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

Michael Stoll

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arXiv · 2509.24604

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

Michael Stoll

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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 $J(\mathbb Q)$.

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Michael Stoll. 2025-09-29. Determining the rational points on a curve of genus 2 and Mordell-Weil rank 1. https://arxiv.org/abs/2509.24604

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