Rational points on rank 2 genus 2 bielliptic curves in the LMFDB

Building on work of Balakrishnan, Dogra, and of the first author, we provide some improvements to the explicit quadratic Chabauty method to compute rational points on genus \(2\) bielliptic curves over \(\mathbb{Q}\), whose Jacobians have Mordell-Weil rank equal to \(2\). We complement this with a p...

Full description

Saved in:
Bibliographic Details
Published in:arXiv.org 2022-12
Main Authors: Bianchi, Francesca, Padurariu, Oana
Format: Article
Language:English
Subjects:
Jacobians
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:Building on work of Balakrishnan, Dogra, and of the first author, we provide some improvements to the explicit quadratic Chabauty method to compute rational points on genus \(2\) bielliptic curves over \(\mathbb{Q}\), whose Jacobians have Mordell-Weil rank equal to \(2\). We complement this with a precision analysis to guarantee correct outputs. Together with the Mordell-Weil sieve, this bielliptic quadratic Chabauty method is then the main tool that we use to compute the rational points on the \(411\) locally solvable curves from the LMFDB which satisfy the aforementioned conditions.
ISSN:2331-8422