Elliptic Exceptional Belyi Coverings

TL;DR

This paper introduces a Maple algorithm and provides a table for classifying elliptic exceptional Belyi coverings up to degree 12, based on their ramification schemes on genus 1 surfaces.

Contribution

The authors develop a computational method and compile a comprehensive table for elliptic exceptional Belyi coverings, advancing the classification of these mathematical objects.

Findings

Algorithm successfully computes coverings up to degree 12.

Table summarizes classifications and ramification schemes.

Provides new data for elliptic Belyi coverings with genus 1.

Abstract

An elliptic exceptional Belyi covering is a connected Belyi covering uniquely determined by its ramification scheme or the respective dessin d'enfant when the underlying compact Riemann surface has genus 1. We give our Maple algorithm and table that display our calculations for elliptic exceptional Belyi coverings up to degree 12.