Bounding the $j$-invariant of integral points on modular curves

TL;DR

This paper provides effective bounds on the $j$-invariant for integral points on modular curves over number fields, under the condition that the curves have at least three cusps.

Contribution

It introduces new explicit bounds for the $j$-invariant of integral points on modular curves with at least three cusps over arbitrary number fields.

Findings

Established effective bounds for the $j$-invariant.

Applicable to modular curves over arbitrary number fields.

Assumes the modular curves have at least three cusps.

Abstract

In this paper, we give some effective bounds for the $j$-invariant of integral points on arbitrary modular curves over arbitrary number fields assuming that the number of cusps is not less than 3.