English

Computing rational points on rank 0 genus 3 hyperelliptic curves

Number Theory 2020-09-25 v2 Algebraic Geometry

Abstract

We compute rational points on genus 33 odd degree hyperelliptic curves CC over Q\mathbb{Q} that have Jacobians of Mordell-Weil rank 00. The computation applies the Chabauty-Coleman method to find the zero set of a certain system of pp-adic integrals, which is known to be finite and include the set of rational points C(Q)C(\mathbb{Q}). We implemented an algorithm in Sage to carry out the Chabauty-Coleman method on a database of 58705870 curves.

Keywords

Cite

@article{arxiv.1909.04808,
  title  = {Computing rational points on rank 0 genus 3 hyperelliptic curves},
  author = {María Inés de Frutos-Fernández and Sachi Hashimoto},
  journal= {arXiv preprint arXiv:1909.04808},
  year   = {2020}
}

Comments

revisions to Section 2

R2 v1 2026-06-23T11:11:50.117Z