Shimura curves of genus at most two

TL;DR

This paper systematically enumerates all Shimura curves of genus at most two, providing a comprehensive classification of these algebraic curves with low genus.

Contribution

It offers the first complete enumeration of low-genus Shimura curves, filling a gap in the classification of these important algebraic objects.

Findings

All Shimura curves of genus ≤ 2 are explicitly listed.

The enumeration includes curves with various discriminants and levels.

Results contribute to the understanding of the structure of Shimura curves.

Abstract

In this article, we enumerate all Shimura curves X^D_0(N) of genus at most two.