#10832: bug in simon_two_descent()
-------------------------------+--------------------------------------------
Reporter: cremona | Owner: cremona
Type: defect | Status: positive_review
Priority: major | Milestone: sage-4.7
Component: elliptic curves | Keywords:
Author: John Cremona | Upstream: N/A
Reviewer: Chris Wuthrich | Merged:
Work_issues: |
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Old description:
> This is similar to, but different to, #10745.
> {{{
> sage: E = EllipticCurve([1,0,0,-6664,86543])
> sage: E.simon_two_descent()
> (2, 3, [(173 : 1943 : 1), (-73 : -394 : 1), (323/4 : 1891/8 : 1)])
> sage: E.rank()
> 3
> sage: E.gens()
> [(-73 : -394 : 1), (323/4 : 1891/8 : 1), (173 : 1943 : 1)]
> }}}
> This is _wrong_. The rank is 2; the first point in the output has order
> 4. The mistake is that in discarding torsion points from the generators
> of E/2E, only points of exact order 2 are omitted!
>
> Apply trac_10872.patch
New description:
This is similar to, but different to, #10745.
{{{
sage: E = EllipticCurve([1,0,0,-6664,86543])
sage: E.simon_two_descent()
(2, 3, [(173 : 1943 : 1), (-73 : -394 : 1), (323/4 : 1891/8 : 1)])
sage: E.rank()
3
sage: E.gens()
[(-73 : -394 : 1), (323/4 : 1891/8 : 1), (173 : 1943 : 1)]
}}}
This is _wrong_. The rank is 2; the first point in the output has order
4. The mistake is that in discarding torsion points from the generators
of E/2E, only points of exact order 2 are omitted!
Apply trac_10872-descent.v3.patch
--
Comment(by kini):
Whoops, comment for the patchbot fixed
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/10832#comment:12>
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