Triangular modular curves of small genus

DOI10.1007/s40993-022-00395-wOpenAlexW4310481427MaRDI QIDQ2679111

John Voight, Juanita Duque-Rosero

Publication date: 19 January 2023

Published in: Research in Number Theory (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2203.08593

zbMATH Keywords

modular curvescongruence subgroupstriangle groupsBelyi maps

Mathematics Subject Classification ID

Elliptic curves (14H52) Arithmetic aspects of modular and Shimura varieties (11G18)

Uses Software

• Magma
• GitHub
• ell-adic-galois-images

Cites Work

• Arithmetic Fuchsian groups of genus zero.
• Arithmetic triangle groups
• Rational isogenies of prime degree. (With an appendix by D. Goldfeld)
• The Magma algebra system. I: The user language
• Numerical calculation of three-point branched covers of the projective line
• On the arithmetic dimension of triangle groups
• Shimura curves of genus at most two
• Modular embeddings for some non-arithmetic Fuchsian groups
• Diophantine equations and modular forms
• Hypergeometric Abelian Varieties
• Algebraic curves uniformized by congruence subgroups of triangle groups
• Congruence Subgroups of PSL(2, Z) of Genus Less than or Equal to 24
• -adic images of Galois for elliptic curves over (and an appendix with John Voight)
• Die elliptischen Funktionen und ihre Anwendungen
• Hyperelliptic modular curves
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