Functions and differentials on the non-split Cartan modular curve of level 11
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- by Julio Fernández and Josep González PDF
- Math. Comp. 86 (2017), 437-454 Request permission
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 $X_0(121)$.References
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Additional Information
- Julio Fernández
- Affiliation: Departament de Matemàtiques, Universitat Politècnica de Catalunya, EPSEVG, Avinguda Víctor Balaguer 1, 08800 Vilanova i la Geltrú, Spain
- MR Author ID: 704910
- 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
- MR Author ID: 319937
- Email: josep.gonzalez@upc.edu
- 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
- © Copyright 2016 American Mathematical Society
- Journal: Math. Comp. 86 (2017), 437-454
- MSC (2010): Primary 11F46, 14G35, 14Q05; Secondary 14H45, 11F03
- DOI: https://doi.org/10.1090/mcom/3109
- MathSciNet review: 3557806