#16743: Extend IsogenyClass_EC to work over number fields
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Reporter: cremona | Owner:
Type: enhancement | Status: new
Priority: major | Milestone: sage-6.3
Component: elliptic curves | Keywords: isogeny class
Merged in: | Authors: John Cremona
Reviewers: | Report Upstream: N/A
Work issues: | Branch:
Commit: | Dependencies:
Stopgaps: |
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If E is an elliptic curve over QQ then E.isogeny_class() is an object of
type (class) IsogenyClass_EC which which one can work in a nice way. This
should be extended to number fields. Two reasons why this is notn-trivial
(and hence was not done at the same time as over QQ): (1) bounding the
possible primes degrees of isogenies; (2) handling curves with CM. For
(1), the module {{{gal_reps_number_field}}} does what is required. For
(2) new code has been written.
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Ticket URL: <http://trac.sagemath.org/ticket/16743>
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