"Source: Text/Geometry/Crv.text";
"Line: 7400";
"Date: Thu Sep 25 14:47:45 2025";
"Main: Fri Sep 26 14:29:19 2025";
// original file: Text/Geometry/Crv.text, line: 7400
// Example: H124E44 ()
print "Example: H124E44";
ei := GetEchoInput();
SetEchoInput(true);
X := X0NQuotient(58,[]);
X;
boo,mp := Genus6PlaneCurveModel(X : IsCanonical := true);
boo;
assert $1;
C<x,y,z> := Codomain(mp); //the plane model
C;
mp;
P4<x,y,z,t,u> := ProjectiveSpace(Rationals(),4);
X42 := Curve(P4,[x*z+z^2+x*t-x*u,
  y^2-2*y*z+z^2-x*t-2*y*t+z*t-2*y*u+z*u+t*u,
  x^2+x*t+y*t+y*u ]);
// use pointsearch to pick rational point on X42
boo,mp := Genus5PlaneCurveModel(X42 : IsCanonical := true);
boo;
assert $1;
C<x,y,z> := Codomain(mp);
C;
mp;
// use nicer chosen point for nicer map
boo,mp := Genus5PlaneCurveModel(X42,X42![0,0,0,0,1] : IsCanonical := true);
C<x,y,z> := Codomain(mp);
C;
mp;
SetEchoInput(ei);
