"Source: Text/Geometry/Lseries.text";
"Line: 3288";
"Date: Thu Sep 25 14:47:45 2025";
"Main: Fri Sep 26 14:29:19 2025";
// original file: Text/Geometry/Lseries.text, line: 3288
// Example: H139E42 ()
print "Example: H139E42";
ei := GetEchoInput();
SetEchoInput(true);
P<x> := PolynomialRing(Integers());
C := HyperellipticCurve([x^5+x^4,x^3+x+1]); C;
Abs(Discriminant(C));
assert $1 eq 169;
Factorization(Integers()!$1);
A<X,Y> := AffineSpace(GF(13,1),2);
C13 := Curve(A,Equation(AffinePatch(C,1)));
GeometricGenus(C), GeometricGenus(C13);
SingularPoints(C13);
p := $1[1]; IsNode(p), IsCusp(p);
C13A := Translation(C13,p)(C13);
C13B := Blowup(C13A); C13B;
E := EllipticCurve(ProjectiveClosure(C13B));
EulerFactor(E);
J := Jacobian(C);
loc := func<p,d|p eq 13 select EulerFactor(E) else EulerFactor(J, GF(p,1))>;
L := LSeries(2,[0,0,1,1],13^2,loc);
CFENew(L);
Evaluate(L,1);
Evaluate(L,2);
LC:=LSeries(C);
CFENew(LC);
Evaluate(LC,1);
Evaluate(LC,2);
SetEchoInput(ei);
