#3416: Weierstrass form and Jacobian for cubics and certain other genus-one
curves
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Reporter: moretti |
Owner: was
Type: enhancement |
Status: needs_review
Priority: major |
Milestone: sage-5.7
Component: elliptic curves |
Resolution:
Keywords: nagell, weierstrass, cubic, elliptic curves, editor_wstein |
Work issues:
Report Upstream: N/A |
Reviewers: John Cremona, Marco Streng, Nils Bruin
Authors: Niels Duif, Volker Braun |
Merged in:
Dependencies: #12553, #13084, #13458 |
Stopgaps:
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Comment (by cremona):
Replying to [comment:62 was]:
> I not sure I agree with the assertion that people/algorithms will always
compute the morphism. There are alternative algorithms for computing the
jacobian of a genus 1 curve that give the Jacobian without giving the
morphism -- one involves computing the a_p and doing a search for curves
with those a_p, and another involves "Fermionic Fock Spaces" (I think).
>
A basic (plane cubic) --> (Jacobian elliptic curve) function could be very
much simpler, you just compute the classical S, T invariants as in Salmon
and these are the c4,c6 (up to constant factors) of the Jacobian.
My guess is that most of the use this function will get will be from
people who want to find rational points on the elliptic curve and map them
back to "their" cubic, so we should make this easy and not requiring a PhD
to understand.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/3416#comment:67>
Sage <http://www.sagemath.org>
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