#5153: bug in simon_two_descent for elliptic curves
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Reporter: was | Owner:
Type: defect | Status: new
Priority: major | Milestone: sage-4.3.2
Component: elliptic curves | Keywords:
Author: | Upstream: N/A
Reviewer: | Merged:
Work_issues: |
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Comment(by cremona):
Replying to [comment:8 nbruin]:
> Replying to [comment:6 was]:
> > Another excellent trick I learned from Cremona for getting
independence is to use *homomorphic images*. I.e., reduce to a direct sum
of groups of points over a finite field (all tensored with F_p, with p
coprime to torsion). Then the rank of the group you have is a bounded
below by the dimension of the image.
>
> And those same images can also yield information on p-saturation of the
group generated by the given points inside the Mordell-Weil group
> (just as an independence proof via 2-Selmer groups also gives
2-saturation)
> This starts to sound like a nice student project.
It was! The thesis of my student Martin Prickett was about saturating
Mordell-Weil groups this way, and he implemented it in Magma. See
http://www.warwick.ac.uk/staff/J.E.Cremona/theses/index.html . I have
Martin's magma code but it is not easy to use. Hence the project still
remains, namely to rewrite all that.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/5153#comment:9>
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