Incorrect Arithmetic on Jacobians of Hyperelliptic Curves

[zlscherr]

The following code:

R.<x> = QQ[]
f = 144*x^6 - 240*x^5 + 148*x^4 + 16*x^3 - 16*x^2 - 4*x + 1
H = HyperellipticCurve(f)
J = Jacobian(H)
P = J(H(0,1))-J(H(0,-1))
(5*P).is_zero()

seems to suggest that P is a torsion point with order 5. However, the same code in Magma

R<x> := PolynomialRing(Rationals());
f := 144*x^6 - 240*x^5 + 148*x^4 + 16*x^3 - 16*x^2 - 4*x + 1;
H := HyperellipticCurve(f);
J := Jacobian(H);
P := H![0,1] - H![0,-1];
IsZero(5*P);

suggests that P does not have order 5, and in fact Magma says that J has trivial torsion subgroup.

I have confirmed that P does not have order 5, and I have reason to believe that P is not a torsion point at all.

There is some brief discussion about this issue at https://groups.google.com/g/sage-support/c/j1Y9yuu-VuE

Component: algebraic geometry

Issue created by migration from https://trac.sagemath.org/ticket/32024