Bielliptic modular curves $X_0^*(N)$ with square-free levels
| Autor: | Josep González Rovira, Francesc Bars |
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| Rok vydání: | 2018 |
| Předmět: |
Pure mathematics
Algebra and Number Theory Mathematics - Number Theory business.industry Applied Mathematics Mathematics::Number Theory Square-free integer Matemàtiques i estadística::Àlgebra [Àrees temàtiques de la UPC] Modular design Curves Modular Computational Mathematics Mathematics - Algebraic Geometry Corbes modulars FOS: Mathematics Geometria algebraica aritmètica Arithmetical algebraic geometry Number Theory (math.NT) business Algebraic Geometry (math.AG) Mathematics |
| Zdroj: | Dipòsit Digital de Documents de la UAB Universitat Autònoma de Barcelona UPCommons. Portal del coneixement obert de la UPC Universitat Politècnica de Catalunya (UPC) Recercat. Dipósit de la Recerca de Catalunya instname |
| DOI: | 10.48550/arxiv.1812.11746 |
| Popis: | Let $N\geq 1$ be a square-free integer such that the modular curve $X_0^*(N)$ has genus $\geq 2$. We prove that $X_0^*(N)$ is bielliptic exactly for $19$ values of $N$, and we determine the automorphism group of these bielliptic curves. In particular, we obtain the first examples of nontrivial $Aut(X_0^*(N))$ when the genus of $X_0^*(N)$ is $\geq 3$. Moreover, we prove that the set of all quadratic points over $\mathbb{Q}$ for the modular curve $X_0^*(N)$ with genus $\geq 2$ and $N$ square-free is not finite exactly for $51$ values of $N$. |
| Databáze: | OpenAIRE |
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