#5153: bug in simon_two_descent for elliptic curves
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Reporter: was | Owner:
Type: defect | Status: needs_review
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:
u/wuthrich/ticket/5153 | c3c480d23c265ddb93f8f58ab79233dcfe8ea0fa
Dependencies: #13593 | Stopgaps:
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Description changed by cremona:
Old description:
> 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.
New description:
[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.
--
--
Ticket URL: <http://trac.sagemath.org/ticket/5153#comment:20>
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