#4900: [with patch, not ready for review] New BSGS point counting on elliptic
curves over finite fields
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Reporter: cremona | Owner: was
Type: enhancement | Status: new
Priority: minor | Milestone: sage-3.4
Component: number theory | Resolution:
Keywords: elliptic curves finite fields |
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Comment (by cremona):
Testing has revealed a bug (an embarrassing one in code of mine) in
_p_primary_torsion_basis() as exemplified here:
{{{
sage: p=10^60+3201
sage: K=GF(p)
sage: a=804515977734860566494239770982282063895480484302363715494873
sage: b=584772221603632866665682322899297141793188252000674256662071
sage: E=EllipticCurve(K,[0,a,0,b,0])
sage: E.cardinality().factor()
2^17 * 13115567671 * 581705246972988608203110387504181554514650287
sage: E._p_primary_torsion_basis(2)
[[(656068448840236768725810484116830935925716002501543862440466 :
324360550482744921974063628110267202720852104214117741680354 : 1),
2],
[(21059802536298599082171845328893691100757301985761775129713 : 0 : 1),
1]]
}}}
Here the 2-sylow subgroup has structure 2^16 * 2 but
E._p_primary_torsion_basis(2) only gives 2^2*2^1. I know what the problem
is and am working out how to fix it.
NB This function is called in ell_torsion.py in computing torsion groups
over number fields, which is rather likely to give wrong answers (though
not over Q where pari is used ;)) until this is fixed. So I will make
this a separate ticket marked "major defect"!
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/4900#comment:5>
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