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

2025/09/29 by Stoll, Michael
#11-04 #11D41 #11G10 #11G30 #11Y50 #14G05 #14G25 #14H25 #14H40 #14Q05 #Algebraic Geometry (math.AG) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2509.24604

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 ∈ J(\mathbb Q) generating a subgroup of finite index in J(\mathbb Q).

Citations

• Conditional algorithmic Mordell
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• Rational Points on Curves of Genus 2: Experiments and Speculations
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• A method for construction of rational points over elliptic curves
• Rational points on rank 2 genus 2 bielliptic curves in the LMFDB