Update the rank function of elliptic curves to use pari

[chriswuthrich]

Is there an existing issue for this?

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

Problem Description

Pari has now a very good in-built algorithm to determine the rank and a set of generators of the Mordell-Weil group of elliptic curves over the rational. It is, as far as I understand, a port of Denis Simon's script ellQ.gp. It performs a 2-descent and uses the Cassels Tate pairing to conclude the rank in many cases - when Sha has no 4-torsion elements.

Proposed Solution

The function rank should allow the algorithm to be pari. The simon_two_descent over Q should be deprecated. Whether or not to replace mwrank as the default algorithm might be decided later. I have no experience which is better for what type of curves.

Alternatives Considered

None.

Additional Information

I am working on this as will put a PR forward soon.