#7096: bug in dual isogeny computation
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Reporter: cremona | Owner:
Type: defect | Status: new
Priority: major | Milestone: sage-4.1.3
Component: elliptic curves | Keywords: elliptic curve isogeny
Work_issues: | Author:
Reviewer: | Merged:
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Comment(by wuthrich):
Yet another, bigger problem with dual() : Say E -> E' is an isogeny of
degree d, then all the algorithm does is creating an isogeny E' -> E of
degree d. This does not guarantee that it is the dual; it could be the
dual composed with an automorphism, like [-1]. This probably happens quite
often as it uses {{{WeierstrassIsomorphism(E,E')}}}. This returns one of
the isomorphisms without any control of it, hence often the sign will be
wrong.
The function dual definitely needs a lot of work.
Now, the actual bug reported in this ticket is not in dual but occurs as
{{{
E1 = EllipticCurve(GF(1013),[1,-1,0,288,19])
E2 = EllipticCurve(GF(1013),[7,970,0,363,464])
EllipticCurveIsogeny(E1,None,E2,7)
}}}
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Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/7096#comment:3>
Sage <http://www.sagemath.org>
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