Functions and differentials on the non-split Cartan modular curve of level 11

2014/11/24 by Julio Fernández, J.A. Fernandez, Fernández, Julio +3
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Number Theory (math.NT) #math.NT

paper · pdf · doi:10.48550/arxiv.1411.6639

arxiv created 2014/11/24 · openalex publication_date 2014/11/24 · arxiv updated 2014/11/26 · openalex created_date 2022/10/02 · openalex updated_date 2026/07/28

Abstract

The genus 4 modular curve X_ns(11) attached to a non-split Cartan group of level 11 admits a model defined over ℚ. We compute generators for its function field in terms of Siegel modular functions. We also show that its Jacobian is isomorphic over ℚ to the new part of the Jacobian of the classical modular curve X₀(121).

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