#5153: bug in simon_two_descent for elliptic curves
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Reporter: was | Owner:
Type: defect | Status: new
Priority: major | Milestone: sage-6.1
Component: elliptic curves | Resolution:
Keywords: simon_two_descent | Merged in:
Authors: Chris Wuthrich | Reviewers:
Report Upstream: N/A | Work issues:
Branch: | Commit:
Dependencies: #13593 | Stopgaps:
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Changes (by {'newvalue': u'Chris Wuthrich', 'oldvalue': ''}):
* dependencies: => #13593
* author: => Chris Wuthrich
Comment:
The actual issue reported to fix here, seemed first to me just a question
of rewording the documentation. But then I realised that there is a bug,
quite hidden, but unpleasant, linked to ticket #11372.
So we want simon_two_descent (over the rationals of number fields) to
return three things
* A proven lower bound for the rank
* The rank of the 2-Selmer group (this is an upper bound but not sharp in
general)
* A list of points.
I propose that the list of points is a list of points of infinite order.
So I filter out the ones that are of order 2 in the list that the script
returns. However they are not lin. indep. This was already done over
number fields in #13593. So here I modify the function over rationals.
Over Q, this function then also saturates these points and, if there are
sufficiently many, sets them for {{{E.gens()}}}.
That is what my proposed changes in the forthcoming commit will do.
Now, there are related issues, but they don't belong to this ticket
really. The curve 438e1 gives the wrong 2-Selmer and that is #10735. The
fact that we don't saturate over number field should not belong to this
ticket. One should open a new one for this. Also the script is outdated
(see #11005) and has plenty of other issues (#11041).
The bug introduced by #11372: In the example in the documentation, the
only point found is of order 2, while the second descent concludes that
the rank is 1. The result shown in the documentation were in fact from
mwrank not from simon_two_descent.
--
Ticket URL: <http://trac.sagemath.org/ticket/5153#comment:16>
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