#7368: Further work on isogenies and endomorphisms of elliptic curves
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Reporter: wuthrich | Owner: cremona
Type: enhancement | Status: new
Priority: major | Milestone: sage-
Component: elliptic curves | wishlist
Keywords: elliptic curves, isogeny, | Resolution:
isogenies, endomorphism ring | Merged in:
Authors: | Reviewers:
Report Upstream: N/A | Work issues:
Branch: | Commit:
Dependencies: | Stopgaps:
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Description changed by sbesnier:
Old description:
> 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.
> * Non seperable isogenies, i.e. Frobenii should be there too. See
> also #6413.
> * One should be able to compose them
> * Is there a way of constructing a (not necessarily normalized)
> isogeny knowing the degree and the domain and codomain ?
> * There should be an addition for isogenies with the same domain
> and codomain.
> * There should be an endomorphism_ring for ellliptic curves whose
> elements are isogenies.
> * Similar automorphisms should give a group of isogenies.
New description:
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.
* Non seperable isogenies, i.e. Frobenii should be there too. See
also #6413.
* One should be able to compose them -> see #16245
* Is there a way of constructing a (not necessarily normalized)
isogeny knowing the degree and the domain and codomain ?
* There should be an addition for isogenies with the same domain
and codomain.
* There should be an endomorphism_ring for ellliptic curves whose
elements are isogenies.
* Similar automorphisms should give a group of isogenies.
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Ticket URL: <http://trac.sagemath.org/ticket/7368#comment:3>
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