Integral points on the modular curves $X_0(p)$

TL;DR

This paper establishes explicit height bounds for integral points on the modular curves $X_0(p)$, improving previous bounds by employing a detailed version of the Chevalley-Weil principle.

Contribution

It provides a more precise explicit bound for integral points on $X_0(p)$, enhancing earlier results by Sha through a refined Chevalley-Weil approach.

Findings

Explicit height bounds for integral points on $X_0(p)$

Improved bounds over previous results by Sha

Application of a detailed Chevalley-Weil principle

Abstract

In this paper, we give an explicit bound for the height of integral points on $X_0(p)$ by using a very explicit version of the Chevalley-Weil principle. We improve the bound given by Sha in \cite{sha2014bounding1}.