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