Re: Transforming general cubic to standard form

[Bill Allombert <Bill.Allombert@math.u-bordeaux.fr>]

On Thu, Nov 04, 2021 at 01:54:20PM +0000, Grechuk, Bogdan (Dr.) wrote:
> Dear Bill, John, and everyone,
> 
> Thank you very much for the answers and comments!
> 
> May I have one follow up question? If I have a general genus 1 cubic
> and a rational point exists (so this is elliptic curve), but the
> transformation to Weierstrass form is rational but non-linear, it of
> course does not present the internality of the points. I can use Magma
> or SageMath to find integral points on the Weierstrass model. Is there
> any implementation for finding integer points on the original (general
> cubic) model?

At least cubics of the form

a*x^3+b*x^2*y+c*x*y^2+d*y^3=e

can be handled as Thue equations and solved using thue().

Cheers,
Bill.