#11474: Elliptic curves should be unique parent structures
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Reporter: SimonKing | Owner: cremona
Type: defect | Status: needs_info
Priority: major | Milestone: sage-6.2
Component: elliptic curves | Resolution:
Keywords: unique parent | Merged in:
Authors: Simon King | Reviewers:
Report Upstream: N/A | Work issues:
Branch: | Commit:
Dependencies: | Stopgaps:
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Comment (by cremona):
I also like the idea of having a separate object for the group of points.
Then for an elliptic curve E defined over K one could have different point
groups for E(K) and for E(L) for extensions L of K. Magma did that a few
years ago and it was very convenient. I have not thought at all about how
to implement it though.
About isogeny (c)domains it is not so clear to me. An isogeny is both a
map from one curve to another (preserving the base point), and also a
group homomorphism. If we are going to separate out the curve E from its
group(s) E(K), E(L), then should we not keep these separate for isogenies
too?
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Ticket URL: <http://trac.sagemath.org/ticket/11474#comment:11>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica,
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