"Source: Text/Commut/AlgAff.text";
"Line: 594";
"Date: Tue Jun  7 22:27:15 2016";
"Main: Thu May 25 10:02:38 2023";
// original file: Text/Commut/AlgAff.text, line: 594
// Example: H115E4 ()
print "Example: H115E4";
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);
