#12080: manin constant
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Reporter: wuthrich | Owner: cremona
Type: defect | Status: positive_review
Priority: major | Milestone: sage-5.0
Component: elliptic curves | Resolution:
Keywords: manin constant, isogeny | Work issues:
Report Upstream: N/A | Reviewers:
Authors: wuthrich | Merged in:
Dependencies: | Stopgaps: todo
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Changes (by was):
* status: needs_review => positive_review
Comment:
Mark Watkins says: "Sage is definitely correct. Sympow code I wrote
agrees with Sage here. Magma has a bug."
So... positive review. (Also, I checked up to 1200 and Sage and Magma
agree in the rest of the cases.)
Incidentally, Magma's code is way faster:
{{{
sage: E = list(cremona_curves([1200]))[0]
sage: E
Elliptic Curve defined by y^2 = x^3 - x^2 + 17*x - 38 over Rational Field
sage: time E.manin_constant()
1
Time: CPU 0.71 s, Wall: 0.82 s
sage: F = magma(E)
sage: time F.ManinConstant()
1
Time: CPU 0.00 s, Wall: 0.06 s
}}}
However, according to Mark Watkins, Magma is fast because it assumes
'''every''' imaginable conjecture in that implementation (and doesn't
actually compute any periods, etc.)
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/12080#comment:15>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica,
and MATLAB
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