This mathoverflow question and this asksage question raise an issue with p-adic heights. The algorithm currently assumes silently that the equation is minimal.

Here is the incorrect results pointed out in the questions. The regulator must be independent of the model used:

sage: E = EllipticCurve([-1728,-100656])
sage: E.padic_regulator(7)
3*7 + 3*7^2 + 4*7^3 + 3*7^4 + 5*7^6 + 7^8 + 3*7^9 + 5*7^11 + 7^12 + 2*7^13 + 3*7^15 + 3*7^16 + 4*7^17 + 6*7^18 + 5*7^19 + O(7^20)
sage: Emin = E.global_minimal_model()
sage: Emin.padic_regulator(7)
2*7^2 + 5*7^3 + 7^4 + 5*7^5 + 3*7^6 + 5*7^7 + 7^8 + 5*7^9 + 5*7^10 + 6*7^11 + 3*7^12 + 5*7^13 + 7^14 + 6*7^15 + 4*7^16 + 3*7^17 + 5*7^18 + 6*7^19 + O(7^20)

The problem is that the algorithm needs the points on which it evaluates the p-adic height to have good reduction in the model it works with.

One solution would be to raise a NotImplementedError.

But better, especially if one wants to generalise this to number fields where elliptic curve do not have minimal models, one should find the correct multiple to use.

Component: elliptic curves

Author: Chris Wuthrich

Branch/Commit: u/wuthrich/trac34790 @ a12a6d0

Issue created by migration from https://trac.sagemath.org/ticket/34790