#14060: Improve minimal_quadratic_twist()
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Reporter: cremona | Owner: cremona
Type: defect | Status: new
Priority: major | Milestone: sage-6.1
Component: elliptic curves | Resolution:
Keywords: pari precision | Merged in:
Authors: | Reviewers:
Report Upstream: N/A | Work issues:
Branch: | Commit:
Dependencies: | Stopgaps:
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Old description:
> This fails on a 32-bit machine (Sage-5.6):
> {{{
> sage: EllipticCurve([0, -1, 0, -360796668980,
> 83414685883377400]).minimal_quadratic_twist()
> }}}
> because it results in pari_curve() being called on some curves with no
> attempt to catch insufficient precision.
>
> Two things needs fixing: (1) Making sure that all calls to pari_curve()
> deal with this precision issue properly; (2) a better implementation of
> minimal_quadratic_twist(), for example if the conductor is square-free
> then there is no need to do so much rwork as is currently done.
> Additionally, when j(E)=0 or 1728 the curve returned is a minimal twist,
> but not necessarily a quadratic twist, so the documentation (or function
> name, or something) needs correcting.
New description:
We need a better implementation of minimal_quadratic_twist(), for example
if the conductor is square-free then there is no need to do so much work
as is currently done. Additionally, when j(E)=0 or 1728 the curve
returned is a minimal twist, but not necessarily a quadratic twist, so the
documentation (or function name, or something) needs correcting.
--
Comment (by jdemeyer):
Precision issue is #13163.
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Ticket URL: <http://trac.sagemath.org/ticket/14060#comment:2>
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