#10973: Integral points on elliptic curves over number fields
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Reporter: justin | Owner: cremona
Type: enhancement | Status:
Priority: major | needs_review
Component: elliptic curves | Milestone: sage-5.13
Keywords: sd32 | Resolution:
Authors: Justin Walker, Aly Deines, | Merged in:
Jennifer Balakrishnan | Reviewers:
Report Upstream: N/A | Work issues:
Branch: | Commit:
Dependencies: | Stopgaps:
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Comment (by cremona):
More seriously,
{{{
sage: E = EllipticCurve('9615d1)
sage: E.integral_points()
}}}
seems to hang, thought I don't know why, while
{{{
sage: E = EllipticCurve('9615d1)
sage: E.integral_points(algorithm="old")
}}}
is fine. I think that this will need investigating before this can be
merged. Hence "needs work".
I systematically checked all curves with conductor < 10000 with Magma
V2.19-8. Note that thaere have been a lot of improvements in Magma's
algorithm, due to Steve DOnelly but not published, since this ticket was
opened. Not just bugfixes; but only over Q.
With the old algorithm in Sage for N<10000 there are only 3 cases where
Sage missed integral points. Of these, 3 (6104b1, 8470g1 and 8470g2), are
very easily fixed, simply by increasing the precision of the function
{{{integral_points_with_bounded_mw_coeffs}}} from 100 to 200, thogh I have
not done the necessary analysis to compute the actual precision required.
The other one is 2082a1, where the MW group is cyclic of rank 1 and the
integral multiples of the generator P are n*P for n=1,2,3,4,13, but the
bound computed by the algorithm is 12. It should be possible to find that
bug using a detailed analysis of the implementation, but I have not done
that yet (though I did find one small bug, in the formula for mu there
should be b2/12 and not b2).
--
Ticket URL: <http://trac.sagemath.org/ticket/10973#comment:44>
Sage <http://www.sagemath.org>
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