Triangular modular curves are a generalization of modular curves that arise from quotients of the upper half-plane by congruence subgroups of hyperbolic triangle groups. These curves also arise naturally as a source of Belyi maps with monodromy $\text{ PGL}_2(\mathbb{ F}_q)$ or $\text{ PSL}_2(\mathbb{ F}_q)$. We present a computational approach to enumerate Borel-type triangular modular curves of low genus, and we carry out this enumeration for prime level and small genus.
Categories: math.NT