id,summary,reporter,owner,description,type,status,priority,milestone,component,resolution,keywords,cc,merged,author,reviewer,upstream,work_issues,branch,commit,dependencies,stopgaps
5153,bug in simon_two_descent for elliptic curves,was,,"[See #15608 for a list of open simon_two_descent tickets]
We have
{{{
sage: E = EllipticCurve('65a1')
sage: G = E.change_ring(QuadraticField(-56,'a'))
sage: G.simon_two_descent()
(3, 4, [(-9/4 : -3/8*a + 9/8 : 1), (-8/7 : -1/49*a + 4/7 : 1), (1 : 0 : 1),
(-6/25*a - 47/25 : 36/125*a - 368/125 : 1), (1/4 : 1/16*a - 1/8 : 1)])
}}}
The documentation for simon_two_descent says that the output of Simon 2-descent is
{{{
OUTPUT:
integer -- ""probably"" the rank of self
integer -- the 2-rank of the Selmer group
list -- list of independent points on the curve.
}}}
Our curve does have rank 3, but the output list above contains *five* points, so they can't be independent!
Our curve has torsion of order 2, so E(K)/2 E(K) has rank four, so the 3 and four output by Simon descent are right. The only problem is the list, which has too many points in it.
Maybe this is simply a documentation issue, and the docs for simon_two_descent should be changed to say that list is a list of points that *generate* a subgroup of the MW group of rank r, where r is the first number output by simon_two_descent. ",defect,closed,major,sage-6.1,elliptic curves,fixed,simon_two_descent,,,Chris Wuthrich,John Cremona,N/A,,u/wuthrich/ticket/5153,ad2ced2b14236b9881121c47eb6ee0f20144d5dd,#13593,