another simple question

[American Citizen <website.reader3@gmail.com>]

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