Effective Siegel's theorem for modular curves

TL;DR

This paper demonstrates that integral points on most modular curves can be effectively identified, significantly advancing the understanding of rational solutions on these curves.

Contribution

It provides an effective method for determining integral points on all but finitely many modular curves, including all but one of prime power level.

Findings

Integral points can be effectively determined on nearly all modular curves.

The result applies to all but finitely many modular curves.

Specifically, it covers all but one modular curve of prime power level.

Abstract

We prove that integral points can be effectively determined on all but finitely many modular curves, and on all but one modular curve of prime power level.