"Source: Text/Geometry/Crv.text";
"Line: 3483";
"Date: Thu Sep 25 14:47:45 2025";
"Main: Fri Sep 26 14:29:19 2025";
// original file: Text/Geometry/Crv.text, line: 3483
// Example: H124E22 ()
print "Example: H124E22";
ei := GetEchoInput();
SetEchoInput(true);
P2<x,y,z> := ProjectiveSpace(Rationals(),2);
C := Curve(P2,x^3*y+y^3*z+z^3*x);
phi := iso<C->C|[y,z,x],[z,x,y]>;
// we will take the quotient by phi
G := AutomorphismGroup(C,[phi]);
CG,prj := CurveQuotient(G);
CG;
Genus(CG);
assert $1 eq 1;
// find a minimal elliptic Weierstrass model
ptCG := prj(C![0,0,1]);
E1, psi1 := EllipticCurve(CG,ptCG);
E, psi := MinimalModel(E1);
prj := Expand(prj * psi1 * psi); // get the composite map C -> E
E;
prj;
Conductor(E);
assert $1 eq 49;
SetEchoInput(ei);
