Re: another simple question

[Gareth Ma <grhkm21@gmail.com>]

I will also note the relation between this and finding minimal polynomial. If you have an approximation x of an algebraic number, you can LLL on the powers of x to find its minpoly. If the degree or the coefficients are too small, the problem is then kind of meaningless. For example, 0.42 is an approximation to a root of 50x-21=0 and x^2+2x-1=0 and more.

(This can be used for modular polynomial stuff and more iirc)

On 17 Apr 2024 at 04:45 +0100, American Citizen <website.reader3@gmail.com>, 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] ??

I strongly suspect that thousands perhaps millions, maybe more? elliptic
curves can be found containing this point.

How can we effectively pare down the possibilities to something we can
work with?

Randall