Papers › Triangular modular curves of low genus

Triangular modular curves of low genus

16 Mar 2022arXiv:2203.08593links table onlyarchive 2025-07-28

Juanita Duque-Rosero, John Voight

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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 PGL₂(𝔽_q) or PSL₂(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.

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