Re: another simple question

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

On Tue, Apr 16, 2024 at 08:45:40PM -0700, American Citizen wrote:
> Recently, we saw a point with thousands of digits posted with the question,
> what elliptic curve might have this point?
> 
> The answer was to use lindep to determine the elliptic curve, and so
> everything went fine.
> 
> However, I am dubious that this general approach using lindep on [y^2, xy,
> y, x^3, x^2, x, 1] will work when we have points of lesser heights.
> 
> Suppose we have the point [1/2, 5/8] ??

Well, your example is interesting, since there is no elliptic curve in Weierstrass
form with integral coefficient having this exact point!

In any case, once you have found a small non-torsion point, it is easy enough to
find a bigger one, so that the curve can be identified without doubt.

But I apologize to have caused confusion with my little game.
The question I expected you to ask was, how did I found such a large point
on a curve with such a large conductor ?

The answer is: by adapting Monsky/Robatino method to twists of the curve 11a1.
So thanks again for pointing me to Robatino thesis.

Cheers,
Bill.