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...
| Authors: | , |
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| Format: | article |
| Publication Date: | 2020 |
| Country: | España |
| Institution: | Universitat Autònoma de Barcelona |
| Repository: | Dipòsit Digital de Documents de la UAB |
| Language: | English |
| OAI Identifier: | oai:ddd.uab.cat:240651 |
| Online Access: | https://ddd.uab.cat/record/240651 https://dx.doi.org/urn:doi:10.1016/j.jalgebra.2020.02.028 |
| Access Level: | Open access |
| Keyword: | Arithmetic geometry Hyperelliptic curves Bielliptic curves Quadratic points Elliptic curves Modular curves Involutions |
| Summary: | 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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