#10973: Integral points on elliptic curves over number fields
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Reporter: justin | Owner: cremona
Type: enhancement | Status: needs_review
Priority: major | Milestone:
Component: elliptic curves | Keywords: sd32
Work_issues: | Upstream: N/A
Reviewer: | Author: Justin Walker, Aly Deines,
Jennifer Balakrishnan
Merged: | Dependencies:
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Comment(by cremona):
Replying to [comment:14 was]:
> Here's a list of curves where your code and the latest (?) Magma V2.17-4
give different answers. I checked these by hand, and Magma is clearly
totally wrong (missing definitely integral points) in each case.
>
> 1264i1, 1328b1, 1656f1, 1848i1
Update. Using Sage-4.7.2 and Magma V2.17-9, these all agree:
{{{
sage: E = EllipticCurve("1264i1")
sage: E.integral_points()
[(2 : 0 : 1), (4 : 10 : 1), (18 : 80 : 1), (246404 : 122312970 : 1)]
sage: magma(E).IntegralPoints()
[ (2 : 0 : 1), (4 : -10 : 1), (18 : 80 : 1), (246404 : 122312970 : 1) ]
sage: E = EllipticCurve("1328b1")
sage: E.integral_points()
[(2 : 2 : 1), (4386 : 290438 : 1)]
sage: magma(E).IntegralPoints()
[ (2 : 2 : 1), (4386 : 290438 : 1) ]
sage: E = EllipticCurve("1656f1")
sage: E.integral_points()
[(3 : 0 : 1), (6 : 18 : 1), (27 : 144 : 1), (336678 : 195353910 : 1)]
sage: magma(E).IntegralPoints()
[ (3 : 0 : 1), (6 : -18 : 1), (27 : 144 : 1), (336678 : -195353910 : 1) ]
sage: E = EllipticCurve("1848i1")
sage: E.integral_points()
[(2 : 3 : 1), (3206 : 181557 : 1)]
sage: magma(E).IntegralPoints()
[ (2 : 3 : 1), (3206 : 181557 : 1) ]
}}}
That is using vanilla Sage (i.e. without any patches from this ticket).
I am about to do a more systematic test.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/10973#comment:17>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica,
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