elliptic curve canonical height bug for non-minimal models

[cremona]

For canonical heights of points on elliptic curves defined over QQ, we call the pari function ellheight(), BUT that function only gives the correct value for global minimal models! (At primes where the model is not minimal the local component is wrong).

Here is an example to show this:

sage: E = EllipticCurve([-5580472329446114952805505804593498080000,
....:           -157339733785368110382973689903536054787700497223306368000000])
sage: P3=E([204885147732879546487576840131729064308289385547094673627174585676211859152978311600/23625501907057948132262217188983681204856907657753178415430361,92736254270288706000052529616433462503893110244786566575440613880920567197984949809570153263207165494624214991751142500000000/114834283590033957142081201488956527887145361353994063932282392800295014255070987824900081891])
sage: P3.height()
157.086024926474
sage: 4*(P3.height())-(2*P3).height() # should == 0
-1.38629436111989

while on the minimal model:

sage: Emin = E.minimal_model()
sage: urst = E.isomorphism_to(Emin)
sage: 4*urst(P3).height()-urst(2*P3).height()
0.000000000000000

The cure is to compute the minimal model and transfer the point there before computing the height, as illustrated above. (Of course, pari could do that too, but this behaviour has been tolerated by pari users for many years!)

[cremona]

Applies to 4.3.3

[cremona]

The patch implements the cure. I did not bother putting in a test for minimality of the original model, since all that does is to compute the minimal model anyway and compare! Also, the minimal model is cached, so that would only be done once. We do not cache the isomorphism to the minimal model, but that is cheap to compute.

[wuthrich]

Looks fine to me. All tests pass.