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: | ; |
|---|---|
| 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 |
| _version_ | 1878731393259798528 |
|---|---|
| author | Bars Cortina, Francesc|||0000-0003-4779-3995 |
| author2 | González Rovira, Josep |
| author2_role | author |
| author_browse | Bars Cortina, Francesc|||0000-0003-4779-3995 González Rovira, Josep |
| author_facet | Bars Cortina, Francesc|||0000-0003-4779-3995 González Rovira, Josep |
| author_role | author |
| collection | Dipòsit Digital de Documents de la UAB |
| description | 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. |
| eu_rights_str_mv | openAccess |
| format | article |
| id | ES_2ea83f8aef6be0bb2baf7c83a97af7b2 |
| institution | Universitat Autònoma de Barcelona |
| instname_str | Universitat Autònoma de Barcelona |
| language | eng |
| network_acronym_str | ES |
| network_name_str | España |
| oai_identifier_str | oai:ddd.uab.cat:240651 |
| publishDate | 2020 |
| publishDateSort | 2020 |
| reponame_str | Dipòsit Digital de Documents de la UAB |
| spelling | Bielliptic modular curves X0* (N) Bars Cortina, Francesc|||0000-0003-4779-3995 González Rovira, Josep Arithmetic geometry Hyperelliptic curves Bielliptic curves Quadratic points Elliptic curves Modular curves Involutions 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. https://ddd.uab.cat/record/240651 https://dx.doi.org/urn:doi:10.1016/j.jalgebra.2020.02.028 |
| spellingShingle | Bielliptic modular curves X0* (N) Bars Cortina, Francesc|||0000-0003-4779-3995 Arithmetic geometry Hyperelliptic curves Bielliptic curves Quadratic points Elliptic curves Modular curves Involutions |
| title | Bielliptic modular curves X0* (N) |
| title_full | Bielliptic modular curves X0* (N) |
| title_fullStr | Bielliptic modular curves X0* (N) |
| title_full_unstemmed | Bielliptic modular curves X0* (N) |
| title_short | Bielliptic modular curves X0* (N) |
| title_sort | Bielliptic modular curves X0* (N) |
| topic | Arithmetic geometry Hyperelliptic curves Bielliptic curves Quadratic points Elliptic curves Modular curves Involutions |
| topic_facet | Arithmetic geometry Hyperelliptic curves Bielliptic curves Quadratic points Elliptic curves Modular curves Involutions |
| url | https://ddd.uab.cat/record/240651 https://dx.doi.org/urn:doi:10.1016/j.jalgebra.2020.02.028 |