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

TL;DR

This paper establishes effective bounds for the $j$-invariant of integral points on specific modular curves with positive genus and fewer than three cusps, advancing understanding in number theory and algebraic geometry.

Contribution

It provides the first effective bounds for the $j$-invariant on these particular modular curves, which was previously unknown.

Findings

Two explicit bounds for the $j$-invariant are derived.

The bounds apply to modular curves with positive genus and less than three cusps.

Results contribute to the study of integral points on modular curves.

Abstract

In this paper, we obtain two effective bounds for the $j$-invariant of integral points on certain modular curves which has positive genus and less than three cusps.