Working on ticket #7096, I realised that there are many functionalities concerning morphisms of elliptic curves that are not implemented or implemented badly.

See also #6887, and #7262.

Here is a wish-list:

• General isogenies, not only cyclic ones should be implemented.
  Possibly this could be done in a clever way, by having it
  internally factored into cyclic isogenies. → composite elliptic-curve isogenies #32744
• Inseparable isogenies (e.g. Frobenii) should be possible too. → inseparable elliptic-curve isogenies #33915 (See also Retrieving the multiplication-by-p isogeny on elliptic curves over fields of characteristic p fails. #6413.)
• One should be able to compose isogenies. → Compose isogenies #16245, composite elliptic-curve isogenies #32744
• There should be an addition for isogenies with the same domain
  and codomain.
• There should be an endomorphism_ring for elliptic curves whose
  elements are isogenies.
• Similarly, automorphisms should give a group of isogenies.
• Isogenies of large prime degree ℓ can be computed in time Õ(√ℓ) using https://velusqrt.isogeny.org/ → √élu algorithm: asymptotically faster elliptic-curve isogenies #34303
• Is there a way of constructing a (not necessarily normalized)
  isogeny knowing the degree and the domain and codomain?

CC: @sagetrac-weigandt @pjbruin @sagetrac-sbesnier @yyyyx4

Component: elliptic curves

Keywords: isogeny, isogenies, endomorphism ring

Issue created by migration from https://trac.sagemath.org/ticket/7368