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Re: Integral points on elliptic curves

  • To: mathgroup at smc.vnet.net
  • Subject: [mg122335] Re: Integral points on elliptic curves
  • From: Emu <samuel.thomas.blake at gmail.com>
  • Date: Tue, 25 Oct 2011 06:19:21 -0400 (EDT)
  • Delivered-to: l-mathgroup@mail-archive0.wolfram.com
  • References: <j80q8p$adb$1@smc.vnet.net>

On Oct 23, 9:28 pm, Artur <gra... at csl.pl> wrote:
> Dear Mathematica Gurus,
> Who know that existed any Mathematica procedure (library) to finding
> integral points on elliptic curves?
> Or how to find example to e.g.
>
> FindInstance[y^3 - x^2 == 1641843, {x, y}, Integers]
>
> if FindInstance doesn't work what inspite???
>
> Unfortunatelly Wolfram Research is developing some branches of
> Mathematics in new versions of Mathematica and complete leave anothers
> (good samples are elliptic curves, Chabauty method, determining Galois
> groups of polynomials etc.).
>
> Best wishes
> Artur Jasinski

How about something as naive as

In[31]:= Cases[Join @@ Table[{x, y, y^3 - x^2 == 1641843}, {x, 1,
1000}, {y, 1, 1000}], {__, True}]
Out[31]= {{468, 123, True}}

In[32]:= 123^3 - 468^2 == 1641843
Out[32]= True

Sam Blake



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