"Source: Text/Geometry/SmallModCrv.text";
"Line: 363";
"Date: Thu Sep 25 14:47:45 2025";
"Main: Fri Sep 26 14:29:19 2025";
// original file: Text/Geometry/SmallModCrv.text, line: 363
// Example: H141E3 ()
print "Example: H141E3";
ei := GetEchoInput();
SetEchoInput(true);
C := SmallModularCurve(37);
C;
AtkinLehnerInvolution(C,37,37);
ExtraAutomorphism(C,37,1); //the hyperelliptic involution
C<x,y,z> := SmallModularCurve(48);
C;
AtkinLehnerInvolution(C,48,3);
Type($1);
G := AutomorphismGroupOverQ(C,48);
#G;
assert $1 eq 16;
AtkinLehnerInvolution(C,48,3);
Type($1);
PermutationRepresentation(G);
// D8 X C2
K<i> := QuadraticField(-1);
CK<x,y,z> := SmallModularCurve(48,K);
G := AutomorphismGroupOverCyclotomicExtension(CK,48,4);
#G;
assert $1 eq 48;
SrAutomorphism(CK,48,4,i); // z -> z+(1/4)
SetEchoInput(ei);
