#3416: Weierstrass form for cubics
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Reporter: moretti |
Owner: was
Type: enhancement |
Status: needs_work
Priority: major |
Milestone: sage-5.6
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 |
Merged in:
Dependencies: |
Stopgaps:
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Comment (by vbraun):
There is also the pointless version #13084, #13458. The way I see it, it
has the advantage that you don't have to specify a point to get the
Weierstrass form. The price to pay is that you don't get an explicit
isomorphism with the Weierstrass cubic.
Actually, the Magma `aInvariants` function that the current code calls
{{{
cmd = 'aInvariants(MinimalModel(EllipticCurve(Curve(Scheme(P,
%s)),P!%s)));'%(F, P)
s = magma.eval(cmd)
return EllipticCurve(rings.RationalField(), eval(s))
}}}
implements the same algorithm as #13084, see
http://magma.maths.usyd.edu.au/magma/handbook/text/1379. Which is why it
doesn't return a morphism.
I'm not entirely sure how to merge the two approaches but it seems that
you should only require a point if you actually need the isomorphism to
the Weierstrass model.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/3416#comment:36>
Sage <http://www.sagemath.org>
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