Bielliptic modular curves X0⁎(N)
| Autor: | Francesc Bars, Josep González |
|---|---|
| Rok vydání: | 2020 |
| Předmět: |
Algebra and Number Theory
business.industry 010102 general mathematics Base field Modular design 01 natural sciences Modular curve Set (abstract data type) Combinatorics Elliptic curve Quadratic equation Integer Genus (mathematics) 0103 physical sciences 010307 mathematical physics 0101 mathematics business Mathematics |
| Zdroj: | Journal of Algebra. 559:726-759 |
| ISSN: | 0021-8693 |
| DOI: | 10.1016/j.jalgebra.2020.02.028 |
| 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 ( − 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 |
| Externí odkaz: |
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