specialized (much faster) method to compute elliptic-curve division field over finite fields

[yyyyx4]

The current general implementation of .division_field() works by constructing the splitting field of the division polynomial (and then some).

In this patch, we implement two much faster algorithms for finite base fields: One for supersingular curves, based on the fact that Frobenius acts as a scalar after taking an extension of degree O(1), and one for ordinary curves, which is due to Van Tuyl.

Example (supersingular):

sage: E = EllipticCurve(GF(419), [1,0])
sage: assert E.is_supersingular()
sage: %time E.division_field(32)

Sage 10.8: CPU times: user 6.73 s, sys: 1.96 ms, total: 6.73 s
This branch: CPU times: user 29.9 ms, sys: 1.93 ms, total: 31.8 ms

Example (ordinary):

E = EllipticCurve(GF(101), [1,1])
assert E.is_ordinary()
%time E.division_field(13)

Sage 10.8: CPU times: user 7.5 s, sys: 1.03 ms, total: 7.5 s
This branch: CPU times: user 126 ms, sys: 5.93 ms, total: 132 ms

As a byproduct, this leads to massive speedups in many other algorithms where .division_field() is used. For example:

sage: E = EllipticCurve(GF((419,2)), [1,0])
sage: i = E.automorphisms()[2]
sage: j = E.frobenius_isogeny()
sage: %time (i + 3*j).to_isogeny_chain()

Sage 10.8: CPU times: user 12.5 s, sys: 2.98 ms, total: 12.5 s
This branch: CPU times: user 461 ms, sys: 0 ns, total: 461 ms

[github-actions]

Documentation preview for this PR (built with commit be0ef19; changes) is ready! 🎉
This preview will update shortly after each push to this PR.