#16743: Extend IsogenyClass_EC to work over number fields
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Reporter: cremona | Owner:
Type: enhancement | Status: needs_work
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 | 06d9eb2226151a35bb2d3779e5309f4d066af8ca
Dependencies: #11327, #16764, | Stopgaps:
#16806 |
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Comment (by cremona):
Replying to [comment:20 jdemeyer]:
> Replying to [comment:15 cremona]:
> > Background: I am making databases of things like elliptic curves over
number fields, and am having to be very explicit indeed about how various
objects are ordered.
> Before worrying about ideals, first consider the ring O_K. Since the HNF
is essentially coordinates w.r.t. to a basis, the chosen Z-basis of O_K
also matters a lot. For quadratic fields, one can easily define a
canonical basis, but in higher degree that gets a lot more tricky.
Absolutely right! We have had alot of such discussions with the LMFDB
project. Personally, I will stick to quadratic fields at least as far as
making databases of elliptic curves is concerned (though the LMFDB does
have some over the cubic field of discriminant -23).....
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Ticket URL: <http://trac.sagemath.org/ticket/16743#comment:21>
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