Re: another simple question

[John Cremona <john.cremona@gmail.com>]

Is it really a sensible question to ask?  You can assign arbitrary values to all coefficients except the constant term and then solve for that.  For example, set k=y^-x^3, then (x,y) is on y^2=x^3+k.

I know that this is not exactly in the spirit of the question.

John

On Wed, 17 Apr 2024 at 04:45, 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