#16743: Extend IsogenyClass_EC to work over number fields
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Reporter: cremona | Owner:
Type: enhancement | Status: needs_review
Priority: major | Milestone: sage-6.4
Component: elliptic curves | Resolution:
Keywords: isogeny class | Merged in:
Authors: John Cremona | Reviewers:
Report Upstream: N/A | Work issues:
Branch: | Commit:
u/cremona/ticket/16743 | e54356510afe82102e9dc66a08683476f0ab7d7b
Dependencies: #11327, #16764, | Stopgaps:
#16806 |
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Changes (by cremona):
* dependencies: #11327, #16764 => #11327, #16764, #16806
Comment:
I added #16806 as a dependency: that ticket concerns Gal Reps over number
fields and provides an isogeny_bound() function (method) for those, to
which I have added a function reducible_primes() for compatibility with
the class for Gal Reps over QQ, which takes the primes in isogeny_bounds()
and actually checks if there are isogenies of those degrees. At the same
time I simplified the reducible_primes() method for the Gap Reps class
over Q so that it does not compute the whole isogeny class but is slightly
more clever, since apart from 2,3,5,7,13 one can tell by looking at a list
of special j-invariants.
TODO (but not on this ticket): unify the two GaloisRepresentation
classes! Perhaps there should be a base class which is rather abstract
but defines the interface, with child classes for Galois Reps attached to
(1) elliptic curves over number fields, (1') same over QQ, (2) modular
forms, etc etc.
--
Ticket URL: <http://trac.sagemath.org/ticket/16743#comment:6>
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