Mathematics of Computation

Author(s): Enrique González-Jiménez; Josep González.
Journal: Math. Comp. 72 (2003), 397-418.
MSC (2000): Primary 14G35, 14H45; Secondary 11F11, 11G10
Posted: June 4, 2002
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Abstract: We prove that there are exactly

genus two curves

defined over $\mathbb{Q}$ such that there exists a nonconstant morphism $\pi:X_1(N)\rightarrow C$ defined over $\mathbb{Q}$ and the jacobian of

is $\mathbb{Q}$ -isogenous to the abelian variety

attached by Shimura to a newform $f\in S_2(\Gamma_1(N))$ . We determine the corresponding newforms and present equations for all these curves.

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Retrieve articles in Mathematics of Computation with MSC (2000): 14G35, 14H45, 11F11, 11G10

Enrique González-Jiménez
Affiliation: Department de Matemàtiques, Universitat Autònoma de Barcelona, Bellaterra, Barcelona, E-08193, Spain
Email: enrikegj@mat.uab.es

Josep González
Affiliation: Escola Universitària Politècnica de Vilanova i la Geltrú, Av. Victor Balaguer s/n, E-08800 Vilanova i la Geltrú, Spain
Email: josepg@mat.upc.es

DOI: 10.1090/S0025-5718-02-01458-8
PII: S 0025-5718(02)01458-8
Keywords: Hyperelliptic modular curves
Received by editor(s): October 10, 2000
Received by editor(s) in revised form: April 4, 2001
Posted: June 4, 2002
Additional Notes: The first author was supported in part by DGI Grant BHA2000-0180
The second author was supported in part by DGI Grant BFM2000-0794-C02-02
Copyright of article: Copyright 2002, American Mathematical Society

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