"Source: Text/Geometry/CrvHyp.text";
"Line: 2346";
"Date: Fri Sep 26 09:12:34 2025";
"Main: Fri Sep 26 14:29:19 2025";
// original file: Text/Geometry/CrvHyp.text, line: 2346
// Example: H137E15 ()
print "Example: H137E15";
ei := GetEchoInput();
SetEchoInput(true);
_<x> := PolynomialRing(Rationals());
C := HyperellipticCurve(x^6-6);
J := Jacobian(C);
pt := J![x^2-2, x];
pt;  // What is pt? 
Parent(pt);  // Where does pt live? 
pt eq J!0;  // Is pt equal to 0 on J?
assert not $1;
Order(pt);
assert $1 eq 0;
P<X,Y,Z> := CoordinateRing(Ambient(C));
D := Divisor(C, ideal<P | X^2-2*Z^2, Y-X*Z^2> );
pt1 := J!D;
pt eq pt1;
assert $1;
SetEchoInput(ei);
