#16942: Construct isogenies graph in elliptic curves
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Reporter: sbesnier | Owner:
Type: enhancement | Status: needs_review
Priority: major | Milestone: sage-6.8
Component: elliptic curves | Resolution:
Keywords: | Merged in:
Authors: sbesnier | Reviewers:
Report Upstream: N/A | Work issues:
Branch: | Commit:
public/ticket/16942 | e5b72e8afdaaf726e5191fa5db86ac43994ffe72
Dependencies: | Stopgaps:
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Comment (by pbruin):
Replying to [comment:16 cremona]:
> Using the modular polynomial is one way to do it. You could also make
use of the existing method E.isogenies_prime_degree(). But in fact as it
stands this function is not a method of elliptic curves at all, the input
is really just and element j of a finite field. So surely there could be
a separate function (not a class method) with input an element of F_q and
a prime l, and output a graph on some subset of Fq, and then the elliptic
curve class method would call that on its j-invariant.
Actually, the method should perhaps even (optionally?) return the graph of
actual elliptic curves instead of the graph of ''j''-invariants. It is
likely that the user will want to know exactly which curves over the base
field appear in the isogeny graph; if you just have the ''j''-invariants,
you only know them up to twist.
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Ticket URL: <http://trac.sagemath.org/ticket/16942#comment:17>
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