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


Authors: Julio Fernández and Josep González
Journal: Math. Comp. 86 (2017), 437-454
MSC (2010): Primary 11F46, 14G35, 14Q05; Secondary 14H45, 11F03
DOI: https://doi.org/10.1090/mcom/3109
Published electronically: April 13, 2016
MathSciNet review: 3557806
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Abstract: The genus $ 4$ modular curve $ X_{ns}(11)$ attached to a non-split Cartan group of level $ 11$ admits a model defined over $ \mathbb{Q}$. We compute generators for its function field in terms of Siegel modular functions. We also show that its Jacobian is isomorphic over $ \mathbb{Q}$ to the new part of the Jacobian of the classical modular curve $ X_0(121)$.


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Julio Fernández
Affiliation: Departament de Matemàtiques, Universitat Politècnica de Catalunya, EPSEVG, Avinguda Víctor Balaguer 1, 08800 Vilanova i la Geltrú, Spain
Email: julio.fernandez.g@upc.edu

Josep González
Affiliation: Departament de Matemàtiques, Universitat Politècnica de Catalunya, EPSEVG, Avinguda Víctor Balaguer 1, 08800 Vilanova i la Geltrú, Spain
Email: josep.gonzalez@upc.edu

DOI: https://doi.org/10.1090/mcom/3109
Received by editor(s): December 3, 2014
Received by editor(s) in revised form: June 10, 2015
Published electronically: April 13, 2016
Additional Notes: The authors were partially supported by DGICYT Grant MTM2015-66180-R
Article copyright: © Copyright 2016 American Mathematical Society