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Modular curves of genus 2 |
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| Authors: | Enrique Gonzá lez-Jimé nez Josep Gonzá lez. |
| Affiliation: | Department de Matemàtiques, Universitat Autònoma de Barcelona, Bellaterra, Barcelona, E-08193, Spain ; Escola Universitària Politècnica de Vilanova i la Geltrú, Av. Victor Balaguer s/n, E-08800 Vilanova i la Geltrú, Spain |
| Abstract: | We prove that there are exactly  genus two curves  defined over  such that there exists a nonconstant morphism  defined over  and the jacobian of  is  -isogenous to the abelian variety  attached by Shimura to a newform  . We determine the corresponding newforms and present equations for all these curves. |
| Keywords: | Hyperelliptic modular curves |
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