Computing integral points on hyperelliptic curves using quadratic Chabauty

TL;DR

This paper introduces a novel method combining p-adic approximation and the Mordell-Weil sieve to compute integral points on hyperelliptic curves of odd degree where the genus equals the Mordell-Weil rank.

Contribution

It presents a new computational approach for integral points on hyperelliptic curves, extending previous techniques with a combined p-adic and sieve method.

Findings

Successfully computes integral points on specific hyperelliptic curves

Demonstrates effectiveness of combined p-adic and Mordell-Weil sieve techniques

Provides a practical implementation for curves with genus equal to Mordell-Weil rank

Abstract

We give a method for the computation of integral points on a hyperelliptic curve of odd degree over the rationals whose genus equals the Mordell-Weil rank of its Jacobian. Our approach consists of a combination of the $p$-adic approximation techniques introduced in previous work with the Mordell-Weil sieve