"Source: Text/Geometry/Crv.text";
"Line: 3283";
"Date: Thu Sep 25 14:47:45 2025";
"Main: Fri Sep 26 14:29:19 2025";
// original file: Text/Geometry/Crv.text, line: 3283
// Example: H124E20 ()
print "Example: H124E20";
ei := GetEchoInput();
SetEchoInput(true);
SetSeed(1);
k := GF(7^2);
A<x,y> := AffineSpace(k,2);
C := ProjectiveClosure(Curve(A,y^4-x^7+x));
G := AutomorphismGroup(C);
Gp,rep := PermutationRepresentation(G);
Gp;
[Order(G.i) : i in [1..Ngens(G)]];
Z := Centre(Gp); Z;
(Z.1)@@rep;
Gp1 := quo<Gp|Z>;
boo := IsIsomorphic(Gp1,PGL(2,GF(7)));
boo;
assert $1;
// Find the representation on the 176 Weierstrass places.
// Only need the action of the generators of Gp (or G)
wpls := WeierstrassPlaces(C);
wpls_perms := [[Index(wpls,g(w)) : w in wpls]: g in Generators(G)];
G_wpls := SymmetricGroup(#wpls);
weier_rep := hom<Gp->G_wpls|[G_wpls!p : p in wpls_perms]>;
//Check that its faithful
K := Kernel(weier_rep);
#K;
assert $1 eq 1;
SetEchoInput(ei);
