#13100: EllipticCurve_from_j (over QQ) should not always compute minimal twist
-----------------------------------------------+----------------------------
Reporter: cremona | Owner: cremona
Type: enhancement | Status: needs_work
Priority: minor | Milestone: sage-5.2
Component: elliptic curves | Resolution:
Keywords: elliptic curve construction | Work issues:
Report Upstream: N/A | Reviewers: David Roe
Authors: John Cremona | Merged in:
Dependencies: #13109 | Stopgaps:
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Changes (by jhpalmieri):
* cc: vbraun (added)
* status: positive_review => needs_work
* dependencies: => #13109
Old description:
> Currently when constructing an elliptic curve from a j-invariant over QQ,
> a curve with minimal conductor is created (the so-called "minimal
> twist"). This could be expensive since it involves factoring j and
> j-1728, so an option to *not* find the minimal twist should be allowed,
> with the current behaviour as default for backwards compatibility.
>
> For example:
> {{{
> sage: EllipticCurve(j=2^256+1)
> }}}
> currently triggers factorization of {{{F_8}}} (which is quite quick) but
> also {{{F_8-1728}}} (which is not).
New description:
Currently when constructing an elliptic curve from a j-invariant over QQ,
a curve with minimal conductor is created (the so-called "minimal twist").
This could be expensive since it involves factoring j and j-1728, so an
option to *not* find the minimal twist should be allowed, with the current
behaviour as default for backwards compatibility.
For example:
{{{
sage: EllipticCurve(j=2^256+1)
}}}
currently triggers factorization of {{{F_8}}} (which is quite quick) but
also {{{F_8-1728}}} (which is not).
Apply [attachment:trac13100-elliptic.patch] and [attachment:trac13100
-rebase-on-13109.patch].
--
Comment:
This needs to be rebased to #13109. Patch attached, and I've cc'ed Volker,
who should be able to review it quickly.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/13100#comment:7>
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