#13757: The conversion from E to E.abelian_group() does not perserve group order
for elliptic curves over finite fields.
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Reporter: mderickx | Owner: joyner
Type: defect | Status: new
Priority: critical | Milestone: sage-5.11
Component: group theory | Resolution:
Keywords: | Merged in:
Authors: | Reviewers:
Report Upstream: N/A | Work issues:
Branch: | Dependencies:
Stopgaps: |
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Comment (by chapoton):
trying to look at the problem, here is part of the problem maybe:
{{{
sage: p=709
sage: E2=EllipticCurve(GF(p),[606,486])
sage: ab=E2.abelian_group()
sage: ab((2,0))
(11 : 229 : 1)
sage: ab(vector((2,0)))
(409 : 94 : 1)
sage: ab((0,2))
(409 : 94 : 1)
sage: ab(vector((0,2)))
(11 : 229 : 1)
}}}
so there is a strange transposition of the arguments.
'''But''' there is also something random happening in the choice of the
embedding:
{{{
sage: ab=EllipticCurve(GF(p),[606,486]).abelian_group()
sage: ab(vector((2,0)))
(534 : 340 : 1)
sage: ab=EllipticCurve(GF(p),[606,486]).abelian_group()
sage: ab(vector((2,0)))
(350 : 542 : 1)
}}}
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Ticket URL: <http://trac.sagemath.org/ticket/13757#comment:5>
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