#10735: Simon 2-descent may not check for solubility at archimedean places.
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Reporter: weigandt | Owner: cremona
Type: PLEASE CHANGE | Status: new
Priority: major | Milestone: sage-4.7
Component: elliptic curves | Keywords: simon_two_descent
Author: | Upstream: N/A
Reviewer: | Merged:
Work_issues: |
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Given an elliptic curve E the method E.simon_two_descent() returns an
ordered triple. This consists of a lower bound on the Mordell-Weil rank of
E, an integer which is supposed to be the F_2 dimension of the 2-Selmer
group of E, and list of points, generating the part of the Mordell-Weil
group that has been found.
Sometimes the second entry is larger than the actual 2-Selmer rank as
computed by mwrank, and predicted by BSD. The first curve I know of for
which this happens is the elliptic curve '438e1' from Cremona's tables.
This curve definitely possesses 2-covers which are everywhere locally
soluble EXCEPT at that infinite place. These probably explain the
discrepancy.
{{{
sage: E=EllipticCurve('438e1')
sage: E.simon_two_descent()
(0, 3, [(13 : -7 : 1)])
sage: E.selmer_rank() #uses mwrank
1
sage: E.sha().an()
1
}}}
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/10735>
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