Computing rational points on rank 0 genus 3 hyperelliptic curves

2019/09/11 by María Inés de Frutos-Fernández, de Frutos-Fernández, María Inés, Sachi Hashimoto +1 · 1 citation
Computer Science · Mathematics · #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Cryptography and Residue Arithmetic #FOS: Mathematics #Number Theory (math.NT) #Polynomial and algebraic computation

paper · pdf · doi:10.48550/arxiv.1909.04808

openalex publication_date 2019/09/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We compute rational points on genus 3 odd degree hyperelliptic curves C over ℚ that have Jacobians of Mordell-Weil rank 0. The computation applies the Chabauty-Coleman method to find the zero set of a certain system of p-adic integrals, which is known to be finite and include the set of rational points C(ℚ). We implemented an algorithm in Sage to carry out the Chabauty-Coleman method on a database of 5870 curves.

Cited by

• Rational and isolated quadratic points on hyperelliptic curves of rank 0 and small genus

Related

• Chabauty-Coleman experiments for genus 3 hyperelliptic curves
• Computing integral points on hyperelliptic curves using quadratic\n Chabauty
• Rational Points of some genus 3 curves from the rank 0 quotient strategy
• Rational Points on a Family of Genus 3 Hyperelliptic Curves
• Rational and isolated quadratic points on hyperelliptic curves of rank 0 and small genus