Bielliptic modular curves X0* (N)
Let N ≥ 1 be a integer such that the modular curve X0* (N) has genus ≥ 2. We prove that X0* (N) is bielliptic exactly for 69 values of N. In particular, we obtain that X0* (N) is bielliptic over the base field for all these values of N, except X0*(160) that is not bielliptic over Q but it does over...
| Autores: | ; |
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| Tipo de documento: | Artigo |
| Data de publicação: | 2020 |
| País: | España |
| Recursos: | Universitat Autònoma de Barcelona |
| Repositório: | Dipòsit Digital de Documents de la UAB |
| Idioma: | Inglês |
| OAI Identifier: | oai:ddd.uab.cat:240651 |
| Acesso em linha: | https://ddd.uab.cat/record/240651 https://dx.doi.org/urn:doi:10.1016/j.jalgebra.2020.02.028 |
| Nível de acesso: | Acesso aberto |
| Palavra-chave: | Arithmetic geometry Hyperelliptic curves Bielliptic curves Quadratic points Elliptic curves Modular curves Involutions |
| Resumo: | Let N ≥ 1 be a integer such that the modular curve X0* (N) has genus ≥ 2. We prove that X0* (N) is bielliptic exactly for 69 values of N. In particular, we obtain that X0* (N) is bielliptic over the base field for all these values of N, except X0*(160) that is not bielliptic over Q but it does over Q(√-1). Moreover, we prove that the set of all quadratic points over Q for the modular curve X0* (N) is infinite exactly for 100 values of N. |
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