Integer sequences from elliptic curves

Abstract

We indicate that given an integer coordinate point on an elliptic curve y^2+axy+by=x^3+cx^2+dx+e we can identify an integer sequence whose Hankel transform is a Somos-4 sequence, and whose Hankel determinants can be used to determine the coordinates of the multiples of this point. In reverse, given the coordinates of the multiples of an integer point on such an elliptic curve, we conjecture the form of a continued fraction generating function that expands to give a sequence with the above properties.