An explicit bound for integral points on modular curves

TL;DR

This paper provides an explicit numerical bound for the number of integral points on modular curves by applying an explicit version of Baker's inequality, improving the concreteness of previous theoretical bounds.

Contribution

The paper introduces an explicit constant for bounding integral points on modular curves, making the bounds more practical and computable.

Findings

Derived an explicit constant C for bounds

Applied explicit Baker's inequality to modular curves

Enhanced the concreteness of bounds on integral points

Abstract

In this paper, we give a constant $C$ in \cite[Theorem 1.2]{sha2014bounding} by using an explicit Baker's inequality, hence we have an explicit bound of the integral points on modular curves.