#5153: bug in simon_two_descent for elliptic curves
---------------------------+------------------------------------------------
Reporter: was | Owner: was
Type: defect | Status: new
Priority: major | Milestone: sage-3.3
Component: number theory | Keywords:
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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/sage_trac/ticket/5153>
Sage <http://sagemath.org/>
Sage - Open Source Mathematical Software: Building the Car Instead of
Reinventing the Wheel
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