#10152: bug in integral_points (for elliptic curves over Q)
-------------------------------+--------------------------------------------
Reporter: cremona | Owner: cremona
Type: defect | Status: new
Priority: major | Milestone: sage-4.6.1
Component: elliptic curves | Keywords: integral points
Author: | Upstream: N/A
Reviewer: | Merged:
Work_issues: |
-------------------------------+--------------------------------------------
{{{
sage: E = EllipticCurve('2082a1')
sage: [P[0] for P in E.integral_points()]
[-11, -2, 4, 13]
}}}
but
{{{
sage: E.lift_x(507525709)
(507525709 : 11433453531221 : 1)
}}}
so we miss one point. Note that this point is 13*P where P is the
generator, and our code computes the bound to be 12.
John Cannon is sending me a complete list of integral points for all
curves in the Cremona database, computed using Magma, using some recent
enhancements. Previously I had checked that Sage and Magma agreed to
conductor 10000, so their enhancements must also fix bugs.
{{{
Magma V2.15-15 Thu Oct 21 2010 20:56:33 on John-laptop [Seed =
2704111428]
Type ? for help. Type <Ctrl>-D to quit.
Loading startup file "/home/john/magma/Startup/startup.m"
> E:=EllipticCurve([1,0,1,-118,584]);
> IntegralPoints(E);
[ (13 : 29 : 1), (4 : 11 : 1), (-11 : 29 : 1), (-2 : -28 : 1), (507525709
: -11433961056931
: 1) ]
[
[ <(13 : 29 : 1), 1> ],
[ <(13 : 29 : 1), 2> ],
[ <(13 : 29 : 1), 3> ],
[ <(13 : 29 : 1), 4> ],
[ <(13 : 29 : 1), 13> ]
]
19
}}}
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/10152>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica,
and MATLAB
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