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10735 Simon 2-descent only returns an upper bound on the 2-Selmer rank Jamie Weigandt John Cremona "[See #15608 for a list of open simon_two_descent tickets]
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.
{{{
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
}}}
The explanation for this is that `E.simon_two_descent()`, unlike Cremona's `mwrank`, does not do a second descent and therefore only determines an upper bound on the 2-Selmer rank." defect closed minor sage-6.2 elliptic curves fixed simon_two_descent John Cremona William Stein Robert Miller Peter Bruin Chris Wuthrich Reported upstream. No feedback yet. 732191df41bcc093230a41e747514bcdef46fd40 732191df41bcc093230a41e747514bcdef46fd40 #11005, #9322