Determining the rational points on a curve of genus 2 and Mordell-Weil rank 1

Abstract

We explain how one can efficiently determine the (finite) set of rational points on a curve of genus 2 over $\mathbb{Q}$ with Jacobian variety $J$, given a point $P\in J(\mathbb{Q})$ generating a subgroup of finite index in $J(\mathbb{Q})$.

19 pages