"Source: Text/Geometry/CrvHyp.text";
"Line: 8043";
"Date: Fri Sep 26 09:12:34 2025";
"Main: Fri Sep 26 14:29:19 2025";
// original file: Text/Geometry/CrvHyp.text, line: 8043
// Example: H137E49 ()
print "Example: H137E49";
ei := GetEchoInput();
SetEchoInput(true);
P<x> := PolynomialRing(GF(3));
C1 := HyperellipticCurve(x^3+x);
G1, m1 := AutomorphismGroup(C1);
#G1;
[ m1(g) : g in G1 ];
f := m1(G1.3);
f;
g := Inverse(f);
g;
f eq g;
assert $1;
K<t> := GF(3,2);
C2 := BaseExtend(C1, K);
G2, m2 := AutomorphismGroup(C2);
#G2;
assert $1 eq 48;
O := C2![1,0,0];
auts := [ m2(g) : g in G2 ];
[ f : f in auts | O@f eq O ];
#$1;
assert $1 eq 12;
E1 := EllipticCurve(C1);
A1 := AbelianGroup(E1);
A1;
SetEchoInput(ei);
