Bielliptic modular curves X0* (N)
| Autor: | Bars Cortina, Francesc, González Rovira, Josep |
|---|---|
| Přispěvatelé: | Universitat Politècnica de Catalunya. Departament de Matemàtiques |
| Jazyk: | angličtina |
| Rok vydání: | 2020 |
| Předmět: |
Curves
Modular Corbes modulars Arithmetic geometry Quadratic points Geometria algebraica aritmètica Elliptic curves Matemàtiques i estadística::Geometria::Geometria algebraica [Àrees temàtiques de la UPC] Arithmetical algebraic geometry Involutions Hyperelliptic curves Modular curves Bielliptic curves |
| Zdroj: | UPCommons. Portal del coneixement obert de la UPC Universitat Politècnica de Catalunya (UPC) Dipòsit Digital de Documents de la UAB Universitat Autònoma de Barcelona |
| Popis: | 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. |
| Databáze: | OpenAIRE |
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