Computing Galois representations and equations for modular curves X_H(ℓ)

2013/12/24 by Maarten Derickx, Mark van Hoeij, Derickx, Maarten +3
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1312.6819

openalex publication_date 2013/12/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We construct plane models of the modular curve X_H(ℓ), and use their explicit equations to compute Galois representations associated to modular forms for values of ℓ that are significantly higher than in prior works.

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