"Source: Text/Geometry/GrpPSL2Shim.text";
"Line: 1242";
"Date: Thu Sep 25 14:47:45 2025";
"Main: Fri Sep 26 14:29:19 2025";
// original file: Text/Geometry/GrpPSL2Shim.text, line: 1242
// Example: H143E10 ()
print "Example: H143E10";
ei := GetEchoInput();
SetEchoInput(true);
SetSeed(1);
G := ArithmeticTriangleGroup(2,3,9);
O := BaseRing(G);
Z_F := BaseRing(O);
Z_K := ext<Z_F | Polynomial([3,-1,1])>;
Discriminant(Z_K);
IsMaximal(Z_K);
assert $1;
ClassNumber(AbsoluteOrder(Z_K));
assert $1 eq 3;
mu := Embed(Z_K, O);
time f, js := CMPoints(G, mu);
f;
D := Discriminant(f);
Denominator(D);        
assert $1 eq 1;
Factorization(Numerator(D));
K := AbsoluteField(NumberField(Z_K));
H := ext<K | f>;
Factorization(Discriminant(MaximalOrder(H)));
IsAbelian(GaloisGroup(H));
assert $1;
SetEchoInput(ei);
