Test failure with elliptic point addition

[user202729]

CI: https://github.com/sagemath/sage/actions/runs/12462007486/job/34782318635

sage -t --warn-long 5.0 --random-seed=48801491517978841838174003125576793861 src/sage/schemes/elliptic_curves/ell_point.py
**********************************************************************
File "src/sage/schemes/elliptic_curves/ell_point.py", line 277, in sage.schemes.elliptic_curves.ell_point.?._add_
Failed example:
    for d in N.divisors():
        if d > 1:
            assert R.change_ring(Zmod(d)) == P.change_ring(Zmod(d)) + Q.change_ring(Zmod(d))
Exception raised:
    Traceback (most recent call last):
      File "/home/runner/work/sage/sage/src/sage/doctest/forker.py", line 716, in _run
        self.compile_and_execute(example, compiler, test.globs)
      File "/home/runner/work/sage/sage/src/sage/doctest/forker.py", line 1137, in compile_and_execute
        exec(compiled, globs)
      File "<doctest sage.schemes.elliptic_curves.ell_point.?._add_[14]>", line 3, in <module>
        assert R.change_ring(Zmod(d)) == P.change_ring(Zmod(d)) + Q.change_ring(Zmod(d))
    AssertionError
**********************************************************************
1 item had failures:
   1 of  34 in sage.schemes.elliptic_curves.ell_point.?._add_
    [1025 tests, 1 failure, 16.38s wall]

Looks like it's in the code touched by #39036 . @yyyyx4 ?

Environment

• OS: CI
• Sage Version: latest develop

Checklist

• I have searched the existing issues for a bug report that matches the one I want to file, without success.
• I have read the documentation and troubleshoot guide

[S17A05]

Here is a simplified version of what fails (simplified from the same failure for random_seed = 312749927201941374195931348514437892724):

sage: E = EllipticCurve(Zmod(4), [2, 2, 3, 3, 3])
sage: P = E(2,1,0)
sage: Q = E(0,1,0)
sage: R = P + Q
sage: R == P
False

[vincentmacri]

Here is a simplified version of what fails (simplified from the same failure for random_seed = 312749927201941374195931348514437892724):

sage: E = EllipticCurve(Zmod(4), [2, 2, 3, 3, 3])
sage: P = E(2,1,0)
sage: Q = E(0,1,0)
sage: R = P + Q
sage: R == P
False

This also gives False in Sage 10.5, which released before #39036 was merged into the develop branch. So I don't think #39036 broke anything, but it may have touched code that already had a bug or maybe added tests that cover this case.