"Source: Text/Geometry/CrvHyp.text";
"Line: 1789";
"Date: Fri Sep 26 09:12:34 2025";
"Main: Fri Sep 26 14:29:19 2025";
// original file: Text/Geometry/CrvHyp.text, line: 1789
// Example: H137E11 ()
print "Example: H137E11";
ei := GetEchoInput();
SetEchoInput(true);
R<x>:=PolynomialRing(Rationals());
C:=HyperellipticCurve(x^5+x);
J:=Jacobian(C);
RichelotIsogenousSurfaces(J);
codomains,kernels:=RichelotIsogenousSurfaces(J:Kernels);
Q:=kernels[1];
LX<X>:=Parent(Q);
L<alpha>:=BaseRing(LX);
Q;
L;
_,swp:=SwapExtension(LX);
Norm(swp(Q));
codomains[1] eq RichelotIsogenousSurface(J,Q);
assert $1;
LC:=LSeries(C : LocalData:="Ogg");
myL:=func< A|  
    case<Type(A) | SetCart : LSeries(A[1])*LSeries(A[2]),
                   JacHyp  : LSeries(Curve(A) : LocalData:="Ogg"),
                   CrvEll  : LSeries(A),
                   default : false>>;
cfs:=[c: c in LGetCoefficients(LC,1000)];
[[c: c in LGetCoefficients(myL(A),1000)] eq cfs : A in codomains];
SetEchoInput(ei);
