"Source: Text/Ring/Char.text";
"Line: 1387";
"Date: Fri Sep 26 12:10:11 2025";
"Main: Fri Sep 26 14:29:19 2025";
// original file: Text/Ring/Char.text, line: 1387
// Example: H43E17 ()
print "Example: H43E17";
ei := GetEchoInput();
SetEchoInput(true);
E := EllipticCurve("49a"); // cm by -7
G := Grossencharacter(QuadraticTwist(E,5*29));
Conductor(QuadraticTwist(EllipticCurve(G),5*29));
//
E := EllipticCurve([2^2 * 3 * 5^3 * 7 * 11^2 * 13^3, 0]);
G := Grossencharacter(E);
assert IsIsogenous(E,EllipticCurve(G));
//
E := EllipticCurve([0, 2 * 3^5 * 5^3 * 7^4 * 11^2 * 13^5]);
G := Grossencharacter(E);
assert IsIsogenous(E,EllipticCurve(G));
//
K := QuadraticField(-163);
p := Factorization(163*Integers(K))[1][1];
psi := HeckeCharacterGroup(p).0;
G := Grossencharacter(psi,[[1,0]]);
E := EllipticCurve(G);
b, cm := HasComplexMultiplication(E);
assert b; assert cm eq -163;
Conductor(E);
SetEchoInput(ei);
