"Source: Text/Commut/AlgAff.text";
"Line: 595";
"Date: Thu Sep 25 14:47:46 2025";
"Main: Fri Sep 26 14:29:19 2025";
// original file: Text/Commut/AlgAff.text, line: 595
// Example: H118E4 ()
print "Example: H118E4";
ei := GetEchoInput();
SetEchoInput(true);
Q := RationalField();
F<x, a, b> := FunctionField(Q, 3);
A<y> := AffineAlgebra<F, y | y^2 - (x^3 + a*x + b)>;
IsField(A);
assert $1;
y^2;
y^-1;
E := EllipticCurve([A | a, b]);
E;
p := E ! [x, y];                                                             
p;
q := 2*p;
q;
c := LeadingCoefficient(q[2]);
Denominator(c);
Factorization($1);
SetEchoInput(ei);
