#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 nbruin):
Replying to [comment:65 vbraun]:
> Totally OT, but elliptic curves currently don't even attempt to be
unique.
OK! perhaps elliptic curves provide a way out of the quagmire of
uniqueness of parents:
{{{
sage: E=EllipticCurve([1,2,3,4,3])
sage: E([0,1,0])
(0 : 1 : 0)
sage: P=E([0,1,0])
sage: P.parent()
Abelian group of points on Elliptic Curve defined by y^2 + x*y + 3*y = x^3
+ 2*x^2 + 4*x + 3 over Rational Field
}}}
It seems elliptic curves are parents: `E.parent()` gives an error and
`E.category()` does not (although it returns a rather questionable
"Category of sets", but who cares), but the example above suggest they
don't actually occur as parents of elements. I guess they do occur as
domains and codomains of maps, though (see
`E.multiplication_by_m_isogeny(2)`). If those get trapped in the coercion
framework, something might choke on uniqueness assumptions.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/3416#comment:66>
Sage <http://www.sagemath.org>
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