Computing Rational Points on Elliptic Curves

Abstract

Rational points on an elliptic curve $E$ forms an abelian group, and by a theorem of Mordell, it is a finitely generated group. One of the major question in computational number theory is about computing a set of generators of $E(\mathbb{Q}$. This is problem is very hard in general, and in this talk, we will discuss how the method of 2-descent can be used to compute the group in certain cases.