Bielliptic modular curves X-0*(N)
Let N = 1 be a integer such that the modular curve X* 0 (N) has genus = 2. We prove that X* 0 (N) is bielliptic exactly for 69 values of N. In particular, we obtain that X* 0 (N) is bielliptic over the base field for all these values of N, except X* 0 (160) that is not bielliptic over Q but it does...
| Autores: | , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2020 |
| País: | España |
| Institución: | Universitat Politècnica de Catalunya (UPC) |
| Repositorio: | UPCommons. Portal del coneixement obert de la UPC |
| Idioma: | inglés |
| OAI Identifier: | oai:upcommons.upc.edu:2117/330853 |
| Acceso en línea: | https://hdl.handle.net/2117/330853 https://dx.doi.org/10.1016/j.jalgebra.2020.02.028 |
| Access Level: | acceso abierto |
| Palabra clave: | Curves, Modular Arithmetical algebraic geometry Arithmetic geometry Hyperelliptic curves Bielliptic curves Quadratic points Elliptic curves Modular curves Involutions Corbes modulars Geometria algebraica aritmètica Àrees temàtiques de la UPC::Matemàtiques i estadística::Geometria::Geometria algebraica |
| Sumario: | Let N = 1 be a integer such that the modular curve X* 0 (N) has genus = 2. We prove that X* 0 (N) is bielliptic exactly for 69 values of N. In particular, we obtain that X* 0 (N) is bielliptic over the base field for all these values of N, except X* 0 (160) that is not bielliptic over Q but it does over Q( v -1). Moreover, we prove that the set of all quadratic points over Q for the modular curve X* 0 (N) is infinite exactly for 100 values of N. |
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