a Diophantine equation question

[Warut Roonguthai]

On 5/27/07, Jaap Spies <j.spies at hccnet.nl> wrote:

> As far as we can trust Computer Algebra! Maybe an independent result is needed.
> I tried to compile SIMATH to that matter, but I failed. Maybe there is someone
> on the seqfan list who can confirm the calculations on the elliptic curve.
>
> Jaap

With the single command:

IntegralPoints(EllipticCurve([18,0]))

Magma Calculator at http://magma.maths.usyd.edu.au/calc/
has confirmed SAGE's result with

Magma V2.13-11    Mon May 28 2007 05:51:11    [Seed = 3891806395]
   -------------------------------------

[ (0 : 0 : 1), (3 : 9 : 1), (6 : -18 : 1), (72 : 612 : 1) ]
[
    [ <(0 : 0 : 1), 1> ],
    [ <(3 : 9 : 1), 1> ],
    [ <(3 : 9 : 1), 1>, <(0 : 0 : 1), 1> ],
    [ <(3 : 9 : 1), 2>, <(0 : 0 : 1), 1> ]
]
3

Total time: 0.460 seconds, Total memory usage: 8.20MB

Warut