id	summary	reporter	owner	description	type	status	priority	milestone	component	resolution	keywords	cc	work_issues	upstream	reviewer	author	merged	dependencies	stopgaps
10152	bug in integral_points (for elliptic curves over Q)	cremona	cremona	"{{{
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
}}}
"	defect	closed	major	sage-duplicate/invalid/wontfix	elliptic curves	duplicate	integral points sd32	gaganskehon weigandt		N/A	William Stein