#5674: [with patch, needs review] Enhanced handling of elliptic curve twists
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Reporter: cremona | Owner: was
Type: enhancement | Status: new
Priority: minor | Milestone: sage-3.4.1
Component: number theory | Keywords: elliptic curve twist
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The patch does the following related things:
1. Implements in ell_generic functions is_quadratic_twist(),
is_quartic_twist(), is_sextic_twist(), which detect twists between curves
(returning the appropriate twisting paramenter)
2. Deprecates the EllipticCurve(j) constructor, replacing it with
EllipticCurve_from_j(j). Over Q this gives the minimal twist, i.e. a
curve with the correct j and minimal conductor.
3. Rewrites the function minimal_quadratic_twist() introduced in #4667
to use the previous function, with extra work in case j=0, 1728 since we
need the minimal __quadratic__ twist, not the minimal twist.
There is likely to be a necessary change to documentation (pages 38 and 39
of the tutorial) which have not yet been made.
The patch is based on 3.4.1.alpha0 + patches at #4667.
I have tested all files in sage/schemes/elliptic_curves. There are two
failures in sha_tate which I do not understand, so I am posting the patch
anyway.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/5674>
Sage <http://sagemath.org/>
Sage - Open Source Mathematical Software: Building the Car Instead of
Reinventing the Wheel
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