Implemented order computation and identity checking for automorphisms of elliptic curves

[r98inver]

The WeierstrassIsomorphism class is also used to represent automorphisms of elliptic curves. Sometimes one is looking for a particular automorphism (say, of order 3 or 4), and this check is simplified with the .order() method for elliptic-curve automorphisms.
The is_identity() method is added for convenience.

#sd123

[grhkm21]

(Please correct me if I'm wrong!) If the elliptic curve is not over a field, e.g. over Zmod(35), and when the automorphism has order $3$ when restricted to over $E / \mathbb{F}_5$ and $4$ when restricted to over $E / \mathbb{F}_7$, then it will have order $12$ over $E / \mathbb{F}_{35}$. This can be a doctest

[grhkm21]

Just for completeness sake, here's an update. Currently it can't be a doctest since WeierstrassIsomorphism assumes the base ring is a field, which is not really necessary. However, this demonstrates the idea:

sage: E = EllipticCurve(Zmod(13 * 19), [19, 13])
....: assert E.change_ring(GF(13)).j_invariant() == 1728 # % 13
....: assert E.change_ring(GF(19)).j_invariant() == 0
....: 
....: # E.automorphisms() # this fails
....: aut_13 = E.change_ring(GF(13)).automorphisms()
....: aut_19 = E.change_ring(GF(19)).automorphisms()
....: 
....: # Since it's an isomorphism, only the *u* matters
....: import itertools
....: for phi_13, phi_19 in itertools.product(aut_13, aut_19):
....:     u = Mod(CRT([ZZ(phi_13.u), ZZ(phi_19.u)], [13, 19]), 13 * 19)
....:     order = u.multiplicative_order()
....:     if order > 6:
....:         print(phi_13, phi_19, order, sep="\n")
....:         break
....: 
Elliptic-curve endomorphism of Elliptic Curve defined by y^2 = x^3 + 6*x over Finite Field of size 13
  Via:  (u,r,s,t) = (5, 0, 0, 0)
Elliptic-curve endomorphism of Elliptic Curve defined by y^2 = x^3 + 13 over Finite Field of size 19
  Via:  (u,r,s,t) = (7, 0, 0, 0)
12

[grhkm21]

Thanks for contributing #sd123 🚀

styling issues

[grhkm21]

Hi, is there any update on this? :)

[r98inver]

Forgot to push, should be ok now

[grhkm21]

Very sorry for not spotting these earlier. After these changes it should be ready.

[grhkm21]

Looks good

[r98inver]

Thanks for the review and the suggestions!

[grhkm21]

No problem! Great work for a first contribution :D

[github-actions]

Documentation preview for this PR (built with commit aa7c27a; changes) is ready! 🎉