#3416: Weierstrass form for cubics
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Reporter: moretti | Owner: was
Type: enhancement | Status: needs_work
Priority: major | Milestone: sage-4.6.1
Component: number theory | Keywords: nagell, weierstrass, cubic,
elliptic curves, editor_wstein
Author: | Upstream: N/A
Reviewer: | Merged:
Work_issues: |
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Comment(by cremona):
Replying to [comment:16 cremona]:
> See #10297 for a separate report on this (and, soon, a patch).
The patch is there, so please review it! The example I used there is one
of the examples from the patch here.
Replacing the curve E used there with
{{{
sage: E=EllipticCurve([0,0,0,0,-6400/3])
sage: H=C.Hom(E)
sage: f = H([zbar,xbar-ybar,-(xbar+ybar)/80])
sage: f
Scheme morphism:
From: Projective Curve over Rational Field defined by x^3 + y^3 + 60*z^3
To: Elliptic Curve defined by y^2 = x^3 - 6400/3 over Rational Field
Defn: Defined on coordinates by sending (x : y : z) to
(zbar : xbar - ybar : -1/80*xbar - 1/80*ybar)
}}}
successfully defines the morphism. I recommend that the function here
just returns the morphism, since one can recover E from
{{{
sage: f.codomain()
Elliptic Curve defined by y^2 = x^3 - 6400/3 over Rational Field
}}}
This will not be the end of the story, as I now cannot apply f to a point
on C to get a point on E, but that's because of another difficulty like
the one at #10297, so should be fixed separately.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/3416#comment:17>
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