3() const;
+  // jc_c4() is not in the paper, its sign is sign(h1) so is >=0 for a
+  // reduced form with C1=0, i.e. with h0=h1:
   bigint j_c4() const;
 
   bigcomplex hess_root() const;
@@ -130,6 +174,21 @@
   {return ((a()==0) || (rational_roots().size()>0));}
   int is_irreducible() const
   {return ((a()!=0) && (rational_roots().size()==0));}
+
+  bigint content() const
+  {
+    return gcd(gcd(gcd(coeffs[0], coeffs[1]), coeffs[2]), coeffs[3]);
+  }
+  int is_primitive() const
+  {
+    return content()==1;
+  }
+  // divide by a constant factor (which should divide all the coefficients)
+  cubic operator/(const bigint& g) const
+  {
+    return cubic(coeffs[0]/g, coeffs[1]/g, coeffs[2]/g, coeffs[3]/g);
+  }
+
 };
 
 
@@ -138,11 +197,12 @@
   return os<<"["<<g.a()<<","<<g.b()<<","<<g.c() <<","<<g.d()<<"]";
 }
 
-// Functions for listing all reduced cubics
+// Functions for listing all reduced cubics (exactly one per SL(2,Z)- or GL(2,Z)-orbit).
+
 // verbose=1 shows original cubics found before final reduction and elimination of duplicates
 // verbose=2 also shows details of triple loop
 
-// All reduced cubics with a single discriminant (positive or negative):
+// (1) All reduced cubics with a single discriminant (positive or negative):
 // Set include_reducibles=0 to omit reducible cubics and any with a=0
 // Set gl2=1 to get GL(2,Z)-inequivalent cubics (default is SL(2,Z))
 vector<cubic> reduced_cubics(const bigint& disc, int include_reducibles=1, int gl2=0, int verbose=0);
diff -Nru eclib-20220621/progs/in/list_cubics.in eclib-20221012/progs/in/list_cubics.in
--- eclib-20220621/progs/in/list_cubics.in	2022-06-21 14:25:26.000000000 +0000
+++ eclib-20221012/progs/in/list_cubics.in	2022-10-12 11:04:09.000000000 +0000
@@ -1,4 +1,4 @@
-0
+0 0
 200 0 0
 200 0 1
 200 1 0
diff -Nru eclib-20220621/progs/list_cubics.cc eclib-20221012/progs/list_cubics.cc
--- eclib-20220621/progs/list_cubics.cc	2022-06-21 14:25:26.000000000 +0000
+++ eclib-20221012/progs/list_cubics.cc	2022-10-12 11:04:09.000000000 +0000
@@ -1,7 +1,7 @@
-// list_cubics.cc: Program for listing integer cubics with given discriminant bound
+// list_cubics.cc: Program for listing integer cubics with given or bounded discriminant
 //////////////////////////////////////////////////////////////////////////
 //
-// Copyright 1990-2012 John Cremona
+// Copyright 1990-2022 John Cremona
 // 
 // This file is part of the eclib package.
 // 
@@ -26,61 +26,85 @@
 #include <eclib/polys.h>
 #include <eclib/cubic.h>
 
+void output_cubics(const bigint& disc, int include_reducibles=1, int gl2=0, int verbose=0)
+{
+  vector<cubic> glist = reduced_cubics(disc, include_reducibles, gl2, verbose);
+  if (glist.size()==0)
+    {
+      if(verbose>1)
+        {
+          cout<< "No ";
+          if (!include_reducibles) cout << "irreducible";
+          cout << " cubics with discriminant " << disc << endl;
+        }
+    }
+  else
+    {
+      if (verbose)
+        cout << glist.size() << " with discriminant ";
+      cout << disc << " " << glist << endl;
+    }
+}
+
 int main()
 {
   initprimes("PRIMES");
   bigint disc, absdisc, maxdisc;
-  int neg;
-  int verbose=0, include_reducibles=1, gl2=0;
+  int neg, verbose=0, include_reducibles=1, gl2=0, single=0;
+
   cerr << "Verbosity level (0, 1 or 2): ";
   cin >> verbose;
 
-  while(cerr << "Enter discriminant bound (positive or negative, 0 to stop): ",	cin >> maxdisc, !is_zero(maxdisc))
+  cerr << "Single discriminants (1) or a range (0)? ";
+  cin >> single;
+
+  if (single)
     {
       cerr << "Include reducible cubics? (0 or 1): ";
       cin >> include_reducibles;
+
       cerr << "Use GL(2,Z)-equivalence instead of SL(2,Z)? (0 or 1): ";
       cin >> gl2;
-      neg=(maxdisc<0);
-      if (include_reducibles)
-        cout << "Cubics with ";
-      else
-        cout << "Irreducible cubics with ";
-      if(neg)
-	{
-	  ::negate(maxdisc);
-	  cout << "negative discriminant down to -";
-	}
-      else
-	{
-	  cout << "positive discriminant  up  to ";
-	}
-      cout << maxdisc;
-      cout << " up to " << (gl2?"GL":"SL") << "(2,Z)-equivalence";
-      cout << endl;
 
-      for(absdisc=1; absdisc<=maxdisc; absdisc++)
+      while(cerr << "Enter discriminant (positive or negative, 0 to stop): ",	cin >> disc, !is_zero(disc))
+        {
+          if (verbose)
+            {
+              cout << (include_reducibles? "Cubics": "Irreducible cubics") << " with discriminant ";
+              cout << disc;
+              cout << " up to " << (gl2?"GL":"SL") << "(2,Z)-equivalence";
+              cout << endl;
+            }
+          output_cubics(disc, include_reducibles, gl2, verbose);
+        }
+    }
+  else
+    {
+      while(cerr << "Enter discriminant bound (positive or negative, 0 to stop): ",	cin >> maxdisc, !is_zero(maxdisc))
+        {
+          cerr << "Include reducible cubics? (0 or 1): ";
+          cin >> include_reducibles;
+
+          cerr << "Use GL(2,Z)-equivalence instead of SL(2,Z)? (0 or 1): ";
+          cin >> gl2;
+
+          neg=(maxdisc<0);
+
+          cout << (include_reducibles? "Cubics with ": "Irreducible cubics with ");
+          cout << (neg? "negative discriminant down to ": "positive discriminant up to ");
+          cout << maxdisc;
+          cout << ", up to " << (gl2? "GL": "SL") << "(2,Z)-equivalence";
+          cout << endl;
+
+          if (neg)
+            ::negate(maxdisc);
+          for(absdisc=1; absdisc<=maxdisc; absdisc++)
 	    {
 	      disc=absdisc;
 	      if(neg) ::negate(disc);
-              vector<cubic> glist = reduced_cubics(disc, include_reducibles, gl2, verbose);
-              if (glist.size()==0)
-                {
-                  if(verbose>1)
-                    {
-                      cout<< "No ";
-                      if (!include_reducibles) cout << "irreducible";
-                      cout << " cubics with discriminant " << disc << endl;
-                    }
-                }
-              else
-                {
-                  cout << glist.size();
-                  cout << " with discriminant " << disc;
-                  if (glist.size()>0) cout<< " : " << glist;
-                  cout << endl;
-                }
+              output_cubics(disc, include_reducibles, gl2, verbose);
 	    }
-      cout<<endl;
+          cout<<endl;
+        }
     }
 }
diff -Nru eclib-20220621/progs/out_no_ntl/cubics.out eclib-20221012/progs/out_no_ntl/cubics.out
--- eclib-20220621/progs/out_no_ntl/cubics.out	2022-06-21 14:25:26.000000000 +0000
+++ eclib-20221012/progs/out_no_ntl/cubics.out	2022-10-12 11:04:09.000000000 +0000
@@ -1,8 +1,8 @@
 1 reduced cubics with discriminant 1 (up to GL(2,Z)-equivalence) : [ [0,1,1,0] ]
 2 irreducible reduced cubics with discriminant 49 (up to SL(2,Z)-equivalence) : [ [1,2,-1,-1] [1,1,-2,-1] ]
 1 irreducible reduced cubics with discriminant 49 (up to GL(2,Z)-equivalence) : [ [1,2,-1,-1] ]
-3 reduced cubics with discriminant 49 (up to SL(2,Z)-equivalence) : [ [0,1,1,-12] [1,2,-1,-1] [1,1,-2,-1] ]
-2 reduced cubics with discriminant 49 (up to GL(2,Z)-equivalence) : [ [0,1,1,-12] [1,2,-1,-1] ]
+3 reduced cubics with discriminant 49 (up to SL(2,Z)-equivalence) : [ [0,1,-1,-12] [1,2,-1,-1] [1,1,-2,-1] ]
+2 reduced cubics with discriminant 49 (up to GL(2,Z)-equivalence) : [ [0,1,-1,-12] [1,2,-1,-1] ]
 2 reduced cubics with discriminant 148 (up to GL(2,Z)-equivalence) : [ [0,1,0,-37] [1,-1,-3,1] ]
 2 reduced cubics with discriminant -23 (up to GL(2,Z)-equivalence) : [ [0,1,1,6] [1,-1,0,1] ]
 2 reduced cubics with discriminant -199 (up to GL(2,Z)-equivalence) : [ [0,1,1,50] [1,1,4,1] ]
diff -Nru eclib-20220621/progs/out_no_ntl/list_cubics.out eclib-20221012/progs/out_no_ntl/list_cubics.out
--- eclib-20220621/progs/out_no_ntl/list_cubics.out	2022-06-21 14:25:26.000000000 +0000
+++ eclib-20221012/progs/out_no_ntl/list_cubics.out	2022-10-12 11:04:09.000000000 +0000
@@ -1,464 +1,464 @@
-Irreducible cubics with positive discriminant  up  to 200 up to SL(2,Z)-equivalence
-2 with discriminant 49 : [ [1,2,-1,-1] [1,1,-2,-1] ]
-2 with discriminant 81 : [ [1,3,0,-1] [1,0,-3,-1] ]
-2 with discriminant 148 : [ [1,-1,-3,1] [1,1,-3,-1] ]
-2 with discriminant 169 : [ [1,-1,-4,-1] [1,4,1,-1] ]
+Irreducible cubics with positive discriminant up to 200, up to SL(2,Z)-equivalence
+49 [ [1,2,-1,-1] [1,1,-2,-1] ]
+81 [ [1,3,0,-1] [1,0,-3,-1] ]
+148 [ [1,-1,-3,1] [1,1,-3,-1] ]
+169 [ [1,-1,-4,-1] [1,4,1,-1] ]
 
-Irreducible cubics with positive discriminant  up  to 200 up to GL(2,Z)-equivalence
-1 with discriminant 49 : [ [1,2,-1,-1] ]
-1 with discriminant 81 : [ [1,3,0,-1] ]
-1 with discriminant 148 : [ [1,-1,-3,1] ]
-1 with discriminant 169 : [ [1,-1,-4,-1] ]
+Irreducible cubics with positive discriminant up to 200, up to GL(2,Z)-equivalence
+49 [ [1,2,-1,-1] ]
+81 [ [1,3,0,-1] ]
+148 [ [1,-1,-3,1] ]
+169 [ [1,-1,-4,-1] ]
 
-Cubics with positive discriminant  up  to 200 up to SL(2,Z)-equivalence
-1 with discriminant 1 : [ [0,1,1,0] ]
-1 with discriminant 4 : [ [0,1,0,-1] ]
-1 with discriminant 5 : [ [0,1,1,-1] ]
-1 with discriminant 8 : [ [0,1,0,-2] ]
-1 with discriminant 9 : [ [0,1,1,-2] ]
-1 with discriminant 12 : [ [0,1,0,-3] ]
-1 with discriminant 13 : [ [0,1,1,-3] ]
-2 with discriminant 16 : [ [0,1,0,-4] [0,2,2,0] ]
-1 with discriminant 17 : [ [0,1,1,-4] ]
-1 with discriminant 20 : [ [0,1,0,-5] ]
-1 with discriminant 21 : [ [0,1,1,-5] ]
-1 with discriminant 24 : [ [0,1,0,-6] ]
-1 with discriminant 25 : [ [0,1,1,-6] ]
-1 with discriminant 28 : [ [0,1,0,-7] ]
-1 with discriminant 29 : [ [0,1,1,-7] ]
-2 with discriminant 32 : [ [0,1,0,-8] [0,2,0,-1] ]
-1 with discriminant 33 : [ [0,1,1,-8] ]
-3 with discriminant 36 : [ [0,1,0,-9] [0,2,-1,-1] [0,2,1,-1] ]
-1 with discriminant 37 : [ [0,1,1,-9] ]
-1 with discriminant 40 : [ [0,1,0,-10] ]
-1 with discriminant 41 : [ [0,1,1,-10] ]
-1 with discriminant 44 : [ [0,1,0,-11] ]
-1 with discriminant 45 : [ [0,1,1,-11] ]
-2 with discriminant 48 : [ [0,1,0,-12] [0,2,2,-1] ]
-3 with discriminant 49 : [ [0,1,1,-12] [1,2,-1,-1] [1,1,-2,-1] ]
-1 with discriminant 52 : [ [0,1,0,-13] ]
-1 with discriminant 53 : [ [0,1,1,-13] ]
-1 with discriminant 56 : [ [0,1,0,-14] ]
-1 with discriminant 57 : [ [0,1,1,-14] ]
-1 with discriminant 60 : [ [0,1,0,-15] ]
-1 with discriminant 61 : [ [0,1,1,-15] ]
-2 with discriminant 64 : [ [0,1,0,-16] [0,2,0,-2] ]
-1 with discriminant 65 : [ [0,1,1,-16] ]
-3 with discriminant 68 : [ [0,1,0,-17] [0,2,-1,-2] [0,2,1,-2] ]
-1 with discriminant 69 : [ [0,1,1,-17] ]
-1 with discriminant 72 : [ [0,1,0,-18] ]
-1 with discriminant 73 : [ [0,1,1,-18] ]
-1 with discriminant 76 : [ [0,1,0,-19] ]
-1 with discriminant 77 : [ [0,1,1,-19] ]
-2 with discriminant 80 : [ [0,1,0,-20] [0,2,2,-2] ]
-4 with discriminant 81 : [ [0,1,1,-20] [0,3,3,0] [1,3,0,-1] [1,0,-3,-1] ]
-1 with discriminant 84 : [ [0,1,0,-21] ]
-1 with discriminant 85 : [ [0,1,1,-21] ]
-1 with discriminant 88 : [ [0,1,0,-22] ]
-1 with discriminant 89 : [ [0,1,1,-22] ]
-1 with discriminant 92 : [ [0,1,0,-23] ]
-1 with discriminant 93 : [ [0,1,1,-23] ]
-2 with discriminant 96 : [ [0,1,0,-24] [0,2,0,-3] ]
-1 with discriminant 97 : [ [0,1,1,-24] ]
-3 with discriminant 100 : [ [0,1,0,-25] [0,2,-1,-3] [0,2,1,-3] ]
-1 with discriminant 101 : [ [0,1,1,-25] ]
-1 with discriminant 104 : [ [0,1,0,-26] ]
-1 with discriminant 105 : [ [0,1,1,-26] ]
-3 with discriminant 108 : [ [0,1,0,-27] [0,3,0,-1] [1,0,-3,0] ]
-1 with discriminant 109 : [ [0,1,1,-27] ]
-2 with discriminant 112 : [ [0,1,0,-28] [0,2,2,-3] ]
-1 with discriminant 113 : [ [0,1,1,-28] ]
-1 with discriminant 116 : [ [0,1,0,-29] ]
-5 with discriminant 117 : [ [0,1,1,-29] [0,3,-1,-1] [0,3,1,-1] [0,-3,1,1] [0,-3,-1,1] ]
-1 with discriminant 120 : [ [0,1,0,-30] ]
-1 with discriminant 121 : [ [0,1,1,-30] ]
-1 with discriminant 124 : [ [0,1,0,-31] ]
-2 with discriminant 125 : [ [0,1,1,-31] [1,2,-2,-1] ]
-2 with discriminant 128 : [ [0,1,0,-32] [0,2,0,-4] ]
-1 with discriminant 129 : [ [0,1,1,-32] ]
-3 with discriminant 132 : [ [0,1,0,-33] [0,2,-1,-4] [0,2,1,-4] ]
-1 with discriminant 133 : [ [0,1,1,-33] ]
-1 with discriminant 136 : [ [0,1,0,-34] ]
-1 with discriminant 137 : [ [0,1,1,-34] ]
-1 with discriminant 140 : [ [0,1,0,-35] ]
-1 with discriminant 141 : [ [0,1,1,-35] ]
-6 with discriminant 144 : [ [0,1,0,-36] [0,2,2,-4] [0,3,-2,-1] [0,3,2,-1] [0,-3,-2,1] [0,-3,2,1] ]
-1 with discriminant 145 : [ [0,1,1,-36] ]
-3 with discriminant 148 : [ [0,1,0,-37] [1,-1,-3,1] [1,1,-3,-1] ]
-1 with discriminant 149 : [ [0,1,1,-37] ]
-1 with discriminant 152 : [ [0,1,0,-38] ]
-1 with discriminant 153 : [ [0,1,1,-38] ]
-1 with discriminant 156 : [ [0,1,0,-39] ]
-1 with discriminant 157 : [ [0,1,1,-39] ]
-2 with discriminant 160 : [ [0,1,0,-40] [0,2,0,-5] ]
-1 with discriminant 161 : [ [0,1,1,-40] ]
-3 with discriminant 164 : [ [0,1,0,-41] [0,2,-1,-5] [0,2,1,-5] ]
-1 with discriminant 165 : [ [0,1,1,-41] ]
-1 with discriminant 168 : [ [0,1,0,-42] ]
-3 with discriminant 169 : [ [0,1,1,-42] [1,-1,-4,-1] [1,4,1,-1] ]
-1 with discriminant 172 : [ [0,1,0,-43] ]
-1 with discriminant 173 : [ [0,1,1,-43] ]
-2 with discriminant 176 : [ [0,1,0,-44] [0,2,2,-5] ]
-1 with discriminant 177 : [ [0,1,1,-44] ]
-1 with discriminant 180 : [ [0,1,0,-45] ]
-1 with discriminant 181 : [ [0,1,1,-45] ]
-1 with discriminant 184 : [ [0,1,0,-46] ]
-1 with discriminant 185 : [ [0,1,1,-46] ]
-1 with discriminant 188 : [ [0,1,0,-47] ]
-2 with discriminant 189 : [ [0,1,1,-47] [0,3,3,-1] ]
-2 with discriminant 192 : [ [0,1,0,-48] [0,2,0,-6] ]
-1 with discriminant 193 : [ [0,1,1,-48] ]
-3 with discriminant 196 : [ [0,1,0,-49] [0,2,-1,-6] [0,2,1,-6] ]
-1 with discriminant 197 : [ [0,1,1,-49] ]
-1 with discriminant 200 : [ [0,1,0,-50] ]
+Cubics with positive discriminant up to 200, up to SL(2,Z)-equivalence
+1 [ [0,1,1,0] ]
+4 [ [0,1,0,-1] ]
+5 [ [0,1,-1,-1] ]
+8 [ [0,1,0,-2] ]
+9 [ [0,1,-1,-2] ]
+12 [ [0,1,0,-3] ]
+13 [ [0,1,-1,-3] ]
+16 [ [0,1,0,-4] [0,2,2,0] ]
+17 [ [0,1,-1,-4] ]
+20 [ [0,1,0,-5] ]
+21 [ [0,1,-1,-5] ]
+24 [ [0,1,0,-6] ]
+25 [ [0,1,-1,-6] ]
+28 [ [0,1,0,-7] ]
+29 [ [0,1,-1,-7] ]
+32 [ [0,1,0,-8] [0,2,0,-1] ]
+33 [ [0,1,-1,-8] ]
+36 [ [0,1,0,-9] [0,2,-1,-1] [0,2,1,-1] ]
+37 [ [0,1,-1,-9] ]
+40 [ [0,1,0,-10] ]
+41 [ [0,1,-1,-10] ]
+44 [ [0,1,0,-11] ]
+45 [ [0,1,-1,-11] ]
+48 [ [0,1,0,-12] [0,2,-2,-1] ]
+49 [ [0,1,-1,-12] [1,2,-1,-1] [1,1,-2,-1] ]
+52 [ [0,1,0,-13] ]
+53 [ [0,1,-1,-13] ]
+56 [ [0,1,0,-14] ]
+57 [ [0,1,-1,-14] ]
+60 [ [0,1,0,-15] ]
+61 [ [0,1,-1,-15] ]
+64 [ [0,1,0,-16] [0,2,0,-2] ]
+65 [ [0,1,-1,-16] ]
+68 [ [0,1,0,-17] [0,2,-1,-2] [0,2,1,-2] ]
+69 [ [0,1,-1,-17] ]
+72 [ [0,1,0,-18] ]
+73 [ [0,1,-1,-18] ]
+76 [ [0,1,0,-19] ]
+77 [ [0,1,-1,-19] ]
+80 [ [0,1,0,-20] [0,2,-2,-2] ]
+81 [ [0,1,-1,-20] [0,3,3,0] [1,3,0,-1] [1,0,-3,-1] ]
+84 [ [0,1,0,-21] ]
+85 [ [0,1,-1,-21] ]
+88 [ [0,1,0,-22] ]
+89 [ [0,1,-1,-22] ]
+92 [ [0,1,0,-23] ]
+93 [ [0,1,-1,-23] ]
+96 [ [0,1,0,-24] [0,2,0,-3] ]
+97 [ [0,1,-1,-24] ]
+100 [ [0,1,0,-25] [0,2,-1,-3] [0,2,1,-3] ]
+101 [ [0,1,-1,-25] ]
+104 [ [0,1,0,-26] ]
+105 [ [0,1,-1,-26] ]
+108 [ [0,1,0,-27] [1,0,-3,0] ]
+109 [ [0,1,-1,-27] ]
+112 [ [0,1,0,-28] [0,2,-2,-3] ]
+113 [ [0,1,-1,-28] ]
+116 [ [0,1,0,-29] ]
+117 [ [0,1,-1,-29] [0,3,-1,-1] [0,3,1,-1] ]
+120 [ [0,1,0,-30] ]
+121 [ [0,1,-1,-30] ]
+124 [ [0,1,0,-31] ]
+125 [ [0,1,-1,-31] [1,2,-2,-1] ]
+128 [ [0,1,0,-32] [0,2,0,-4] ]
+129 [ [0,1,-1,-32] ]
+132 [ [0,1,0,-33] [0,2,-1,-4] [0,2,1,-4] ]
+133 [ [0,1,-1,-33] ]
+136 [ [0,1,0,-34] ]
+137 [ [0,1,-1,-34] ]
+140 [ [0,1,0,-35] ]
+141 [ [0,1,-1,-35] ]
+144 [ [0,1,0,-36] [0,2,-2,-4] [0,3,-2,-1] [0,3,2,-1] ]
+145 [ [0,1,-1,-36] ]
+148 [ [0,1,0,-37] [1,-1,-3,1] [1,1,-3,-1] ]
+149 [ [0,1,-1,-37] ]
+152 [ [0,1,0,-38] ]
+153 [ [0,1,-1,-38] ]
+156 [ [0,1,0,-39] ]
+157 [ [0,1,-1,-39] ]
+160 [ [0,1,0,-40] [0,2,0,-5] ]
+161 [ [0,1,-1,-40] ]
+164 [ [0,1,0,-41] [0,2,-1,-5] [0,2,1,-5] ]
+165 [ [0,1,-1,-41] ]
+168 [ [0,1,0,-42] ]
+169 [ [0,1,-1,-42] [1,-1,-4,-1] [1,4,1,-1] ]
+172 [ [0,1,0,-43] ]
+173 [ [0,1,-1,-43] ]
+176 [ [0,1,0,-44] [0,2,-2,-5] ]
+177 [ [0,1,-1,-44] ]
+180 [ [0,1,0,-45] ]
+181 [ [0,1,-1,-45] ]
+184 [ [0,1,0,-46] ]
+185 [ [0,1,-1,-46] ]
+188 [ [0,1,0,-47] ]
+189 [ [0,1,-1,-47] [0,3,-3,-1] ]
+192 [ [0,1,0,-48] [0,2,0,-6] ]
+193 [ [0,1,-1,-48] ]
+196 [ [0,1,0,-49] [0,2,-1,-6] [0,2,1,-6] ]
+197 [ [0,1,-1,-49] ]
+200 [ [0,1,0,-50] ]
 
-Cubics with positive discriminant  up  to 200 up to GL(2,Z)-equivalence
-1 with discriminant 1 : [ [0,1,1,0] ]
-1 with discriminant 4 : [ [0,1,0,-1] ]
-1 with discriminant 5 : [ [0,1,1,-1] ]
-1 with discriminant 8 : [ [0,1,0,-2] ]
-1 with discriminant 9 : [ [0,1,1,-2] ]
-1 with discriminant 12 : [ [0,1,0,-3] ]
-1 with discriminant 13 : [ [0,1,1,-3] ]
-2 with discriminant 16 : [ [0,1,0,-4] [0,2,2,0] ]
-1 with discriminant 17 : [ [0,1,1,-4] ]
-1 with discriminant 20 : [ [0,1,0,-5] ]
-1 with discriminant 21 : [ [0,1,1,-5] ]
-1 with discriminant 24 : [ [0,1,0,-6] ]
-1 with discriminant 25 : [ [0,1,1,-6] ]
-1 with discriminant 28 : [ [0,1,0,-7] ]
-1 with discriminant 29 : [ [0,1,1,-7] ]
-2 with discriminant 32 : [ [0,1,0,-8] [0,2,0,-1] ]
-1 with discriminant 33 : [ [0,1,1,-8] ]
-3 with discriminant 36 : [ [0,1,0,-9] [0,2,-1,-1] [0,2,1,-1] ]
-1 with discriminant 37 : [ [0,1,1,-9] ]
-1 with discriminant 40 : [ [0,1,0,-10] ]
-1 with discriminant 41 : [ [0,1,1,-10] ]
-1 with discriminant 44 : [ [0,1,0,-11] ]
-1 with discriminant 45 : [ [0,1,1,-11] ]
-2 with discriminant 48 : [ [0,1,0,-12] [0,2,2,-1] ]
-2 with discriminant 49 : [ [0,1,1,-12] [1,2,-1,-1] ]
-1 with discriminant 52 : [ [0,1,0,-13] ]
-1 with discriminant 53 : [ [0,1,1,-13] ]
-1 with discriminant 56 : [ [0,1,0,-14] ]
-1 with discriminant 57 : [ [0,1,1,-14] ]
-1 with discriminant 60 : [ [0,1,0,-15] ]
-1 with discriminant 61 : [ [0,1,1,-15] ]
-2 with discriminant 64 : [ [0,1,0,-16] [0,2,0,-2] ]
-1 with discriminant 65 : [ [0,1,1,-16] ]
-3 with discriminant 68 : [ [0,1,0,-17] [0,2,-1,-2] [0,2,1,-2] ]
-1 with discriminant 69 : [ [0,1,1,-17] ]
-1 with discriminant 72 : [ [0,1,0,-18] ]
-1 with discriminant 73 : [ [0,1,1,-18] ]
-1 with discriminant 76 : [ [0,1,0,-19] ]
-1 with discriminant 77 : [ [0,1,1,-19] ]
-2 with discriminant 80 : [ [0,1,0,-20] [0,2,2,-2] ]
-3 with discriminant 81 : [ [0,1,1,-20] [0,3,3,0] [1,3,0,-1] ]
-1 with discriminant 84 : [ [0,1,0,-21] ]
-1 with discriminant 85 : [ [0,1,1,-21] ]
-1 with discriminant 88 : [ [0,1,0,-22] ]
-1 with discriminant 89 : [ [0,1,1,-22] ]
-1 with discriminant 92 : [ [0,1,0,-23] ]
-1 with discriminant 93 : [ [0,1,1,-23] ]
-2 with discriminant 96 : [ [0,1,0,-24] [0,2,0,-3] ]
-1 with discriminant 97 : [ [0,1,1,-24] ]
-3 with discriminant 100 : [ [0,1,0,-25] [0,2,-1,-3] [0,2,1,-3] ]
-1 with discriminant 101 : [ [0,1,1,-25] ]
-1 with discriminant 104 : [ [0,1,0,-26] ]
-1 with discriminant 105 : [ [0,1,1,-26] ]
-3 with discriminant 108 : [ [0,1,0,-27] [0,3,0,-1] [1,0,-3,0] ]
-1 with discriminant 109 : [ [0,1,1,-27] ]
-2 with discriminant 112 : [ [0,1,0,-28] [0,2,2,-3] ]
-1 with discriminant 113 : [ [0,1,1,-28] ]
-1 with discriminant 116 : [ [0,1,0,-29] ]
-3 with discriminant 117 : [ [0,1,1,-29] [0,3,-1,-1] [0,3,1,-1] ]
-1 with discriminant 120 : [ [0,1,0,-30] ]
-1 with discriminant 121 : [ [0,1,1,-30] ]
-1 with discriminant 124 : [ [0,1,0,-31] ]
-2 with discriminant 125 : [ [0,1,1,-31] [1,2,-2,-1] ]
-2 with discriminant 128 : [ [0,1,0,-32] [0,2,0,-4] ]
-1 with discriminant 129 : [ [0,1,1,-32] ]
-3 with discriminant 132 : [ [0,1,0,-33] [0,2,-1,-4] [0,2,1,-4] ]
-1 with discriminant 133 : [ [0,1,1,-33] ]
-1 with discriminant 136 : [ [0,1,0,-34] ]
-1 with discriminant 137 : [ [0,1,1,-34] ]
-1 with discriminant 140 : [ [0,1,0,-35] ]
-1 with discriminant 141 : [ [0,1,1,-35] ]
-4 with discriminant 144 : [ [0,1,0,-36] [0,2,2,-4] [0,3,-2,-1] [0,3,2,-1] ]
-1 with discriminant 145 : [ [0,1,1,-36] ]
-2 with discriminant 148 : [ [0,1,0,-37] [1,-1,-3,1] ]
-1 with discriminant 149 : [ [0,1,1,-37] ]
-1 with discriminant 152 : [ [0,1,0,-38] ]
-1 with discriminant 153 : [ [0,1,1,-38] ]
-1 with discriminant 156 : [ [0,1,0,-39] ]
-1 with discriminant 157 : [ [0,1,1,-39] ]
-2 with discriminant 160 : [ [0,1,0,-40] [0,2,0,-5] ]
-1 with discriminant 161 : [ [0,1,1,-40] ]
-3 with discriminant 164 : [ [0,1,0,-41] [0,2,-1,-5] [0,2,1,-5] ]
-1 with discriminant 165 : [ [0,1,1,-41] ]
-1 with discriminant 168 : [ [0,1,0,-42] ]
-2 with discriminant 169 : [ [0,1,1,-42] [1,-1,-4,-1] ]
-1 with discriminant 172 : [ [0,1,0,-43] ]
-1 with discriminant 173 : [ [0,1,1,-43] ]
-2 with discriminant 176 : [ [0,1,0,-44] [0,2,2,-5] ]
-1 with discriminant 177 : [ [0,1,1,-44] ]
-1 with discriminant 180 : [ [0,1,0,-45] ]
-1 with discriminant 181 : [ [0,1,1,-45] ]
-1 with discriminant 184 : [ [0,1,0,-46] ]
-1 with discriminant 185 : [ [0,1,1,-46] ]
-1 with discriminant 188 : [ [0,1,0,-47] ]
-2 with discriminant 189 : [ [0,1,1,-47] [0,3,3,-1] ]
-2 with discriminant 192 : [ [0,1,0,-48] [0,2,0,-6] ]
-1 with discriminant 193 : [ [0,1,1,-48] ]
-3 with discriminant 196 : [ [0,1,0,-49] [0,2,-1,-6] [0,2,1,-6] ]
-1 with discriminant 197 : [ [0,1,1,-49] ]
-1 with discriminant 200 : [ [0,1,0,-50] ]
+Cubics with positive discriminant up to 200, up to GL(2,Z)-equivalence
+1 [ [0,1,1,0] ]
+4 [ [0,1,0,-1] ]
+5 [ [0,1,-1,-1] ]
+8 [ [0,1,0,-2] ]
+9 [ [0,1,-1,-2] ]
+12 [ [0,1,0,-3] ]
+13 [ [0,1,-1,-3] ]
+16 [ [0,1,0,-4] [0,2,2,0] ]
+17 [ [0,1,-1,-4] ]
+20 [ [0,1,0,-5] ]
+21 [ [0,1,-1,-5] ]
+24 [ [0,1,0,-6] ]
+25 [ [0,1,-1,-6] ]
+28 [ [0,1,0,-7] ]
+29 [ [0,1,-1,-7] ]
+32 [ [0,1,0,-8] [0,2,0,-1] ]
+33 [ [0,1,-1,-8] ]
+36 [ [0,1,0,-9] [0,2,-1,-1] ]
+37 [ [0,1,-1,-9] ]
+40 [ [0,1,0,-10] ]
+41 [ [0,1,-1,-10] ]
+44 [ [0,1,0,-11] ]
+45 [ [0,1,-1,-11] ]
+48 [ [0,1,0,-12] [0,2,-2,-1] ]
+49 [ [0,1,-1,-12] [1,2,-1,-1] ]
+52 [ [0,1,0,-13] ]
+53 [ [0,1,-1,-13] ]
+56 [ [0,1,0,-14] ]
+57 [ [0,1,-1,-14] ]
+60 [ [0,1,0,-15] ]
+61 [ [0,1,-1,-15] ]
+64 [ [0,1,0,-16] [0,2,0,-2] ]
+65 [ [0,1,-1,-16] ]
+68 [ [0,1,0,-17] [0,2,-1,-2] ]
+69 [ [0,1,-1,-17] ]
+72 [ [0,1,0,-18] ]
+73 [ [0,1,-1,-18] ]
+76 [ [0,1,0,-19] ]
+77 [ [0,1,-1,-19] ]
+80 [ [0,1,0,-20] [0,2,-2,-2] ]
+81 [ [0,1,-1,-20] [0,3,3,0] [1,3,0,-1] ]
+84 [ [0,1,0,-21] ]
+85 [ [0,1,-1,-21] ]
+88 [ [0,1,0,-22] ]
+89 [ [0,1,-1,-22] ]
+92 [ [0,1,0,-23] ]
+93 [ [0,1,-1,-23] ]
+96 [ [0,1,0,-24] [0,2,0,-3] ]
+97 [ [0,1,-1,-24] ]
+100 [ [0,1,0,-25] [0,2,-1,-3] ]
+101 [ [0,1,-1,-25] ]
+104 [ [0,1,0,-26] ]
+105 [ [0,1,-1,-26] ]
+108 [ [0,1,0,-27] [1,0,-3,0] ]
+109 [ [0,1,-1,-27] ]
+112 [ [0,1,0,-28] [0,2,-2,-3] ]
+113 [ [0,1,-1,-28] ]
+116 [ [0,1,0,-29] ]
+117 [ [0,1,-1,-29] [0,3,-1,-1] ]
+120 [ [0,1,0,-30] ]
+121 [ [0,1,-1,-30] ]
+124 [ [0,1,0,-31] ]
+125 [ [0,1,-1,-31] [1,2,-2,-1] ]
+128 [ [0,1,0,-32] [0,2,0,-4] ]
+129 [ [0,1,-1,-32] ]
+132 [ [0,1,0,-33] [0,2,-1,-4] ]
+133 [ [0,1,-1,-33] ]
+136 [ [0,1,0,-34] ]
+137 [ [0,1,-1,-34] ]
+140 [ [0,1,0,-35] ]
+141 [ [0,1,-1,-35] ]
+144 [ [0,1,0,-36] [0,2,-2,-4] [0,3,-2,-1] ]
+145 [ [0,1,-1,-36] ]
+148 [ [0,1,0,-37] [1,-1,-3,1] ]
+149 [ [0,1,-1,-37] ]
+152 [ [0,1,0,-38] ]
+153 [ [0,1,-1,-38] ]
+156 [ [0,1,0,-39] ]
+157 [ [0,1,-1,-39] ]
+160 [ [0,1,0,-40] [0,2,0,-5] ]
+161 [ [0,1,-1,-40] ]
+164 [ [0,1,0,-41] [0,2,-1,-5] ]
+165 [ [0,1,-1,-41] ]
+168 [ [0,1,0,-42] ]
+169 [ [0,1,-1,-42] [1,-1,-4,-1] ]
+172 [ [0,1,0,-43] ]
+173 [ [0,1,-1,-43] ]
+176 [ [0,1,0,-44] [0,2,-2,-5] ]
+177 [ [0,1,-1,-44] ]
+180 [ [0,1,0,-45] ]
+181 [ [0,1,-1,-45] ]
+184 [ [0,1,0,-46] ]
+185 [ [0,1,-1,-46] ]
+188 [ [0,1,0,-47] ]
+189 [ [0,1,-1,-47] [0,3,-3,-1] ]
+192 [ [0,1,0,-48] [0,2,0,-6] ]
+193 [ [0,1,-1,-48] ]
+196 [ [0,1,0,-49] [0,2,-1,-6] ]
+197 [ [0,1,-1,-49] ]
+200 [ [0,1,0,-50] ]
 
-Irreducible cubics with negative discriminant down to -200 up to SL(2,Z)-equivalence
-2 with discriminant -23 : [ [1,-1,0,1] [1,1,0,-1] ]
-2 with discriminant -31 : [ [1,1,0,1] [1,-1,0,-1] ]
-2 with discriminant -44 : [ [1,-1,1,1] [1,1,1,-1] ]
-2 with discriminant -59 : [ [1,2,0,1] [1,-2,0,-1] ]
-2 with discriminant -76 : [ [1,-1,3,-1] [1,1,3,1] ]
-2 with discriminant -83 : [ [1,-1,1,-2] [1,1,1,2] ]
-2 with discriminant -87 : [ [1,1,2,-1] [1,-1,2,1] ]
-2 with discriminant -104 : [ [1,0,-1,2] [1,0,-1,-2] ]
-2 with discriminant -107 : [ [1,2,4,1] [1,-2,4,-1] ]
-2 with discriminant -108 : [ [1,0,0,2] [1,0,0,-2] ]
-2 with discriminant -116 : [ [1,-1,0,-2] [1,1,0,2] ]
-2 with discriminant -135 : [ [1,0,3,-1] [1,0,3,1] ]
-2 with discriminant -139 : [ [1,-1,1,2] [1,1,1,-2] ]
-2 with discriminant -140 : [ [1,0,2,2] [1,0,2,-2] ]
-2 with discriminant -152 : [ [1,-1,-2,-2] [1,1,-2,2] ]
-2 with discriminant -172 : [ [1,2,0,2] [1,-2,0,-2] ]
-2 with discriminant -175 : [ [1,2,3,-1] [1,-2,3,1] ]
-2 with discriminant -176 : [ [1,-1,3,1] [1,1,3,-1] ]
-2 with discriminant -199 : [ [1,1,4,1] [1,-1,4,-1] ]
-2 with discriminant -200 : [ [1,-1,2,2] [1,1,2,-2] ]
+Irreducible cubics with negative discriminant down to -200, up to SL(2,Z)-equivalence
+-23 [ [1,-1,0,1] [1,1,0,-1] ]
+-31 [ [1,1,0,1] [1,-1,0,-1] ]
+-44 [ [1,-1,1,1] [1,1,1,-1] ]
+-59 [ [1,2,0,1] [1,-2,0,-1] ]
+-76 [ [1,-1,3,-1] [1,1,3,1] ]
+-83 [ [1,-1,1,-2] [1,1,1,2] ]
+-87 [ [1,1,2,-1] [1,-1,2,1] ]
+-104 [ [1,0,-1,2] [1,0,-1,-2] ]
+-107 [ [1,2,4,1] [1,-2,4,-1] ]
+-108 [ [1,0,0,2] [1,0,0,-2] ]
+-116 [ [1,-1,0,-2] [1,1,0,2] ]
+-135 [ [1,0,3,-1] [1,0,3,1] ]
+-139 [ [1,-1,1,2] [1,1,1,-2] ]
+-140 [ [1,0,2,2] [1,0,2,-2] ]
+-152 [ [1,-1,-2,-2] [1,1,-2,2] ]
+-172 [ [1,2,0,2] [1,-2,0,-2] ]
+-175 [ [1,2,3,-1] [1,-2,3,1] ]
+-176 [ [1,-1,3,1] [1,1,3,-1] ]
+-199 [ [1,1,4,1] [1,-1,4,-1] ]
+-200 [ [1,-1,2,2] [1,1,2,-2] ]
 
-Irreducible cubics with negative discriminant down to -200 up to GL(2,Z)-equivalence
-1 with discriminant -23 : [ [1,-1,0,1] ]
-1 with discriminant -31 : [ [1,1,0,1] ]
-1 with discriminant -44 : [ [1,-1,1,1] ]
-1 with discriminant -59 : [ [1,2,0,1] ]
-1 with discriminant -76 : [ [1,-1,3,-1] ]
-1 with discriminant -83 : [ [1,-1,1,-2] ]
-1 with discriminant -87 : [ [1,1,2,-1] ]
-1 with discriminant -104 : [ [1,0,-1,2] ]
-1 with discriminant -107 : [ [1,2,4,1] ]
-1 with discriminant -108 : [ [1,0,0,2] ]
-1 with discriminant -116 : [ [1,-1,0,-2] ]
-1 with discriminant -135 : [ [1,0,3,-1] ]
-1 with discriminant -139 : [ [1,-1,1,2] ]
-1 with discriminant -140 : [ [1,0,2,2] ]
-1 with discriminant -152 : [ [1,-1,-2,-2] ]
-1 with discriminant -172 : [ [1,2,0,2] ]
-1 with discriminant -175 : [ [1,2,3,-1] ]
-1 with discriminant -176 : [ [1,-1,3,1] ]
-1 with discriminant -199 : [ [1,1,4,1] ]
-1 with discriminant -200 : [ [1,-1,2,2] ]
+Irreducible cubics with negative discriminant down to -200, up to GL(2,Z)-equivalence
+-23 [ [1,-1,0,1] ]
+-31 [ [1,1,0,1] ]
+-44 [ [1,-1,1,1] ]
+-59 [ [1,2,0,1] ]
+-76 [ [1,-1,3,-1] ]
+-83 [ [1,-1,1,-2] ]
+-87 [ [1,1,2,-1] ]
+-104 [ [1,0,-1,2] ]
+-107 [ [1,2,4,1] ]
+-108 [ [1,0,0,2] ]
+-116 [ [1,-1,0,-2] ]
+-135 [ [1,0,3,-1] ]
+-139 [ [1,-1,1,2] ]
+-140 [ [1,0,2,2] ]
+-152 [ [1,-1,-2,-2] ]
+-172 [ [1,2,0,2] ]
+-175 [ [1,2,3,-1] ]
+-176 [ [1,-1,3,1] ]
+-199 [ [1,1,4,1] ]
+-200 [ [1,-1,2,2] ]
 
-Cubics with negative discriminant down to -200 up to SL(2,Z)-equivalence
-1 with discriminant -3 : [ [0,1,1,1] ]
-1 with discriminant -4 : [ [0,1,0,1] ]
-1 with discriminant -7 : [ [0,1,1,2] ]
-1 with discriminant -8 : [ [0,1,0,2] ]
-1 with discriminant -11 : [ [0,1,1,3] ]
-1 with discriminant -12 : [ [0,1,0,3] ]
-1 with discriminant -15 : [ [0,1,1,4] ]
-3 with discriminant -16 : [ [0,1,0,4] [0,2,2,1] [1,1,1,1] ]
-1 with discriminant -19 : [ [0,1,1,5] ]
-1 with discriminant -20 : [ [0,1,0,5] ]
-3 with discriminant -23 : [ [0,1,1,6] [1,-1,0,1] [1,1,0,-1] ]
-1 with discriminant -24 : [ [0,1,0,6] ]
-3 with discriminant -27 : [ [0,1,1,7] [1,0,0,1] [1,0,0,-1] ]
-5 with discriminant -28 : [ [0,1,0,7] [0,2,-1,1] [0,2,1,1] [0,2,13,22] [0,2,3,2] ]
-3 with discriminant -31 : [ [0,1,1,8] [1,1,0,1] [1,-1,0,-1] ]
-2 with discriminant -32 : [ [0,1,0,8] [0,2,0,1] ]
-1 with discriminant -35 : [ [0,1,1,9] ]
-1 with discriminant -36 : [ [0,1,0,9] ]
-1 with discriminant -39 : [ [0,1,1,10] ]
-1 with discriminant -40 : [ [0,1,0,10] ]
-1 with discriminant -43 : [ [0,1,1,11] ]
-3 with discriminant -44 : [ [0,1,0,11] [1,-1,1,1] [1,1,1,-1] ]
-1 with discriminant -47 : [ [0,1,1,12] ]
-2 with discriminant -48 : [ [0,1,0,12] [0,2,2,2] ]
-1 with discriminant -51 : [ [0,1,1,13] ]
-1 with discriminant -52 : [ [0,1,0,13] ]
-1 with discriminant -55 : [ [0,1,1,14] ]
-1 with discriminant -56 : [ [0,1,0,14] ]
-3 with discriminant -59 : [ [0,1,1,15] [1,2,0,1] [1,-2,0,-1] ]
-3 with discriminant -60 : [ [0,1,0,15] [0,2,-1,2] [0,2,1,2] ]
-1 with discriminant -63 : [ [0,1,1,16] ]
-2 with discriminant -64 : [ [0,1,0,16] [0,2,0,2] ]
-1 with discriminant -67 : [ [0,1,1,17] ]
-1 with discriminant -68 : [ [0,1,0,17] ]
-1 with discriminant -71 : [ [0,1,1,18] ]
-5 with discriminant -72 : [ [0,1,0,18] [0,3,10,9] [0,3,26,57] [1,2,3,0] [1,-2,3,0] ]
-1 with discriminant -75 : [ [0,1,1,19] ]
-3 with discriminant -76 : [ [0,1,0,19] [1,-1,3,-1] [1,1,3,1] ]
-1 with discriminant -79 : [ [0,1,1,20] ]
-2 with discriminant -80 : [ [0,1,0,20] [0,2,2,3] ]
-3 with discriminant -83 : [ [0,1,1,21] [1,-1,1,-2] [1,1,1,2] ]
-1 with discriminant -84 : [ [0,1,0,21] ]
-3 with discriminant -87 : [ [0,1,1,22] [1,1,2,-1] [1,-1,2,1] ]
-1 with discriminant -88 : [ [0,1,0,22] ]
-1 with discriminant -91 : [ [0,1,1,23] ]
-3 with discriminant -92 : [ [0,1,0,23] [0,2,-1,3] [0,2,1,3] ]
-1 with discriminant -95 : [ [0,1,1,24] ]
-2 with discriminant -96 : [ [0,1,0,24] [0,2,0,3] ]
-5 with discriminant -99 : [ [0,1,1,25] [0,3,5,3] [0,3,31,81] [1,-1,3,0] [1,1,3,0] ]
-3 with discriminant -100 : [ [0,1,0,25] [1,-1,0,2] [1,1,0,-2] ]
-1 with discriminant -103 : [ [0,1,1,26] ]
-3 with discriminant -104 : [ [0,1,0,26] [1,0,-1,2] [1,0,-1,-2] ]
-3 with discriminant -107 : [ [0,1,1,27] [1,2,4,1] [1,-2,4,-1] ]
-5 with discriminant -108 : [ [0,1,0,27] [0,3,0,1] [1,0,0,2] [1,0,0,-2] [1,0,3,0] ]
-1 with discriminant -111 : [ [0,1,1,28] ]
-4 with discriminant -112 : [ [0,1,0,28] [0,2,2,4] [1,0,1,2] [1,0,1,-2] ]
-1 with discriminant -115 : [ [0,1,1,29] ]
-3 with discriminant -116 : [ [0,1,0,29] [1,-1,0,-2] [1,1,0,2] ]
-1 with discriminant -119 : [ [0,1,1,30] ]
-1 with discriminant -120 : [ [0,1,0,30] ]
-1 with discriminant -123 : [ [0,1,1,31] ]
-3 with discriminant -124 : [ [0,1,0,31] [0,2,-1,4] [0,2,1,4] ]
-1 with discriminant -127 : [ [0,1,1,32] ]
-2 with discriminant -128 : [ [0,1,0,32] [0,2,0,4] ]
-1 with discriminant -131 : [ [0,1,1,33] ]
-1 with discriminant -132 : [ [0,1,0,33] ]
-4 with discriminant -135 : [ [0,1,1,34] [0,3,3,2] [1,0,3,-1] [1,0,3,1] ]
-1 with discriminant -136 : [ [0,1,0,34] ]
-3 with discriminant -139 : [ [0,1,1,35] [1,-1,1,2] [1,1,1,-2] ]
-3 with discriminant -140 : [ [0,1,0,35] [1,0,2,2] [1,0,2,-2] ]
-1 with discriminant -143 : [ [0,1,1,36] ]
-2 with discriminant -144 : [ [0,1,0,36] [0,2,2,5] ]
-3 with discriminant -147 : [ [0,1,1,37] [1,-1,-1,-2] [1,1,-1,2] ]
-1 with discriminant -148 : [ [0,1,0,37] ]
-1 with discriminant -151 : [ [0,1,1,38] ]
-3 with discriminant -152 : [ [0,1,0,38] [1,-1,-2,-2] [1,1,-2,2] ]
-1 with discriminant -155 : [ [0,1,1,39] ]
-3 with discriminant -156 : [ [0,1,0,39] [0,2,-1,5] [0,2,1,5] ]
-1 with discriminant -159 : [ [0,1,1,40] ]
-2 with discriminant -160 : [ [0,1,0,40] [0,2,0,5] ]
-1 with discriminant -163 : [ [0,1,1,41] ]
-1 with discriminant -164 : [ [0,1,0,41] ]
-1 with discriminant -167 : [ [0,1,1,42] ]
-1 with discriminant -168 : [ [0,1,0,42] ]
-1 with discriminant -171 : [ [0,1,1,43] ]
-3 with discriminant -172 : [ [0,1,0,43] [1,2,0,2] [1,-2,0,-2] ]
-3 with discriminant -175 : [ [0,1,1,44] [1,2,3,-1] [1,-2,3,1] ]
-4 with discriminant -176 : [ [0,1,0,44] [0,2,2,6] [1,-1,3,1] [1,1,3,-1] ]
-1 with discriminant -179 : [ [0,1,1,45] ]
-3 with discriminant -180 : [ [0,1,0,45] [0,3,-2,2] [0,3,2,2] ]
-1 with discriminant -183 : [ [0,1,1,46] ]
-1 with discriminant -184 : [ [0,1,0,46] ]
-1 with discriminant -187 : [ [0,1,1,47] ]
-3 with discriminant -188 : [ [0,1,0,47] [0,2,-1,6] [0,2,1,6] ]
-1 with discriminant -191 : [ [0,1,1,48] ]
-6 with discriminant -192 : [ [0,1,0,48] [0,2,0,6] [0,4,14,13] [0,4,50,157] [1,2,4,0] [1,-2,4,0] ]
-1 with discriminant -195 : [ [0,1,1,49] ]
-1 with discriminant -196 : [ [0,1,0,49] ]
-3 with discriminant -199 : [ [0,1,1,50] [1,1,4,1] [1,-1,4,-1] ]
-3 with discriminant -200 : [ [0,1,0,50] [1,-1,2,2] [1,1,2,-2] ]
+Cubics with negative discriminant down to -200, up to SL(2,Z)-equivalence
+-3 [ [0,1,1,1] ]
+-4 [ [0,1,0,1] ]
+-7 [ [0,1,1,2] ]
+-8 [ [0,1,0,2] ]
+-11 [ [0,1,1,3] ]
+-12 [ [0,1,0,3] ]
+-15 [ [0,1,1,4] ]
+-16 [ [0,1,0,4] [1,2,2,0] ]
+-19 [ [0,1,1,5] ]
+-20 [ [0,1,0,5] ]
+-23 [ [0,1,1,6] [1,-1,0,1] [1,1,0,-1] ]
+-24 [ [0,1,0,6] ]
+-27 [ [0,1,1,7] [1,0,0,1] ]
+-28 [ [0,1,0,7] [0,2,-1,1] [0,2,1,1] ]
+-31 [ [0,1,1,8] [1,1,0,1] [1,-1,0,-1] ]
+-32 [ [0,1,0,8] [0,2,0,1] ]
+-35 [ [0,1,1,9] ]
+-36 [ [0,1,0,9] ]
+-39 [ [0,1,1,10] ]
+-40 [ [0,1,0,10] ]
+-43 [ [0,1,1,11] ]
+-44 [ [0,1,0,11] [1,-1,1,1] [1,1,1,-1] ]
+-47 [ [0,1,1,12] ]
+-48 [ [0,1,0,12] [0,2,2,2] ]
+-51 [ [0,1,1,13] ]
+-52 [ [0,1,0,13] ]
+-55 [ [0,1,1,14] ]
+-56 [ [0,1,0,14] ]
+-59 [ [0,1,1,15] [1,2,0,1] [1,-2,0,-1] ]
+-60 [ [0,1,0,15] [0,2,-1,2] [0,2,1,2] ]
+-63 [ [0,1,1,16] ]
+-64 [ [0,1,0,16] [0,2,0,2] ]
+-67 [ [0,1,1,17] ]
+-68 [ [0,1,0,17] ]
+-71 [ [0,1,1,18] ]
+-72 [ [0,1,0,18] [0,3,-2,1] [0,3,2,1] [1,2,3,0] [1,-2,3,0] ]
+-75 [ [0,1,1,19] ]
+-76 [ [0,1,0,19] [1,-1,3,-1] [1,1,3,1] ]
+-79 [ [0,1,1,20] ]
+-80 [ [0,1,0,20] [0,2,2,3] ]
+-83 [ [0,1,1,21] [1,-1,1,-2] [1,1,1,2] ]
+-84 [ [0,1,0,21] ]
+-87 [ [0,1,1,22] [1,1,2,-1] [1,-1,2,1] ]
+-88 [ [0,1,0,22] ]
+-91 [ [0,1,1,23] ]
+-92 [ [0,1,0,23] [0,2,-1,3] [0,2,1,3] ]
+-95 [ [0,1,1,24] ]
+-96 [ [0,1,0,24] [0,2,0,3] ]
+-99 [ [0,1,1,25] [0,3,-1,1] [0,3,1,1] [1,-1,3,0] [1,1,3,0] ]
+-100 [ [0,1,0,25] [1,-1,0,2] [1,1,0,-2] ]
+-103 [ [0,1,1,26] ]
+-104 [ [0,1,0,26] [1,0,-1,2] [1,0,-1,-2] ]
+-107 [ [0,1,1,27] [1,2,4,1] [1,-2,4,-1] ]
+-108 [ [0,1,0,27] [1,0,3,0] [1,0,0,2] [1,0,0,-2] ]
+-111 [ [0,1,1,28] ]
+-112 [ [0,1,0,28] [0,2,2,4] [1,0,1,2] [1,0,1,-2] ]
+-115 [ [0,1,1,29] ]
+-116 [ [0,1,0,29] [1,-1,0,-2] [1,1,0,2] ]
+-119 [ [0,1,1,30] ]
+-120 [ [0,1,0,30] ]
+-123 [ [0,1,1,31] ]
+-124 [ [0,1,0,31] [0,2,-1,4] [0,2,1,4] ]
+-127 [ [0,1,1,32] ]
+-128 [ [0,1,0,32] [0,2,0,4] ]
+-131 [ [0,1,1,33] ]
+-132 [ [0,1,0,33] ]
+-135 [ [0,1,1,34] [0,3,3,2] [1,0,3,-1] [1,0,3,1] ]
+-136 [ [0,1,0,34] ]
+-139 [ [0,1,1,35] [1,-1,1,2] [1,1,1,-2] ]
+-140 [ [0,1,0,35] [1,0,2,2] [1,0,2,-2] ]
+-143 [ [0,1,1,36] ]
+-144 [ [0,1,0,36] [0,2,2,5] ]
+-147 [ [0,1,1,37] [1,-1,-1,-2] [1,1,-1,2] ]
+-148 [ [0,1,0,37] ]
+-151 [ [0,1,1,38] ]
+-152 [ [0,1,0,38] [1,-1,-2,-2] [1,1,-2,2] ]
+-155 [ [0,1,1,39] ]
+-156 [ [0,1,0,39] [0,2,-1,5] [0,2,1,5] ]
+-159 [ [0,1,1,40] ]
+-160 [ [0,1,0,40] [0,2,0,5] ]
+-163 [ [0,1,1,41] ]
+-164 [ [0,1,0,41] ]
+-167 [ [0,1,1,42] ]
+-168 [ [0,1,0,42] ]
+-171 [ [0,1,1,43] ]
+-172 [ [0,1,0,43] [1,2,0,2] [1,-2,0,-2] ]
+-175 [ [0,1,1,44] [1,2,3,-1] [1,-2,3,1] ]
+-176 [ [0,1,0,44] [0,2,2,6] [1,-1,3,1] [1,1,3,-1] ]
+-179 [ [0,1,1,45] ]
+-180 [ [0,1,0,45] [0,3,-2,2] [0,3,2,2] ]
+-183 [ [0,1,1,46] ]
+-184 [ [0,1,0,46] ]
+-187 [ [0,1,1,47] ]
+-188 [ [0,1,0,47] [0,2,-1,6] [0,2,1,6] ]
+-191 [ [0,1,1,48] ]
+-192 [ [0,1,0,48] [0,2,0,6] [0,4,-2,1] [0,4,2,1] [1,2,4,0] [1,-2,4,0] ]
+-195 [ [0,1,1,49] ]
+-196 [ [0,1,0,49] ]
+-199 [ [0,1,1,50] [1,1,4,1] [1,-1,4,-1] ]
+-200 [ [0,1,0,50] [1,-1,2,2] [1,1,2,-2] ]
 
-Cubics with negative discriminant down to -200 up to GL(2,Z)-equivalence
-1 with discriminant -3 : [ [0,1,1,1] ]
-1 with discriminant -4 : [ [0,1,0,1] ]
-1 with discriminant -7 : [ [0,1,1,2] ]
-1 with discriminant -8 : [ [0,1,0,2] ]
-1 with discriminant -11 : [ [0,1,1,3] ]
-1 with discriminant -12 : [ [0,1,0,3] ]
-1 with discriminant -15 : [ [0,1,1,4] ]
-3 with discriminant -16 : [ [0,1,0,4] [0,2,2,1] [1,1,1,1] ]
-1 with discriminant -19 : [ [0,1,1,5] ]
-1 with discriminant -20 : [ [0,1,0,5] ]
-2 with discriminant -23 : [ [0,1,1,6] [1,-1,0,1] ]
-1 with discriminant -24 : [ [0,1,0,6] ]
-2 with discriminant -27 : [ [0,1,1,7] [1,0,0,1] ]
-5 with discriminant -28 : [ [0,1,0,7] [0,2,-1,1] [0,2,1,1] [0,2,13,22] [0,2,3,2] ]
-2 with discriminant -31 : [ [0,1,1,8] [1,1,0,1] ]
-2 with discriminant -32 : [ [0,1,0,8] [0,2,0,1] ]
-1 with discriminant -35 : [ [0,1,1,9] ]
-1 with discriminant -36 : [ [0,1,0,9] ]
-1 with discriminant -39 : [ [0,1,1,10] ]
-1 with discriminant -40 : [ [0,1,0,10] ]
-1 with discriminant -43 : [ [0,1,1,11] ]
-2 with discriminant -44 : [ [0,1,0,11] [1,-1,1,1] ]
-1 with discriminant -47 : [ [0,1,1,12] ]
-2 with discriminant -48 : [ [0,1,0,12] [0,2,2,2] ]
-1 with discriminant -51 : [ [0,1,1,13] ]
-1 with discriminant -52 : [ [0,1,0,13] ]
-1 with discriminant -55 : [ [0,1,1,14] ]
-1 with discriminant -56 : [ [0,1,0,14] ]
-2 with discriminant -59 : [ [0,1,1,15] [1,2,0,1] ]
-3 with discriminant -60 : [ [0,1,0,15] [0,2,-1,2] [0,2,1,2] ]
-1 with discriminant -63 : [ [0,1,1,16] ]
-2 with discriminant -64 : [ [0,1,0,16] [0,2,0,2] ]
-1 with discriminant -67 : [ [0,1,1,17] ]
-1 with discriminant -68 : [ [0,1,0,17] ]
-1 with discriminant -71 : [ [0,1,1,18] ]
-4 with discriminant -72 : [ [0,1,0,18] [0,3,10,9] [0,3,26,57] [1,2,3,0] ]
-1 with discriminant -75 : [ [0,1,1,19] ]
-2 with discriminant -76 : [ [0,1,0,19] [1,-1,3,-1] ]
-1 with discriminant -79 : [ [0,1,1,20] ]
-2 with discriminant -80 : [ [0,1,0,20] [0,2,2,3] ]
-2 with discriminant -83 : [ [0,1,1,21] [1,-1,1,-2] ]
-1 with discriminant -84 : [ [0,1,0,21] ]
-2 with discriminant -87 : [ [0,1,1,22] [1,1,2,-1] ]
-1 with discriminant -88 : [ [0,1,0,22] ]
-1 with discriminant -91 : [ [0,1,1,23] ]
-3 with discriminant -92 : [ [0,1,0,23] [0,2,-1,3] [0,2,1,3] ]
-1 with discriminant -95 : [ [0,1,1,24] ]
-2 with discriminant -96 : [ [0,1,0,24] [0,2,0,3] ]
-4 with discriminant -99 : [ [0,1,1,25] [0,3,5,3] [0,3,31,81] [1,-1,3,0] ]
-2 with discriminant -100 : [ [0,1,0,25] [1,-1,0,2] ]
-1 with discriminant -103 : [ [0,1,1,26] ]
-2 with discriminant -104 : [ [0,1,0,26] [1,0,-1,2] ]
-2 with discriminant -107 : [ [0,1,1,27] [1,2,4,1] ]
-4 with discriminant -108 : [ [0,1,0,27] [0,3,0,1] [1,0,0,2] [1,0,3,0] ]
-1 with discriminant -111 : [ [0,1,1,28] ]
-3 with discriminant -112 : [ [0,1,0,28] [0,2,2,4] [1,0,1,2] ]
-1 with discriminant -115 : [ [0,1,1,29] ]
-2 with discriminant -116 : [ [0,1,0,29] [1,-1,0,-2] ]
-1 with discriminant -119 : [ [0,1,1,30] ]
-1 with discriminant -120 : [ [0,1,0,30] ]
-1 with discriminant -123 : [ [0,1,1,31] ]
-3 with discriminant -124 : [ [0,1,0,31] [0,2,-1,4] [0,2,1,4] ]
-1 with discriminant -127 : [ [0,1,1,32] ]
-2 with discriminant -128 : [ [0,1,0,32] [0,2,0,4] ]
-1 with discriminant -131 : [ [0,1,1,33] ]
-1 with discriminant -132 : [ [0,1,0,33] ]
-3 with discriminant -135 : [ [0,1,1,34] [0,3,3,2] [1,0,3,-1] ]
-1 with discriminant -136 : [ [0,1,0,34] ]
-2 with discriminant -139 : [ [0,1,1,35] [1,-1,1,2] ]
-2 with discriminant -140 : [ [0,1,0,35] [1,0,2,2] ]
-1 with discriminant -143 : [ [0,1,1,36] ]
-2 with discriminant -144 : [ [0,1,0,36] [0,2,2,5] ]
-2 with discriminant -147 : [ [0,1,1,37] [1,-1,-1,-2] ]
-1 with discriminant -148 : [ [0,1,0,37] ]
-1 with discriminant -151 : [ [0,1,1,38] ]
-2 with discriminant -152 : [ [0,1,0,38] [1,-1,-2,-2] ]
-1 with discriminant -155 : [ [0,1,1,39] ]
-3 with discriminant -156 : [ [0,1,0,39] [0,2,-1,5] [0,2,1,5] ]
-1 with discriminant -159 : [ [0,1,1,40] ]
-2 with discriminant -160 : [ [0,1,0,40] [0,2,0,5] ]
-1 with discriminant -163 : [ [0,1,1,41] ]
-1 with discriminant -164 : [ [0,1,0,41] ]
-1 with discriminant -167 : [ [0,1,1,42] ]
-1 with discriminant -168 : [ [0,1,0,42] ]
-1 with discriminant -171 : [ [0,1,1,43] ]
-2 with discriminant -172 : [ [0,1,0,43] [1,2,0,2] ]
-2 with discriminant -175 : [ [0,1,1,44] [1,2,3,-1] ]
-3 with discriminant -176 : [ [0,1,0,44] [0,2,2,6] [1,-1,3,1] ]
-1 with discriminant -179 : [ [0,1,1,45] ]
-3 with discriminant -180 : [ [0,1,0,45] [0,3,-2,2] [0,3,2,2] ]
-1 with discriminant -183 : [ [0,1,1,46] ]
-1 with discriminant -184 : [ [0,1,0,46] ]
-1 with discriminant -187 : [ [0,1,1,47] ]
-3 with discriminant -188 : [ [0,1,0,47] [0,2,-1,6] [0,2,1,6] ]
-1 with discriminant -191 : [ [0,1,1,48] ]
-5 with discriminant -192 : [ [0,1,0,48] [0,2,0,6] [0,4,14,13] [0,4,50,157] [1,2,4,0] ]
-1 with discriminant -195 : [ [0,1,1,49] ]
-1 with discriminant -196 : [ [0,1,0,49] ]
-2 with discriminant -199 : [ [0,1,1,50] [1,1,4,1] ]
-2 with discriminant -200 : [ [0,1,0,50] [1,-1,2,2] ]
+Cubics with negative discriminant down to -200, up to GL(2,Z)-equivalence
+-3 [ [0,1,1,1] ]
+-4 [ [0,1,0,1] ]
+-7 [ [0,1,1,2] ]
+-8 [ [0,1,0,2] ]
+-11 [ [0,1,1,3] ]
+-12 [ [0,1,0,3] ]
+-15 [ [0,1,1,4] ]
+-16 [ [0,1,0,4] [1,2,2,0] ]
+-19 [ [0,1,1,5] ]
+-20 [ [0,1,0,5] ]
+-23 [ [0,1,1,6] [1,-1,0,1] ]
+-24 [ [0,1,0,6] ]
+-27 [ [0,1,1,7] [1,0,0,1] ]
+-28 [ [0,1,0,7] [0,2,-1,1] ]
+-31 [ [0,1,1,8] [1,1,0,1] ]
+-32 [ [0,1,0,8] [0,2,0,1] ]
+-35 [ [0,1,1,9] ]
+-36 [ [0,1,0,9] ]
+-39 [ [0,1,1,10] ]
+-40 [ [0,1,0,10] ]
+-43 [ [0,1,1,11] ]
+-44 [ [0,1,0,11] [1,-1,1,1] ]
+-47 [ [0,1,1,12] ]
+-48 [ [0,1,0,12] [0,2,2,2] ]
+-51 [ [0,1,1,13] ]
+-52 [ [0,1,0,13] ]
+-55 [ [0,1,1,14] ]
+-56 [ [0,1,0,14] ]
+-59 [ [0,1,1,15] [1,2,0,1] ]
+-60 [ [0,1,0,15] [0,2,-1,2] ]
+-63 [ [0,1,1,16] ]
+-64 [ [0,1,0,16] [0,2,0,2] ]
+-67 [ [0,1,1,17] ]
+-68 [ [0,1,0,17] ]
+-71 [ [0,1,1,18] ]
+-72 [ [0,1,0,18] [0,3,-2,1] [1,2,3,0] ]
+-75 [ [0,1,1,19] ]
+-76 [ [0,1,0,19] [1,-1,3,-1] ]
+-79 [ [0,1,1,20] ]
+-80 [ [0,1,0,20] [0,2,2,3] ]
+-83 [ [0,1,1,21] [1,-1,1,-2] ]
+-84 [ [0,1,0,21] ]
+-87 [ [0,1,1,22] [1,1,2,-1] ]
+-88 [ [0,1,0,22] ]
+-91 [ [0,1,1,23] ]
+-92 [ [0,1,0,23] [0,2,-1,3] ]
+-95 [ [0,1,1,24] ]
+-96 [ [0,1,0,24] [0,2,0,3] ]
+-99 [ [0,1,1,25] [0,3,-1,1] [1,-1,3,0] ]
+-100 [ [0,1,0,25] [1,-1,0,2] ]
+-103 [ [0,1,1,26] ]
+-104 [ [0,1,0,26] [1,0,-1,2] ]
+-107 [ [0,1,1,27] [1,2,4,1] ]
+-108 [ [0,1,0,27] [1,0,3,0] [1,0,0,2] ]
+-111 [ [0,1,1,28] ]
+-112 [ [0,1,0,28] [0,2,2,4] [1,0,1,2] ]
+-115 [ [0,1,1,29] ]
+-116 [ [0,1,0,29] [1,-1,0,-2] ]
+-119 [ [0,1,1,30] ]
+-120 [ [0,1,0,30] ]
+-123 [ [0,1,1,31] ]
+-124 [ [0,1,0,31] [0,2,-1,4] ]
+-127 [ [0,1,1,32] ]
+-128 [ [0,1,0,32] [0,2,0,4] ]
+-131 [ [0,1,1,33] ]
+-132 [ [0,1,0,33] ]
+-135 [ [0,1,1,34] [0,3,3,2] [1,0,3,-1] ]
+-136 [ [0,1,0,34] ]
+-139 [ [0,1,1,35] [1,-1,1,2] ]
+-140 [ [0,1,0,35] [1,0,2,2] ]
+-143 [ [0,1,1,36] ]
+-144 [ [0,1,0,36] [0,2,2,5] ]
+-147 [ [0,1,1,37] [1,-1,-1,-2] ]
+-148 [ [0,1,0,37] ]
+-151 [ [0,1,1,38] ]
+-152 [ [0,1,0,38] [1,-1,-2,-2] ]
+-155 [ [0,1,1,39] ]
+-156 [ [0,1,0,39] [0,2,-1,5] ]
+-159 [ [0,1,1,40] ]
+-160 [ [0,1,0,40] [0,2,0,5] ]
+-163 [ [0,1,1,41] ]
+-164 [ [0,1,0,41] ]
+-167 [ [0,1,1,42] ]
+-168 [ [0,1,0,42] ]
+-171 [ [0,1,1,43] ]
+-172 [ [0,1,0,43] [1,2,0,2] ]
+-175 [ [0,1,1,44] [1,2,3,-1] ]
+-176 [ [0,1,0,44] [0,2,2,6] [1,-1,3,1] ]
+-179 [ [0,1,1,45] ]
+-180 [ [0,1,0,45] [0,3,-2,2] ]
+-183 [ [0,1,1,46] ]
+-184 [ [0,1,0,46] ]
+-187 [ [0,1,1,47] ]
+-188 [ [0,1,0,47] [0,2,-1,6] ]
+-191 [ [0,1,1,48] ]
+-192 [ [0,1,0,48] [0,2,0,6] [0,4,-2,1] [1,2,4,0] ]
+-195 [ [0,1,1,49] ]
+-196 [ [0,1,0,49] ]
+-199 [ [0,1,1,50] [1,1,4,1] ]
+-200 [ [0,1,0,50] [1,-1,2,2] ]
 
diff -Nru eclib-20220621/progs/out_ntl/cubics.out eclib-20221012/progs/out_ntl/cubics.out
--- eclib-20220621/progs/out_ntl/cubics.out	2022-06-21 14:25:26.000000000 +0000
+++ eclib-20221012/progs/out_ntl/cubics.out	2022-10-12 11:04:09.000000000 +0000
@@ -1,8 +1,8 @@
 1 reduced cubics with discriminant 1 (up to GL(2,Z)-equivalence) : [ [0,1,1,0] ]
 2 irreducible reduced cubics with discriminant 49 (up to SL(2,Z)-equivalence) : [ [1,2,-1,-1] [1,1,-2,-1] ]
 1 irreducible reduced cubics with discriminant 49 (up to GL(2,Z)-equivalence) : [ [1,2,-1,-1] ]
-3 reduced cubics with discriminant 49 (up to SL(2,Z)-equivalence) : [ [0,1,1,-12] [1,2,-1,-1] [1,1,-2,-1] ]
-2 reduced cubics with discriminant 49 (up to GL(2,Z)-equivalence) : [ [0,1,1,-12] [1,2,-1,-1] ]
+3 reduced cubics with discriminant 49 (up to SL(2,Z)-equivalence) : [ [0,1,-1,-12] [1,2,-1,-1] [1,1,-2,-1] ]
+2 reduced cubics with discriminant 49 (up to GL(2,Z)-equivalence) : [ [0,1,-1,-12] [1,2,-1,-1] ]
 2 reduced cubics with discriminant 148 (up to GL(2,Z)-equivalence) : [ [0,1,0,-37] [1,-1,-3,1] ]
 2 reduced cubics with discriminant -23 (up to GL(2,Z)-equivalence) : [ [0,1,1,6] [1,-1,0,1] ]
 2 reduced cubics with discriminant -199 (up to GL(2,Z)-equivalence) : [ [0,1,1,50] [1,1,4,1] ]
diff -Nru eclib-20220621/progs/out_ntl/list_cubics.out eclib-20221012/progs/out_ntl/list_cubics.out
--- eclib-20220621/progs/out_ntl/list_cubics.out	2022-06-21 14:25:26.000000000 +0000
+++ eclib-20221012/progs/out_ntl/list_cubics.out	2022-10-12 11:04:09.000000000 +0000
@@ -1,464 +1,464 @@
-Irreducible cubics with positive discriminant  up  to 200 up to SL(2,Z)-equivalence
-2 with discriminant 49 : [ [1,2,-1,-1] [1,1,-2,-1] ]
-2 with discriminant 81 : [ [1,3,0,-1] [1,0,-3,-1] ]
-2 with discriminant 148 : [ [1,-1,-3,1] [1,1,-3,-1] ]
-2 with discriminant 169 : [ [1,-1,-4,-1] [1,4,1,-1] ]
+Irreducible cubics with positive discriminant up to 200, up to SL(2,Z)-equivalence
+49 [ [1,2,-1,-1] [1,1,-2,-1] ]
+81 [ [1,3,0,-1] [1,0,-3,-1] ]
+148 [ [1,-1,-3,1] [1,1,-3,-1] ]
+169 [ [1,-1,-4,-1] [1,4,1,-1] ]
 
-Irreducible cubics with positive discriminant  up  to 200 up to GL(2,Z)-equivalence
-1 with discriminant 49 : [ [1,2,-1,-1] ]
-1 with discriminant 81 : [ [1,3,0,-1] ]
-1 with discriminant 148 : [ [1,-1,-3,1] ]
-1 with discriminant 169 : [ [1,-1,-4,-1] ]
+Irreducible cubics with positive discriminant up to 200, up to GL(2,Z)-equivalence
+49 [ [1,2,-1,-1] ]
+81 [ [1,3,0,-1] ]
+148 [ [1,-1,-3,1] ]
+169 [ [1,-1,-4,-1] ]
 
-Cubics with positive discriminant  up  to 200 up to SL(2,Z)-equivalence
-1 with discriminant 1 : [ [0,1,1,0] ]
-1 with discriminant 4 : [ [0,1,0,-1] ]
-1 with discriminant 5 : [ [0,1,1,-1] ]
-1 with discriminant 8 : [ [0,1,0,-2] ]
-1 with discriminant 9 : [ [0,1,1,-2] ]
-1 with discriminant 12 : [ [0,1,0,-3] ]
-1 with discriminant 13 : [ [0,1,1,-3] ]
-2 with discriminant 16 : [ [0,1,0,-4] [0,2,2,0] ]
-1 with discriminant 17 : [ [0,1,1,-4] ]
-1 with discriminant 20 : [ [0,1,0,-5] ]
-1 with discriminant 21 : [ [0,1,1,-5] ]
-1 with discriminant 24 : [ [0,1,0,-6] ]
-1 with discriminant 25 : [ [0,1,1,-6] ]
-1 with discriminant 28 : [ [0,1,0,-7] ]
-1 with discriminant 29 : [ [0,1,1,-7] ]
-2 with discriminant 32 : [ [0,1,0,-8] [0,2,0,-1] ]
-1 with discriminant 33 : [ [0,1,1,-8] ]
-3 with discriminant 36 : [ [0,1,0,-9] [0,2,-1,-1] [0,2,1,-1] ]
-1 with discriminant 37 : [ [0,1,1,-9] ]
-1 with discriminant 40 : [ [0,1,0,-10] ]
-1 with discriminant 41 : [ [0,1,1,-10] ]
-1 with discriminant 44 : [ [0,1,0,-11] ]
-1 with discriminant 45 : [ [0,1,1,-11] ]
-2 with discriminant 48 : [ [0,1,0,-12] [0,2,2,-1] ]
-3 with discriminant 49 : [ [0,1,1,-12] [1,2,-1,-1] [1,1,-2,-1] ]
-1 with discriminant 52 : [ [0,1,0,-13] ]
-1 with discriminant 53 : [ [0,1,1,-13] ]
-1 with discriminant 56 : [ [0,1,0,-14] ]
-1 with discriminant 57 : [ [0,1,1,-14] ]
-1 with discriminant 60 : [ [0,1,0,-15] ]
-1 with discriminant 61 : [ [0,1,1,-15] ]
-2 with discriminant 64 : [ [0,1,0,-16] [0,2,0,-2] ]
-1 with discriminant 65 : [ [0,1,1,-16] ]
-3 with discriminant 68 : [ [0,1,0,-17] [0,2,-1,-2] [0,2,1,-2] ]
-1 with discriminant 69 : [ [0,1,1,-17] ]
-1 with discriminant 72 : [ [0,1,0,-18] ]
-1 with discriminant 73 : [ [0,1,1,-18] ]
-1 with discriminant 76 : [ [0,1,0,-19] ]
-1 with discriminant 77 : [ [0,1,1,-19] ]
-2 with discriminant 80 : [ [0,1,0,-20] [0,2,2,-2] ]
-4 with discriminant 81 : [ [0,1,1,-20] [0,3,3,0] [1,3,0,-1] [1,0,-3,-1] ]
-1 with discriminant 84 : [ [0,1,0,-21] ]
-1 with discriminant 85 : [ [0,1,1,-21] ]
-1 with discriminant 88 : [ [0,1,0,-22] ]
-1 with discriminant 89 : [ [0,1,1,-22] ]
-1 with discriminant 92 : [ [0,1,0,-23] ]
-1 with discriminant 93 : [ [0,1,1,-23] ]
-2 with discriminant 96 : [ [0,1,0,-24] [0,2,0,-3] ]
-1 with discriminant 97 : [ [0,1,1,-24] ]
-3 with discriminant 100 : [ [0,1,0,-25] [0,2,-1,-3] [0,2,1,-3] ]
-1 with discriminant 101 : [ [0,1,1,-25] ]
-1 with discriminant 104 : [ [0,1,0,-26] ]
-1 with discriminant 105 : [ [0,1,1,-26] ]
-3 with discriminant 108 : [ [0,1,0,-27] [0,3,0,-1] [1,0,-3,0] ]
-1 with discriminant 109 : [ [0,1,1,-27] ]
-2 with discriminant 112 : [ [0,1,0,-28] [0,2,2,-3] ]
-1 with discriminant 113 : [ [0,1,1,-28] ]
-1 with discriminant 116 : [ [0,1,0,-29] ]
-5 with discriminant 117 : [ [0,1,1,-29] [0,3,-1,-1] [0,3,1,-1] [0,-3,1,1] [0,-3,-1,1] ]
-1 with discriminant 120 : [ [0,1,0,-30] ]
-1 with discriminant 121 : [ [0,1,1,-30] ]
-1 with discriminant 124 : [ [0,1,0,-31] ]
-2 with discriminant 125 : [ [0,1,1,-31] [1,2,-2,-1] ]
-2 with discriminant 128 : [ [0,1,0,-32] [0,2,0,-4] ]
-1 with discriminant 129 : [ [0,1,1,-32] ]
-3 with discriminant 132 : [ [0,1,0,-33] [0,2,-1,-4] [0,2,1,-4] ]
-1 with discriminant 133 : [ [0,1,1,-33] ]
-1 with discriminant 136 : [ [0,1,0,-34] ]
-1 with discriminant 137 : [ [0,1,1,-34] ]
-1 with discriminant 140 : [ [0,1,0,-35] ]
-1 with discriminant 141 : [ [0,1,1,-35] ]
-6 with discriminant 144 : [ [0,1,0,-36] [0,2,2,-4] [0,3,-2,-1] [0,3,2,-1] [0,-3,-2,1] [0,-3,2,1] ]
-1 with discriminant 145 : [ [0,1,1,-36] ]
-3 with discriminant 148 : [ [0,1,0,-37] [1,-1,-3,1] [1,1,-3,-1] ]
-1 with discriminant 149 : [ [0,1,1,-37] ]
-1 with discriminant 152 : [ [0,1,0,-38] ]
-1 with discriminant 153 : [ [0,1,1,-38] ]
-1 with discriminant 156 : [ [0,1,0,-39] ]
-1 with discriminant 157 : [ [0,1,1,-39] ]
-2 with discriminant 160 : [ [0,1,0,-40] [0,2,0,-5] ]
-1 with discriminant 161 : [ [0,1,1,-40] ]
-3 with discriminant 164 : [ [0,1,0,-41] [0,2,-1,-5] [0,2,1,-5] ]
-1 with discriminant 165 : [ [0,1,1,-41] ]
-1 with discriminant 168 : [ [0,1,0,-42] ]
-3 with discriminant 169 : [ [0,1,1,-42] [1,-1,-4,-1] [1,4,1,-1] ]
-1 with discriminant 172 : [ [0,1,0,-43] ]
-1 with discriminant 173 : [ [0,1,1,-43] ]
-2 with discriminant 176 : [ [0,1,0,-44] [0,2,2,-5] ]
-1 with discriminant 177 : [ [0,1,1,-44] ]
-1 with discriminant 180 : [ [0,1,0,-45] ]
-1 with discriminant 181 : [ [0,1,1,-45] ]
-1 with discriminant 184 : [ [0,1,0,-46] ]
-1 with discriminant 185 : [ [0,1,1,-46] ]
-1 with discriminant 188 : [ [0,1,0,-47] ]
-2 with discriminant 189 : [ [0,1,1,-47] [0,3,3,-1] ]
-2 with discriminant 192 : [ [0,1,0,-48] [0,2,0,-6] ]
-1 with discriminant 193 : [ [0,1,1,-48] ]
-3 with discriminant 196 : [ [0,1,0,-49] [0,2,-1,-6] [0,2,1,-6] ]
-1 with discriminant 197 : [ [0,1,1,-49] ]
-1 with discriminant 200 : [ [0,1,0,-50] ]
+Cubics with positive discriminant up to 200, up to SL(2,Z)-equivalence
+1 [ [0,1,1,0] ]
+4 [ [0,1,0,-1] ]
+5 [ [0,1,-1,-1] ]
+8 [ [0,1,0,-2] ]
+9 [ [0,1,-1,-2] ]
+12 [ [0,1,0,-3] ]
+13 [ [0,1,-1,-3] ]
+16 [ [0,1,0,-4] [0,2,2,0] ]
+17 [ [0,1,-1,-4] ]
+20 [ [0,1,0,-5] ]
+21 [ [0,1,-1,-5] ]
+24 [ [0,1,0,-6] ]
+25 [ [0,1,-1,-6] ]
+28 [ [0,1,0,-7] ]
+29 [ [0,1,-1,-7] ]
+32 [ [0,1,0,-8] [0,2,0,-1] ]
+33 [ [0,1,-1,-8] ]
+36 [ [0,1,0,-9] [0,2,-1,-1] [0,2,1,-1] ]
+37 [ [0,1,-1,-9] ]
+40 [ [0,1,0,-10] ]
+41 [ [0,1,-1,-10] ]
+44 [ [0,1,0,-11] ]
+45 [ [0,1,-1,-11] ]
+48 [ [0,1,0,-12] [0,2,-2,-1] ]
+49 [ [0,1,-1,-12] [1,2,-1,-1] [1,1,-2,-1] ]
+52 [ [0,1,0,-13] ]
+53 [ [0,1,-1,-13] ]
+56 [ [0,1,0,-14] ]
+57 [ [0,1,-1,-14] ]
+60 [ [0,1,0,-15] ]
+61 [ [0,1,-1,-15] ]
+64 [ [0,1,0,-16] [0,2,0,-2] ]
+65 [ [0,1,-1,-16] ]
+68 [ [0,1,0,-17] [0,2,-1,-2] [0,2,1,-2] ]
+69 [ [0,1,-1,-17] ]
+72 [ [0,1,0,-18] ]
+73 [ [0,1,-1,-18] ]
+76 [ [0,1,0,-19] ]
+77 [ [0,1,-1,-19] ]
+80 [ [0,1,0,-20] [0,2,-2,-2] ]
+81 [ [0,1,-1,-20] [0,3,3,0] [1,3,0,-1] [1,0,-3,-1] ]
+84 [ [0,1,0,-21] ]
+85 [ [0,1,-1,-21] ]
+88 [ [0,1,0,-22] ]
+89 [ [0,1,-1,-22] ]
+92 [ [0,1,0,-23] ]
+93 [ [0,1,-1,-23] ]
+96 [ [0,1,0,-24] [0,2,0,-3] ]
+97 [ [0,1,-1,-24] ]
+100 [ [0,1,0,-25] [0,2,-1,-3] [0,2,1,-3] ]
+101 [ [0,1,-1,-25] ]
+104 [ [0,1,0,-26] ]
+105 [ [0,1,-1,-26] ]
+108 [ [0,1,0,-27] [1,0,-3,0] ]
+109 [ [0,1,-1,-27] ]
+112 [ [0,1,0,-28] [0,2,-2,-3] ]
+113 [ [0,1,-1,-28] ]
+116 [ [0,1,0,-29] ]
+117 [ [0,1,-1,-29] [0,3,-1,-1] [0,3,1,-1] ]
+120 [ [0,1,0,-30] ]
+121 [ [0,1,-1,-30] ]
+124 [ [0,1,0,-31] ]
+125 [ [0,1,-1,-31] [1,2,-2,-1] ]
+128 [ [0,1,0,-32] [0,2,0,-4] ]
+129 [ [0,1,-1,-32] ]
+132 [ [0,1,0,-33] [0,2,-1,-4] [0,2,1,-4] ]
+133 [ [0,1,-1,-33] ]
+136 [ [0,1,0,-34] ]
+137 [ [0,1,-1,-34] ]
+140 [ [0,1,0,-35] ]
+141 [ [0,1,-1,-35] ]
+144 [ [0,1,0,-36] [0,2,-2,-4] [0,3,-2,-1] [0,3,2,-1] ]
+145 [ [0,1,-1,-36] ]
+148 [ [0,1,0,-37] [1,-1,-3,1] [1,1,-3,-1] ]
+149 [ [0,1,-1,-37] ]
+152 [ [0,1,0,-38] ]
+153 [ [0,1,-1,-38] ]
+156 [ [0,1,0,-39] ]
+157 [ [0,1,-1,-39] ]
+160 [ [0,1,0,-40] [0,2,0,-5] ]
+161 [ [0,1,-1,-40] ]
+164 [ [0,1,0,-41] [0,2,-1,-5] [0,2,1,-5] ]
+165 [ [0,1,-1,-41] ]
+168 [ [0,1,0,-42] ]
+169 [ [0,1,-1,-42] [1,-1,-4,-1] [1,4,1,-1] ]
+172 [ [0,1,0,-43] ]
+173 [ [0,1,-1,-43] ]
+176 [ [0,1,0,-44] [0,2,-2,-5] ]
+177 [ [0,1,-1,-44] ]
+180 [ [0,1,0,-45] ]
+181 [ [0,1,-1,-45] ]
+184 [ [0,1,0,-46] ]
+185 [ [0,1,-1,-46] ]
+188 [ [0,1,0,-47] ]
+189 [ [0,1,-1,-47] [0,3,-3,-1] ]
+192 [ [0,1,0,-48] [0,2,0,-6] ]
+193 [ [0,1,-1,-48] ]
+196 [ [0,1,0,-49] [0,2,-1,-6] [0,2,1,-6] ]
+197 [ [0,1,-1,-49] ]
+200 [ [0,1,0,-50] ]
 
-Cubics with positive discriminant  up  to 200 up to GL(2,Z)-equivalence
-1 with discriminant 1 : [ [0,1,1,0] ]
-1 with discriminant 4 : [ [0,1,0,-1] ]
-1 with discriminant 5 : [ [0,1,1,-1] ]
-1 with discriminant 8 : [ [0,1,0,-2] ]
-1 with discriminant 9 : [ [0,1,1,-2] ]
-1 with discriminant 12 : [ [0,1,0,-3] ]
-1 with discriminant 13 : [ [0,1,1,-3] ]
-2 with discriminant 16 : [ [0,1,0,-4] [0,2,2,0] ]
-1 with discriminant 17 : [ [0,1,1,-4] ]
-1 with discriminant 20 : [ [0,1,0,-5] ]
-1 with discriminant 21 : [ [0,1,1,-5] ]
-1 with discriminant 24 : [ [0,1,0,-6] ]
-1 with discriminant 25 : [ [0,1,1,-6] ]
-1 with discriminant 28 : [ [0,1,0,-7] ]
-1 with discriminant 29 : [ [0,1,1,-7] ]
-2 with discriminant 32 : [ [0,1,0,-8] [0,2,0,-1] ]
-1 with discriminant 33 : [ [0,1,1,-8] ]
-3 with discriminant 36 : [ [0,1,0,-9] [0,2,-1,-1] [0,2,1,-1] ]
-1 with discriminant 37 : [ [0,1,1,-9] ]
-1 with discriminant 40 : [ [0,1,0,-10] ]
-1 with discriminant 41 : [ [0,1,1,-10] ]
-1 with discriminant 44 : [ [0,1,0,-11] ]
-1 with discriminant 45 : [ [0,1,1,-11] ]
-2 with discriminant 48 : [ [0,1,0,-12] [0,2,2,-1] ]
-2 with discriminant 49 : [ [0,1,1,-12] [1,2,-1,-1] ]
-1 with discriminant 52 : [ [0,1,0,-13] ]
-1 with discriminant 53 : [ [0,1,1,-13] ]
-1 with discriminant 56 : [ [0,1,0,-14] ]
-1 with discriminant 57 : [ [0,1,1,-14] ]
-1 with discriminant 60 : [ [0,1,0,-15] ]
-1 with discriminant 61 : [ [0,1,1,-15] ]
-2 with discriminant 64 : [ [0,1,0,-16] [0,2,0,-2] ]
-1 with discriminant 65 : [ [0,1,1,-16] ]
-3 with discriminant 68 : [ [0,1,0,-17] [0,2,-1,-2] [0,2,1,-2] ]
-1 with discriminant 69 : [ [0,1,1,-17] ]
-1 with discriminant 72 : [ [0,1,0,-18] ]
-1 with discriminant 73 : [ [0,1,1,-18] ]
-1 with discriminant 76 : [ [0,1,0,-19] ]
-1 with discriminant 77 : [ [0,1,1,-19] ]
-2 with discriminant 80 : [ [0,1,0,-20] [0,2,2,-2] ]
-3 with discriminant 81 : [ [0,1,1,-20] [0,3,3,0] [1,3,0,-1] ]
-1 with discriminant 84 : [ [0,1,0,-21] ]
-1 with discriminant 85 : [ [0,1,1,-21] ]
-1 with discriminant 88 : [ [0,1,0,-22] ]
-1 with discriminant 89 : [ [0,1,1,-22] ]
-1 with discriminant 92 : [ [0,1,0,-23] ]
-1 with discriminant 93 : [ [0,1,1,-23] ]
-2 with discriminant 96 : [ [0,1,0,-24] [0,2,0,-3] ]
-1 with discriminant 97 : [ [0,1,1,-24] ]
-3 with discriminant 100 : [ [0,1,0,-25] [0,2,-1,-3] [0,2,1,-3] ]
-1 with discriminant 101 : [ [0,1,1,-25] ]
-1 with discriminant 104 : [ [0,1,0,-26] ]
-1 with discriminant 105 : [ [0,1,1,-26] ]
-3 with discriminant 108 : [ [0,1,0,-27] [0,3,0,-1] [1,0,-3,0] ]
-1 with discriminant 109 : [ [0,1,1,-27] ]
-2 with discriminant 112 : [ [0,1,0,-28] [0,2,2,-3] ]
-1 with discriminant 113 : [ [0,1,1,-28] ]
-1 with discriminant 116 : [ [0,1,0,-29] ]
-3 with discriminant 117 : [ [0,1,1,-29] [0,3,-1,-1] [0,3,1,-1] ]
-1 with discriminant 120 : [ [0,1,0,-30] ]
-1 with discriminant 121 : [ [0,1,1,-30] ]
-1 with discriminant 124 : [ [0,1,0,-31] ]
-2 with discriminant 125 : [ [0,1,1,-31] [1,2,-2,-1] ]
-2 with discriminant 128 : [ [0,1,0,-32] [0,2,0,-4] ]
-1 with discriminant 129 : [ [0,1,1,-32] ]
-3 with discriminant 132 : [ [0,1,0,-33] [0,2,-1,-4] [0,2,1,-4] ]
-1 with discriminant 133 : [ [0,1,1,-33] ]
-1 with discriminant 136 : [ [0,1,0,-34] ]
-1 with discriminant 137 : [ [0,1,1,-34] ]
-1 with discriminant 140 : [ [0,1,0,-35] ]
-1 with discriminant 141 : [ [0,1,1,-35] ]
-4 with discriminant 144 : [ [0,1,0,-36] [0,2,2,-4] [0,3,-2,-1] [0,3,2,-1] ]
-1 with discriminant 145 : [ [0,1,1,-36] ]
-2 with discriminant 148 : [ [0,1,0,-37] [1,-1,-3,1] ]
-1 with discriminant 149 : [ [0,1,1,-37] ]
-1 with discriminant 152 : [ [0,1,0,-38] ]
-1 with discriminant 153 : [ [0,1,1,-38] ]
-1 with discriminant 156 : [ [0,1,0,-39] ]
-1 with discriminant 157 : [ [0,1,1,-39] ]
-2 with discriminant 160 : [ [0,1,0,-40] [0,2,0,-5] ]
-1 with discriminant 161 : [ [0,1,1,-40] ]
-3 with discriminant 164 : [ [0,1,0,-41] [0,2,-1,-5] [0,2,1,-5] ]
-1 with discriminant 165 : [ [0,1,1,-41] ]
-1 with discriminant 168 : [ [0,1,0,-42] ]
-2 with discriminant 169 : [ [0,1,1,-42] [1,-1,-4,-1] ]
-1 with discriminant 172 : [ [0,1,0,-43] ]
-1 with discriminant 173 : [ [0,1,1,-43] ]
-2 with discriminant 176 : [ [0,1,0,-44] [0,2,2,-5] ]
-1 with discriminant 177 : [ [0,1,1,-44] ]
-1 with discriminant 180 : [ [0,1,0,-45] ]
-1 with discriminant 181 : [ [0,1,1,-45] ]
-1 with discriminant 184 : [ [0,1,0,-46] ]
-1 with discriminant 185 : [ [0,1,1,-46] ]
-1 with discriminant 188 : [ [0,1,0,-47] ]
-2 with discriminant 189 : [ [0,1,1,-47] [0,3,3,-1] ]
-2 with discriminant 192 : [ [0,1,0,-48] [0,2,0,-6] ]
-1 with discriminant 193 : [ [0,1,1,-48] ]
-3 with discriminant 196 : [ [0,1,0,-49] [0,2,-1,-6] [0,2,1,-6] ]
-1 with discriminant 197 : [ [0,1,1,-49] ]
-1 with discriminant 200 : [ [0,1,0,-50] ]
+Cubics with positive discriminant up to 200, up to GL(2,Z)-equivalence
+1 [ [0,1,1,0] ]
+4 [ [0,1,0,-1] ]
+5 [ [0,1,-1,-1] ]
+8 [ [0,1,0,-2] ]
+9 [ [0,1,-1,-2] ]
+12 [ [0,1,0,-3] ]
+13 [ [0,1,-1,-3] ]
+16 [ [0,1,0,-4] [0,2,2,0] ]
+17 [ [0,1,-1,-4] ]
+20 [ [0,1,0,-5] ]
+21 [ [0,1,-1,-5] ]
+24 [ [0,1,0,-6] ]
+25 [ [0,1,-1,-6] ]
+28 [ [0,1,0,-7] ]
+29 [ [0,1,-1,-7] ]
+32 [ [0,1,0,-8] [0,2,0,-1] ]
+33 [ [0,1,-1,-8] ]
+36 [ [0,1,0,-9] [0,2,-1,-1] ]
+37 [ [0,1,-1,-9] ]
+40 [ [0,1,0,-10] ]
+41 [ [0,1,-1,-10] ]
+44 [ [0,1,0,-11] ]
+45 [ [0,1,-1,-11] ]
+48 [ [0,1,0,-12] [0,2,-2,-1] ]
+49 [ [0,1,-1,-12] [1,2,-1,-1] ]
+52 [ [0,1,0,-13] ]
+53 [ [0,1,-1,-13] ]
+56 [ [0,1,0,-14] ]
+57 [ [0,1,-1,-14] ]
+60 [ [0,1,0,-15] ]
+61 [ [0,1,-1,-15] ]
+64 [ [0,1,0,-16] [0,2,0,-2] ]
+65 [ [0,1,-1,-16] ]
+68 [ [0,1,0,-17] [0,2,-1,-2] ]
+69 [ [0,1,-1,-17] ]
+72 [ [0,1,0,-18] ]
+73 [ [0,1,-1,-18] ]
+76 [ [0,1,0,-19] ]
+77 [ [0,1,-1,-19] ]
+80 [ [0,1,0,-20] [0,2,-2,-2] ]
+81 [ [0,1,-1,-20] [0,3,3,0] [1,3,0,-1] ]
+84 [ [0,1,0,-21] ]
+85 [ [0,1,-1,-21] ]
+88 [ [0,1,0,-22] ]
+89 [ [0,1,-1,-22] ]
+92 [ [0,1,0,-23] ]
+93 [ [0,1,-1,-23] ]
+96 [ [0,1,0,-24] [0,2,0,-3] ]
+97 [ [0,1,-1,-24] ]
+100 [ [0,1,0,-25] [0,2,-1,-3] ]
+101 [ [0,1,-1,-25] ]
+104 [ [0,1,0,-26] ]
+105 [ [0,1,-1,-26] ]
+108 [ [0,1,0,-27] [1,0,-3,0] ]
+109 [ [0,1,-1,-27] ]
+112 [ [0,1,0,-28] [0,2,-2,-3] ]
+113 [ [0,1,-1,-28] ]
+116 [ [0,1,0,-29] ]
+117 [ [0,1,-1,-29] [0,3,-1,-1] ]
+120 [ [0,1,0,-30] ]
+121 [ [0,1,-1,-30] ]
+124 [ [0,1,0,-31] ]
+125 [ [0,1,-1,-31] [1,2,-2,-1] ]
+128 [ [0,1,0,-32] [0,2,0,-4] ]
+129 [ [0,1,-1,-32] ]
+132 [ [0,1,0,-33] [0,2,-1,-4] ]
+133 [ [0,1,-1,-33] ]
+136 [ [0,1,0,-34] ]
+137 [ [0,1,-1,-34] ]
+140 [ [0,1,0,-35] ]
+141 [ [0,1,-1,-35] ]
+144 [ [0,1,0,-36] [0,2,-2,-4] [0,3,-2,-1] ]
+145 [ [0,1,-1,-36] ]
+148 [ [0,1,0,-37] [1,-1,-3,1] ]
+149 [ [0,1,-1,-37] ]
+152 [ [0,1,0,-38] ]
+153 [ [0,1,-1,-38] ]
+156 [ [0,1,0,-39] ]
+157 [ [0,1,-1,-39] ]
+160 [ [0,1,0,-40] [0,2,0,-5] ]
+161 [ [0,1,-1,-40] ]
+164 [ [0,1,0,-41] [0,2,-1,-5] ]
+165 [ [0,1,-1,-41] ]
+168 [ [0,1,0,-42] ]
+169 [ [0,1,-1,-42] [1,-1,-4,-1] ]
+172 [ [0,1,0,-43] ]
+173 [ [0,1,-1,-43] ]
+176 [ [0,1,0,-44] [0,2,-2,-5] ]
+177 [ [0,1,-1,-44] ]
+180 [ [0,1,0,-45] ]
+181 [ [0,1,-1,-45] ]
+184 [ [0,1,0,-46] ]
+185 [ [0,1,-1,-46] ]
+188 [ [0,1,0,-47] ]
+189 [ [0,1,-1,-47] [0,3,-3,-1] ]
+192 [ [0,1,0,-48] [0,2,0,-6] ]
+193 [ [0,1,-1,-48] ]
+196 [ [0,1,0,-49] [0,2,-1,-6] ]
+197 [ [0,1,-1,-49] ]
+200 [ [0,1,0,-50] ]
 
-Irreducible cubics with negative discriminant down to -200 up to SL(2,Z)-equivalence
-2 with discriminant -23 : [ [1,-1,0,1] [1,1,0,-1] ]
-2 with discriminant -31 : [ [1,1,0,1] [1,-1,0,-1] ]
-2 with discriminant -44 : [ [1,-1,1,1] [1,1,1,-1] ]
-2 with discriminant -59 : [ [1,2,0,1] [1,-2,0,-1] ]
-2 with discriminant -76 : [ [1,-1,3,-1] [1,1,3,1] ]
-2 with discriminant -83 : [ [1,-1,1,-2] [1,1,1,2] ]
-2 with discriminant -87 : [ [1,1,2,-1] [1,-1,2,1] ]
-2 with discriminant -104 : [ [1,0,-1,2] [1,0,-1,-2] ]
-2 with discriminant -107 : [ [1,2,4,1] [1,-2,4,-1] ]
-2 with discriminant -108 : [ [1,0,0,2] [1,0,0,-2] ]
-2 with discriminant -116 : [ [1,-1,0,-2] [1,1,0,2] ]
-2 with discriminant -135 : [ [1,0,3,-1] [1,0,3,1] ]
-2 with discriminant -139 : [ [1,-1,1,2] [1,1,1,-2] ]
-2 with discriminant -140 : [ [1,0,2,2] [1,0,2,-2] ]
-2 with discriminant -152 : [ [1,-1,-2,-2] [1,1,-2,2] ]
-2 with discriminant -172 : [ [1,2,0,2] [1,-2,0,-2] ]
-2 with discriminant -175 : [ [1,2,3,-1] [1,-2,3,1] ]
-2 with discriminant -176 : [ [1,-1,3,1] [1,1,3,-1] ]
-2 with discriminant -199 : [ [1,1,4,1] [1,-1,4,-1] ]
-2 with discriminant -200 : [ [1,-1,2,2] [1,1,2,-2] ]
+Irreducible cubics with negative discriminant down to -200, up to SL(2,Z)-equivalence
+-23 [ [1,-1,0,1] [1,1,0,-1] ]
+-31 [ [1,1,0,1] [1,-1,0,-1] ]
+-44 [ [1,-1,1,1] [1,1,1,-1] ]
+-59 [ [1,2,0,1] [1,-2,0,-1] ]
+-76 [ [1,-1,3,-1] [1,1,3,1] ]
+-83 [ [1,-1,1,-2] [1,1,1,2] ]
+-87 [ [1,1,2,-1] [1,-1,2,1] ]
+-104 [ [1,0,-1,2] [1,0,-1,-2] ]
+-107 [ [1,2,4,1] [1,-2,4,-1] ]
+-108 [ [1,0,0,2] [1,0,0,-2] ]
+-116 [ [1,-1,0,-2] [1,1,0,2] ]
+-135 [ [1,0,3,-1] [1,0,3,1] ]
+-139 [ [1,-1,1,2] [1,1,1,-2] ]
+-140 [ [1,0,2,2] [1,0,2,-2] ]
+-152 [ [1,-1,-2,-2] [1,1,-2,2] ]
+-172 [ [1,2,0,2] [1,-2,0,-2] ]
+-175 [ [1,2,3,-1] [1,-2,3,1] ]
+-176 [ [1,-1,3,1] [1,1,3,-1] ]
+-199 [ [1,1,4,1] [1,-1,4,-1] ]
+-200 [ [1,-1,2,2] [1,1,2,-2] ]
 
-Irreducible cubics with negative discriminant down to -200 up to GL(2,Z)-equivalence
-1 with discriminant -23 : [ [1,-1,0,1] ]
-1 with discriminant -31 : [ [1,1,0,1] ]
-1 with discriminant -44 : [ [1,-1,1,1] ]
-1 with discriminant -59 : [ [1,2,0,1] ]
-1 with discriminant -76 : [ [1,-1,3,-1] ]
-1 with discriminant -83 : [ [1,-1,1,-2] ]
-1 with discriminant -87 : [ [1,1,2,-1] ]
-1 with discriminant -104 : [ [1,0,-1,2] ]
-1 with discriminant -107 : [ [1,2,4,1] ]
-1 with discriminant -108 : [ [1,0,0,2] ]
-1 with discriminant -116 : [ [1,-1,0,-2] ]
-1 with discriminant -135 : [ [1,0,3,-1] ]
-1 with discriminant -139 : [ [1,-1,1,2] ]
-1 with discriminant -140 : [ [1,0,2,2] ]
-1 with discriminant -152 : [ [1,-1,-2,-2] ]
-1 with discriminant -172 : [ [1,2,0,2] ]
-1 with discriminant -175 : [ [1,2,3,-1] ]
-1 with discriminant -176 : [ [1,-1,3,1] ]
-1 with discriminant -199 : [ [1,1,4,1] ]
-1 with discriminant -200 : [ [1,-1,2,2] ]
+Irreducible cubics with negative discriminant down to -200, up to GL(2,Z)-equivalence
+-23 [ [1,-1,0,1] ]
+-31 [ [1,1,0,1] ]
+-44 [ [1,-1,1,1] ]
+-59 [ [1,2,0,1] ]
+-76 [ [1,-1,3,-1] ]
+-83 [ [1,-1,1,-2] ]
+-87 [ [1,1,2,-1] ]
+-104 [ [1,0,-1,2] ]
+-107 [ [1,2,4,1] ]
+-108 [ [1,0,0,2] ]
+-116 [ [1,-1,0,-2] ]
+-135 [ [1,0,3,-1] ]
+-139 [ [1,-1,1,2] ]
+-140 [ [1,0,2,2] ]
+-152 [ [1,-1,-2,-2] ]
+-172 [ [1,2,0,2] ]
+-175 [ [1,2,3,-1] ]
+-176 [ [1,-1,3,1] ]
+-199 [ [1,1,4,1] ]
+-200 [ [1,-1,2,2] ]
 
-Cubics with negative discriminant down to -200 up to SL(2,Z)-equivalence
-1 with discriminant -3 : [ [0,1,1,1] ]
-1 with discriminant -4 : [ [0,1,0,1] ]
-1 with discriminant -7 : [ [0,1,1,2] ]
-1 with discriminant -8 : [ [0,1,0,2] ]
-1 with discriminant -11 : [ [0,1,1,3] ]
-1 with discriminant -12 : [ [0,1,0,3] ]
-1 with discriminant -15 : [ [0,1,1,4] ]
-3 with discriminant -16 : [ [0,1,0,4] [0,2,2,1] [1,1,1,1] ]
-1 with discriminant -19 : [ [0,1,1,5] ]
-1 with discriminant -20 : [ [0,1,0,5] ]
-3 with discriminant -23 : [ [0,1,1,6] [1,-1,0,1] [1,1,0,-1] ]
-1 with discriminant -24 : [ [0,1,0,6] ]
-3 with discriminant -27 : [ [0,1,1,7] [1,0,0,1] [1,0,0,-1] ]
-5 with discriminant -28 : [ [0,1,0,7] [0,2,-1,1] [0,2,1,1] [0,2,13,22] [0,2,3,2] ]
-3 with discriminant -31 : [ [0,1,1,8] [1,1,0,1] [1,-1,0,-1] ]
-2 with discriminant -32 : [ [0,1,0,8] [0,2,0,1] ]
-1 with discriminant -35 : [ [0,1,1,9] ]
-1 with discriminant -36 : [ [0,1,0,9] ]
-1 with discriminant -39 : [ [0,1,1,10] ]
-1 with discriminant -40 : [ [0,1,0,10] ]
-1 with discriminant -43 : [ [0,1,1,11] ]
-3 with discriminant -44 : [ [0,1,0,11] [1,-1,1,1] [1,1,1,-1] ]
-1 with discriminant -47 : [ [0,1,1,12] ]
-2 with discriminant -48 : [ [0,1,0,12] [0,2,2,2] ]
-1 with discriminant -51 : [ [0,1,1,13] ]
-1 with discriminant -52 : [ [0,1,0,13] ]
-1 with discriminant -55 : [ [0,1,1,14] ]
-1 with discriminant -56 : [ [0,1,0,14] ]
-3 with discriminant -59 : [ [0,1,1,15] [1,2,0,1] [1,-2,0,-1] ]
-3 with discriminant -60 : [ [0,1,0,15] [0,2,-1,2] [0,2,1,2] ]
-1 with discriminant -63 : [ [0,1,1,16] ]
-2 with discriminant -64 : [ [0,1,0,16] [0,2,0,2] ]
-1 with discriminant -67 : [ [0,1,1,17] ]
-1 with discriminant -68 : [ [0,1,0,17] ]
-1 with discriminant -71 : [ [0,1,1,18] ]
-5 with discriminant -72 : [ [0,1,0,18] [0,3,10,9] [0,3,26,57] [1,2,3,0] [1,-2,3,0] ]
-1 with discriminant -75 : [ [0,1,1,19] ]
-3 with discriminant -76 : [ [0,1,0,19] [1,-1,3,-1] [1,1,3,1] ]
-1 with discriminant -79 : [ [0,1,1,20] ]
-2 with discriminant -80 : [ [0,1,0,20] [0,2,2,3] ]
-3 with discriminant -83 : [ [0,1,1,21] [1,-1,1,-2] [1,1,1,2] ]
-1 with discriminant -84 : [ [0,1,0,21] ]
-3 with discriminant -87 : [ [0,1,1,22] [1,1,2,-1] [1,-1,2,1] ]
-1 with discriminant -88 : [ [0,1,0,22] ]
-1 with discriminant -91 : [ [0,1,1,23] ]
-3 with discriminant -92 : [ [0,1,0,23] [0,2,-1,3] [0,2,1,3] ]
-1 with discriminant -95 : [ [0,1,1,24] ]
-2 with discriminant -96 : [ [0,1,0,24] [0,2,0,3] ]
-5 with discriminant -99 : [ [0,1,1,25] [0,3,5,3] [0,3,31,81] [1,-1,3,0] [1,1,3,0] ]
-3 with discriminant -100 : [ [0,1,0,25] [1,-1,0,2] [1,1,0,-2] ]
-1 with discriminant -103 : [ [0,1,1,26] ]
-3 with discriminant -104 : [ [0,1,0,26] [1,0,-1,2] [1,0,-1,-2] ]
-3 with discriminant -107 : [ [0,1,1,27] [1,2,4,1] [1,-2,4,-1] ]
-5 with discriminant -108 : [ [0,1,0,27] [0,3,0,1] [1,0,0,2] [1,0,0,-2] [1,0,3,0] ]
-1 with discriminant -111 : [ [0,1,1,28] ]
-4 with discriminant -112 : [ [0,1,0,28] [0,2,2,4] [1,0,1,2] [1,0,1,-2] ]
-1 with discriminant -115 : [ [0,1,1,29] ]
-3 with discriminant -116 : [ [0,1,0,29] [1,-1,0,-2] [1,1,0,2] ]
-1 with discriminant -119 : [ [0,1,1,30] ]
-1 with discriminant -120 : [ [0,1,0,30] ]
-1 with discriminant -123 : [ [0,1,1,31] ]
-3 with discriminant -124 : [ [0,1,0,31] [0,2,-1,4] [0,2,1,4] ]
-1 with discriminant -127 : [ [0,1,1,32] ]
-2 with discriminant -128 : [ [0,1,0,32] [0,2,0,4] ]
-1 with discriminant -131 : [ [0,1,1,33] ]
-1 with discriminant -132 : [ [0,1,0,33] ]
-4 with discriminant -135 : [ [0,1,1,34] [0,3,3,2] [1,0,3,-1] [1,0,3,1] ]
-1 with discriminant -136 : [ [0,1,0,34] ]
-3 with discriminant -139 : [ [0,1,1,35] [1,-1,1,2] [1,1,1,-2] ]
-3 with discriminant -140 : [ [0,1,0,35] [1,0,2,2] [1,0,2,-2] ]
-1 with discriminant -143 : [ [0,1,1,36] ]
-2 with discriminant -144 : [ [0,1,0,36] [0,2,2,5] ]
-3 with discriminant -147 : [ [0,1,1,37] [1,-1,-1,-2] [1,1,-1,2] ]
-1 with discriminant -148 : [ [0,1,0,37] ]
-1 with discriminant -151 : [ [0,1,1,38] ]
-3 with discriminant -152 : [ [0,1,0,38] [1,-1,-2,-2] [1,1,-2,2] ]
-1 with discriminant -155 : [ [0,1,1,39] ]
-3 with discriminant -156 : [ [0,1,0,39] [0,2,-1,5] [0,2,1,5] ]
-1 with discriminant -159 : [ [0,1,1,40] ]
-2 with discriminant -160 : [ [0,1,0,40] [0,2,0,5] ]
-1 with discriminant -163 : [ [0,1,1,41] ]
-1 with discriminant -164 : [ [0,1,0,41] ]
-1 with discriminant -167 : [ [0,1,1,42] ]
-1 with discriminant -168 : [ [0,1,0,42] ]
-1 with discriminant -171 : [ [0,1,1,43] ]
-3 with discriminant -172 : [ [0,1,0,43] [1,2,0,2] [1,-2,0,-2] ]
-3 with discriminant -175 : [ [0,1,1,44] [1,2,3,-1] [1,-2,3,1] ]
-4 with discriminant -176 : [ [0,1,0,44] [0,2,2,6] [1,-1,3,1] [1,1,3,-1] ]
-1 with discriminant -179 : [ [0,1,1,45] ]
-3 with discriminant -180 : [ [0,1,0,45] [0,3,-2,2] [0,3,2,2] ]
-1 with discriminant -183 : [ [0,1,1,46] ]
-1 with discriminant -184 : [ [0,1,0,46] ]
-1 with discriminant -187 : [ [0,1,1,47] ]
-3 with discriminant -188 : [ [0,1,0,47] [0,2,-1,6] [0,2,1,6] ]
-1 with discriminant -191 : [ [0,1,1,48] ]
-6 with discriminant -192 : [ [0,1,0,48] [0,2,0,6] [0,4,14,13] [0,4,50,157] [1,2,4,0] [1,-2,4,0] ]
-1 with discriminant -195 : [ [0,1,1,49] ]
-1 with discriminant -196 : [ [0,1,0,49] ]
-3 with discriminant -199 : [ [0,1,1,50] [1,1,4,1] [1,-1,4,-1] ]
-3 with discriminant -200 : [ [0,1,0,50] [1,-1,2,2] [1,1,2,-2] ]
+Cubics with negative discriminant down to -200, up to SL(2,Z)-equivalence
+-3 [ [0,1,1,1] ]
+-4 [ [0,1,0,1] ]
+-7 [ [0,1,1,2] ]
+-8 [ [0,1,0,2] ]
+-11 [ [0,1,1,3] ]
+-12 [ [0,1,0,3] ]
+-15 [ [0,1,1,4] ]
+-16 [ [0,1,0,4] [1,2,2,0] ]
+-19 [ [0,1,1,5] ]
+-20 [ [0,1,0,5] ]
+-23 [ [0,1,1,6] [1,-1,0,1] [1,1,0,-1] ]
+-24 [ [0,1,0,6] ]
+-27 [ [0,1,1,7] [1,0,0,1] ]
+-28 [ [0,1,0,7] [0,2,-1,1] [0,2,1,1] ]
+-31 [ [0,1,1,8] [1,1,0,1] [1,-1,0,-1] ]
+-32 [ [0,1,0,8] [0,2,0,1] ]
+-35 [ [0,1,1,9] ]
+-36 [ [0,1,0,9] ]
+-39 [ [0,1,1,10] ]
+-40 [ [0,1,0,10] ]
+-43 [ [0,1,1,11] ]
+-44 [ [0,1,0,11] [1,-1,1,1] [1,1,1,-1] ]
+-47 [ [0,1,1,12] ]
+-48 [ [0,1,0,12] [0,2,2,2] ]
+-51 [ [0,1,1,13] ]
+-52 [ [0,1,0,13] ]
+-55 [ [0,1,1,14] ]
+-56 [ [0,1,0,14] ]
+-59 [ [0,1,1,15] [1,2,0,1] [1,-2,0,-1] ]
+-60 [ [0,1,0,15] [0,2,-1,2] [0,2,1,2] ]
+-63 [ [0,1,1,16] ]
+-64 [ [0,1,0,16] [0,2,0,2] ]
+-67 [ [0,1,1,17] ]
+-68 [ [0,1,0,17] ]
+-71 [ [0,1,1,18] ]
+-72 [ [0,1,0,18] [0,3,-2,1] [0,3,2,1] [1,2,3,0] [1,-2,3,0] ]
+-75 [ [0,1,1,19] ]
+-76 [ [0,1,0,19] [1,-1,3,-1] [1,1,3,1] ]
+-79 [ [0,1,1,20] ]
+-80 [ [0,1,0,20] [0,2,2,3] ]
+-83 [ [0,1,1,21] [1,-1,1,-2] [1,1,1,2] ]
+-84 [ [0,1,0,21] ]
+-87 [ [0,1,1,22] [1,1,2,-1] [1,-1,2,1] ]
+-88 [ [0,1,0,22] ]
+-91 [ [0,1,1,23] ]
+-92 [ [0,1,0,23] [0,2,-1,3] [0,2,1,3] ]
+-95 [ [0,1,1,24] ]
+-96 [ [0,1,0,24] [0,2,0,3] ]
+-99 [ [0,1,1,25] [0,3,-1,1] [0,3,1,1] [1,-1,3,0] [1,1,3,0] ]
+-100 [ [0,1,0,25] [1,-1,0,2] [1,1,0,-2] ]
+-103 [ [0,1,1,26] ]
+-104 [ [0,1,0,26] [1,0,-1,2] [1,0,-1,-2] ]
+-107 [ [0,1,1,27] [1,2,4,1] [1,-2,4,-1] ]
+-108 [ [0,1,0,27] [1,0,3,0] [1,0,0,2] [1,0,0,-2] ]
+-111 [ [0,1,1,28] ]
+-112 [ [0,1,0,28] [0,2,2,4] [1,0,1,2] [1,0,1,-2] ]
+-115 [ [0,1,1,29] ]
+-116 [ [0,1,0,29] [1,-1,0,-2] [1,1,0,2] ]
+-119 [ [0,1,1,30] ]
+-120 [ [0,1,0,30] ]
+-123 [ [0,1,1,31] ]
+-124 [ [0,1,0,31] [0,2,-1,4] [0,2,1,4] ]
+-127 [ [0,1,1,32] ]
+-128 [ [0,1,0,32] [0,2,0,4] ]
+-131 [ [0,1,1,33] ]
+-132 [ [0,1,0,33] ]
+-135 [ [0,1,1,34] [0,3,3,2] [1,0,3,-1] [1,0,3,1] ]
+-136 [ [0,1,0,34] ]
+-139 [ [0,1,1,35] [1,-1,1,2] [1,1,1,-2] ]
+-140 [ [0,1,0,35] [1,0,2,2] [1,0,2,-2] ]
+-143 [ [0,1,1,36] ]
+-144 [ [0,1,0,36] [0,2,2,5] ]
+-147 [ [0,1,1,37] [1,-1,-1,-2] [1,1,-1,2] ]
+-148 [ [0,1,0,37] ]
+-151 [ [0,1,1,38] ]
+-152 [ [0,1,0,38] [1,-1,-2,-2] [1,1,-2,2] ]
+-155 [ [0,1,1,39] ]
+-156 [ [0,1,0,39] [0,2,-1,5] [0,2,1,5] ]
+-159 [ [0,1,1,40] ]
+-160 [ [0,1,0,40] [0,2,0,5] ]
+-163 [ [0,1,1,41] ]
+-164 [ [0,1,0,41] ]
+-167 [ [0,1,1,42] ]
+-168 [ [0,1,0,42] ]
+-171 [ [0,1,1,43] ]
+-172 [ [0,1,0,43] [1,2,0,2] [1,-2,0,-2] ]
+-175 [ [0,1,1,44] [1,2,3,-1] [1,-2,3,1] ]
+-176 [ [0,1,0,44] [0,2,2,6] [1,-1,3,1] [1,1,3,-1] ]
+-179 [ [0,1,1,45] ]
+-180 [ [0,1,0,45] [0,3,-2,2] [0,3,2,2] ]
+-183 [ [0,1,1,46] ]
+-184 [ [0,1,0,46] ]
+-187 [ [0,1,1,47] ]
+-188 [ [0,1,0,47] [0,2,-1,6] [0,2,1,6] ]
+-191 [ [0,1,1,48] ]
+-192 [ [0,1,0,48] [0,2,0,6] [0,4,-2,1] [0,4,2,1] [1,2,4,0] [1,-2,4,0] ]
+-195 [ [0,1,1,49] ]
+-196 [ [0,1,0,49] ]
+-199 [ [0,1,1,50] [1,1,4,1] [1,-1,4,-1] ]
+-200 [ [0,1,0,50] [1,-1,2,2] [1,1,2,-2] ]
 
-Cubics with negative discriminant down to -200 up to GL(2,Z)-equivalence
-1 with discriminant -3 : [ [0,1,1,1] ]
-1 with discriminant -4 : [ [0,1,0,1] ]
-1 with discriminant -7 : [ [0,1,1,2] ]
-1 with discriminant -8 : [ [0,1,0,2] ]
-1 with discriminant -11 : [ [0,1,1,3] ]
-1 with discriminant -12 : [ [0,1,0,3] ]
-1 with discriminant -15 : [ [0,1,1,4] ]
-3 with discriminant -16 : [ [0,1,0,4] [0,2,2,1] [1,1,1,1] ]
-1 with discriminant -19 : [ [0,1,1,5] ]
-1 with discriminant -20 : [ [0,1,0,5] ]
-2 with discriminant -23 : [ [0,1,1,6] [1,-1,0,1] ]
-1 with discriminant -24 : [ [0,1,0,6] ]
-2 with discriminant -27 : [ [0,1,1,7] [1,0,0,1] ]
-5 with discriminant -28 : [ [0,1,0,7] [0,2,-1,1] [0,2,1,1] [0,2,13,22] [0,2,3,2] ]
-2 with discriminant -31 : [ [0,1,1,8] [1,1,0,1] ]
-2 with discriminant -32 : [ [0,1,0,8] [0,2,0,1] ]
-1 with discriminant -35 : [ [0,1,1,9] ]
-1 with discriminant -36 : [ [0,1,0,9] ]
-1 with discriminant -39 : [ [0,1,1,10] ]
-1 with discriminant -40 : [ [0,1,0,10] ]
-1 with discriminant -43 : [ [0,1,1,11] ]
-2 with discriminant -44 : [ [0,1,0,11] [1,-1,1,1] ]
-1 with discriminant -47 : [ [0,1,1,12] ]
-2 with discriminant -48 : [ [0,1,0,12] [0,2,2,2] ]
-1 with discriminant -51 : [ [0,1,1,13] ]
-1 with discriminant -52 : [ [0,1,0,13] ]
-1 with discriminant -55 : [ [0,1,1,14] ]
-1 with discriminant -56 : [ [0,1,0,14] ]
-2 with discriminant -59 : [ [0,1,1,15] [1,2,0,1] ]
-3 with discriminant -60 : [ [0,1,0,15] [0,2,-1,2] [0,2,1,2] ]
-1 with discriminant -63 : [ [0,1,1,16] ]
-2 with discriminant -64 : [ [0,1,0,16] [0,2,0,2] ]
-1 with discriminant -67 : [ [0,1,1,17] ]
-1 with discriminant -68 : [ [0,1,0,17] ]
-1 with discriminant -71 : [ [0,1,1,18] ]
-4 with discriminant -72 : [ [0,1,0,18] [0,3,10,9] [0,3,26,57] [1,2,3,0] ]
-1 with discriminant -75 : [ [0,1,1,19] ]
-2 with discriminant -76 : [ [0,1,0,19] [1,-1,3,-1] ]
-1 with discriminant -79 : [ [0,1,1,20] ]
-2 with discriminant -80 : [ [0,1,0,20] [0,2,2,3] ]
-2 with discriminant -83 : [ [0,1,1,21] [1,-1,1,-2] ]
-1 with discriminant -84 : [ [0,1,0,21] ]
-2 with discriminant -87 : [ [0,1,1,22] [1,1,2,-1] ]
-1 with discriminant -88 : [ [0,1,0,22] ]
-1 with discriminant -91 : [ [0,1,1,23] ]
-3 with discriminant -92 : [ [0,1,0,23] [0,2,-1,3] [0,2,1,3] ]
-1 with discriminant -95 : [ [0,1,1,24] ]
-2 with discriminant -96 : [ [0,1,0,24] [0,2,0,3] ]
-4 with discriminant -99 : [ [0,1,1,25] [0,3,5,3] [0,3,31,81] [1,-1,3,0] ]
-2 with discriminant -100 : [ [0,1,0,25] [1,-1,0,2] ]
-1 with discriminant -103 : [ [0,1,1,26] ]
-2 with discriminant -104 : [ [0,1,0,26] [1,0,-1,2] ]
-2 with discriminant -107 : [ [0,1,1,27] [1,2,4,1] ]
-4 with discriminant -108 : [ [0,1,0,27] [0,3,0,1] [1,0,0,2] [1,0,3,0] ]
-1 with discriminant -111 : [ [0,1,1,28] ]
-3 with discriminant -112 : [ [0,1,0,28] [0,2,2,4] [1,0,1,2] ]
-1 with discriminant -115 : [ [0,1,1,29] ]
-2 with discriminant -116 : [ [0,1,0,29] [1,-1,0,-2] ]
-1 with discriminant -119 : [ [0,1,1,30] ]
-1 with discriminant -120 : [ [0,1,0,30] ]
-1 with discriminant -123 : [ [0,1,1,31] ]
-3 with discriminant -124 : [ [0,1,0,31] [0,2,-1,4] [0,2,1,4] ]
-1 with discriminant -127 : [ [0,1,1,32] ]
-2 with discriminant -128 : [ [0,1,0,32] [0,2,0,4] ]
-1 with discriminant -131 : [ [0,1,1,33] ]
-1 with discriminant -132 : [ [0,1,0,33] ]
-3 with discriminant -135 : [ [0,1,1,34] [0,3,3,2] [1,0,3,-1] ]
-1 with discriminant -136 : [ [0,1,0,34] ]
-2 with discriminant -139 : [ [0,1,1,35] [1,-1,1,2] ]
-2 with discriminant -140 : [ [0,1,0,35] [1,0,2,2] ]
-1 with discriminant -143 : [ [0,1,1,36] ]
-2 with discriminant -144 : [ [0,1,0,36] [0,2,2,5] ]
-2 with discriminant -147 : [ [0,1,1,37] [1,-1,-1,-2] ]
-1 with discriminant -148 : [ [0,1,0,37] ]
-1 with discriminant -151 : [ [0,1,1,38] ]
-2 with discriminant -152 : [ [0,1,0,38] [1,-1,-2,-2] ]
-1 with discriminant -155 : [ [0,1,1,39] ]
-3 with discriminant -156 : [ [0,1,0,39] [0,2,-1,5] [0,2,1,5] ]
-1 with discriminant -159 : [ [0,1,1,40] ]
-2 with discriminant -160 : [ [0,1,0,40] [0,2,0,5] ]
-1 with discriminant -163 : [ [0,1,1,41] ]
-1 with discriminant -164 : [ [0,1,0,41] ]
-1 with discriminant -167 : [ [0,1,1,42] ]
-1 with discriminant -168 : [ [0,1,0,42] ]
-1 with discriminant -171 : [ [0,1,1,43] ]
-2 with discriminant -172 : [ [0,1,0,43] [1,2,0,2] ]
-2 with discriminant -175 : [ [0,1,1,44] [1,2,3,-1] ]
-3 with discriminant -176 : [ [0,1,0,44] [0,2,2,6] [1,-1,3,1] ]
-1 with discriminant -179 : [ [0,1,1,45] ]
-3 with discriminant -180 : [ [0,1,0,45] [0,3,-2,2] [0,3,2,2] ]
-1 with discriminant -183 : [ [0,1,1,46] ]
-1 with discriminant -184 : [ [0,1,0,46] ]
-1 with discriminant -187 : [ [0,1,1,47] ]
-3 with discriminant -188 : [ [0,1,0,47] [0,2,-1,6] [0,2,1,6] ]
-1 with discriminant -191 : [ [0,1,1,48] ]
-5 with discriminant -192 : [ [0,1,0,48] [0,2,0,6] [0,4,14,13] [0,4,50,157] [1,2,4,0] ]
-1 with discriminant -195 : [ [0,1,1,49] ]
-1 with discriminant -196 : [ [0,1,0,49] ]
-2 with discriminant -199 : [ [0,1,1,50] [1,1,4,1] ]
-2 with discriminant -200 : [ [0,1,0,50] [1,-1,2,2] ]
+Cubics with negative discriminant down to -200, up to GL(2,Z)-equivalence
+-3 [ [0,1,1,1] ]
+-4 [ [0,1,0,1] ]
+-7 [ [0,1,1,2] ]
+-8 [ [0,1,0,2] ]
+-11 [ [0,1,1,3] ]
+-12 [ [0,1,0,3] ]
+-15 [ [0,1,1,4] ]
+-16 [ [0,1,0,4] [1,2,2,0] ]
+-19 [ [0,1,1,5] ]
+-20 [ [0,1,0,5] ]
+-23 [ [0,1,1,6] [1,-1,0,1] ]
+-24 [ [0,1,0,6] ]
+-27 [ [0,1,1,7] [1,0,0,1] ]
+-28 [ [0,1,0,7] [0,2,-1,1] ]
+-31 [ [0,1,1,8] [1,1,0,1] ]
+-32 [ [0,1,0,8] [0,2,0,1] ]
+-35 [ [0,1,1,9] ]
+-36 [ [0,1,0,9] ]
+-39 [ [0,1,1,10] ]
+-40 [ [0,1,0,10] ]
+-43 [ [0,1,1,11] ]
+-44 [ [0,1,0,11] [1,-1,1,1] ]
+-47 [ [0,1,1,12] ]
+-48 [ [0,1,0,12] [0,2,2,2] ]
+-51 [ [0,1,1,13] ]
+-52 [ [0,1,0,13] ]
+-55 [ [0,1,1,14] ]
+-56 [ [0,1,0,14] ]
+-59 [ [0,1,1,15] [1,2,0,1] ]
+-60 [ [0,1,0,15] [0,2,-1,2] ]
+-63 [ [0,1,1,16] ]
+-64 [ [0,1,0,16] [0,2,0,2] ]
+-67 [ [0,1,1,17] ]
+-68 [ [0,1,0,17] ]
+-71 [ [0,1,1,18] ]
+-72 [ [0,1,0,18] [0,3,-2,1] [1,2,3,0] ]
+-75 [ [0,1,1,19] ]
+-76 [ [0,1,0,19] [1,-1,3,-1] ]
+-79 [ [0,1,1,20] ]
+-80 [ [0,1,0,20] [0,2,2,3] ]
+-83 [ [0,1,1,21] [1,-1,1,-2] ]
+-84 [ [0,1,0,21] ]
+-87 [ [0,1,1,22] [1,1,2,-1] ]
+-88 [ [0,1,0,22] ]
+-91 [ [0,1,1,23] ]
+-92 [ [0,1,0,23] [0,2,-1,3] ]
+-95 [ [0,1,1,24] ]
+-96 [ [0,1,0,24] [0,2,0,3] ]
+-99 [ [0,1,1,25] [0,3,-1,1] [1,-1,3,0] ]
+-100 [ [0,1,0,25] [1,-1,0,2] ]
+-103 [ [0,1,1,26] ]
+-104 [ [0,1,0,26] [1,0,-1,2] ]
+-107 [ [0,1,1,27] [1,2,4,1] ]
+-108 [ [0,1,0,27] [1,0,3,0] [1,0,0,2] ]
+-111 [ [0,1,1,28] ]
+-112 [ [0,1,0,28] [0,2,2,4] [1,0,1,2] ]
+-115 [ [0,1,1,29] ]
+-116 [ [0,1,0,29] [1,-1,0,-2] ]
+-119 [ [0,1,1,30] ]
+-120 [ [0,1,0,30] ]
+-123 [ [0,1,1,31] ]
+-124 [ [0,1,0,31] [0,2,-1,4] ]
+-127 [ [0,1,1,32] ]
+-128 [ [0,1,0,32] [0,2,0,4] ]
+-131 [ [0,1,1,33] ]
+-132 [ [0,1,0,33] ]
+-135 [ [0,1,1,34] [0,3,3,2] [1,0,3,-1] ]
+-136 [ [0,1,0,34] ]
+-139 [ [0,1,1,35] [1,-1,1,2] ]
+-140 [ [0,1,0,35] [1,0,2,2] ]
+-143 [ [0,1,1,36] ]
+-144 [ [0,1,0,36] [0,2,2,5] ]
+-147 [ [0,1,1,37] [1,-1,-1,-2] ]
+-148 [ [0,1,0,37] ]
+-151 [ [0,1,1,38] ]
+-152 [ [0,1,0,38] [1,-1,-2,-2] ]
+-155 [ [0,1,1,39] ]
+-156 [ [0,1,0,39] [0,2,-1,5] ]
+-159 [ [0,1,1,40] ]
+-160 [ [0,1,0,40] [0,2,0,5] ]
+-163 [ [0,1,1,41] ]
+-164 [ [0,1,0,41] ]
+-167 [ [0,1,1,42] ]
+-168 [ [0,1,0,42] ]
+-171 [ [0,1,1,43] ]
+-172 [ [0,1,0,43] [1,2,0,2] ]
+-175 [ [0,1,1,44] [1,2,3,-1] ]
+-176 [ [0,1,0,44] [0,2,2,6] [1,-1,3,1] ]
+-179 [ [0,1,1,45] ]
+-180 [ [0,1,0,45] [0,3,-2,2] ]
+-183 [ [0,1,1,46] ]
+-184 [ [0,1,0,46] ]
+-187 [ [0,1,1,47] ]
+-188 [ [0,1,0,47] [0,2,-1,6] ]
+-191 [ [0,1,1,48] ]
+-192 [ [0,1,0,48] [0,2,0,6] [0,4,-2,1] [1,2,4,0] ]
+-195 [ [0,1,1,49] ]
+-196 [ [0,1,0,49] ]
+-199 [ [0,1,1,50] [1,1,4,1] ]
+-200 [ [0,1,0,50] [1,-1,2,2] ]
 
diff -Nru eclib-20220621/progs/reduce_cubics.cc eclib-20221012/progs/reduce_cubics.cc
--- eclib-20220621/progs/reduce_cubics.cc	2022-06-21 14:25:26.000000000 +0000
+++ eclib-20221012/progs/reduce_cubics.cc	2022-10-12 11:04:09.000000000 +0000
@@ -25,12 +25,14 @@
 #include <eclib/unimod.h>
 #include <eclib/polys.h>
 #include <eclib/cubic.h>
+#include <cassert>
 
 int main()
 {
   initprimes("PRIMES");
   bigint a, b, c, d, disc;
   unimod m;
+
   while(cout << "Enter cubic coeffs a, b, c, d: ",
 	cin >> a >> b >> c >> d,
 	!(is_zero(a)&&is_zero(b)&&is_zero(c)&&is_zero(d)))
@@ -44,7 +46,9 @@
       if(disc>0)
 	{
 	  cout << "Using Hessian to reduce...\n";
+          m.reset();
           g.hess_reduce(m);
+          assert (transform(g0,m)==g);
 	  cout << "Hessian reduced cubic = "<<g<<endl;
 	  cout << "after transform by "<<m<<endl;
 	  cout << "Root of Hessian = " << g.hess_root() << endl;
@@ -58,16 +62,20 @@
 	  //cout << "g(alpha) = " << ga << endl;
 // First use Mathews reduction
 	  cout << "Using Mathews reduction ...\n";
+          m.reset();
           g.mathews_reduce(m);
 	  cout << "Mathews reduced cubic = "<<g<<endl;
 	  cout << "after transform by "<<m<<endl;
+          assert (transform(g0,m)==g);
 
 // Now use JC/Julia reduction
 	  cout << "Using JC/Julia reduction ...\n";
 	  g=g0;
+          m.reset();
           g.jc_reduce(m);
 	  cout << "JC/Julia reduced cubic = "<<g<<endl;
 	  cout << "after transform by "<<m<<endl;
+          assert (transform(g0,m)==g);
 	}
     }
   cout<<endl;
diff -Nru eclib-20220621/tests/out_no_ntl/tversion.out eclib-20221012/tests/out_no_ntl/tversion.out
--- eclib-20220621/tests/out_no_ntl/tversion.out	2022-06-21 14:25:26.000000000 +0000
+++ eclib-20221012/tests/out_no_ntl/tversion.out	2022-10-12 11:04:09.000000000 +0000
@@ -1,12 +1,12 @@
-This eclib version is 20220621
-[ year month day ] = [ 2022 6 21 ]
+This eclib version is 20221012
+[ year month day ] = [ 2022 10 12 ]
 
 Configure options and compilation date:
 
-eclib version 20220621, using NTL bigints but no multiprecision floating point
+eclib version 20221012, using NTL bigints but no multiprecision floating point
 
 Testing comparison of version date and various (year, month, day) date triples:
 
-Date 20200101 is before the version date 20220621
-Date 20300611 is after the version date 20220621
-Date 20210317 is before the version date 20220621
+Date 20200101 is before the version date 20221012
+Date 20300611 is after the version date 20221012
+Date 20210317 is before the version date 20221012
diff -Nru eclib-20220621/tests/out_ntl/tversion.out eclib-20221012/tests/out_ntl/tversion.out
--- eclib-20220621/tests/out_ntl/tversion.out	2022-06-21 14:25:26.000000000 +0000
+++ eclib-20221012/tests/out_ntl/tversion.out	2022-10-12 11:04:09.000000000 +0000
@@ -1,12 +1,12 @@
-This eclib version is 20220621
-[ year month day ] = [ 2022 6 21 ]
+This eclib version is 20221012
+[ year month day ] = [ 2022 10 12 ]
 
 Configure options and compilation date:
 
-eclib version 20220621, using NTL bigints and NTL real and complex multiprecision floating point
+eclib version 20221012, using NTL bigints and NTL real and complex multiprecision floating point
 
 Testing comparison of version date and various (year, month, day) date triples:
 
-Date 20200101 is before the version date 20220621
-Date 20300611 is after the version date 20220621
-Date 20210317 is before the version date 20220621
+Date 20200101 is before the version date 20221012
+Date 20300611 is after the version date 20221012
+Date 20210317 is before the version date 20221012