Tetragonal modular quotients of $X_0(N)$
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arXiv
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866915622563086336 |
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| author | Orlić, Petar |
| author_facet | Orlić, Petar |
| contents | Let $N$ be a positive integer. For every $d\mid N$ such that $(d,N/d)=1$ there exists an Atkin-Lehner involution $w_d$ of the modular curve $X_0(N)$. Let $B(N)$ be the group of all such involutions. In this paper we determine all $\mathbb C$ and $\mathbb Q$-tetragonal quotient curves $X_0(N)/W_N$, where $W_N\subseteq B(N)$ such that $4\leq|W_N|\leq 2^{ω(N)-1}$, thus completing the classification of all $\mathbb C$-tetragonal quotients of $X_0(N)$ by Atkin-Lehner involutions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_13230 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Tetragonal modular quotients of $X_0(N)$ Orlić, Petar Number Theory Let $N$ be a positive integer. For every $d\mid N$ such that $(d,N/d)=1$ there exists an Atkin-Lehner involution $w_d$ of the modular curve $X_0(N)$. Let $B(N)$ be the group of all such involutions. In this paper we determine all $\mathbb C$ and $\mathbb Q$-tetragonal quotient curves $X_0(N)/W_N$, where $W_N\subseteq B(N)$ such that $4\leq|W_N|\leq 2^{ω(N)-1}$, thus completing the classification of all $\mathbb C$-tetragonal quotients of $X_0(N)$ by Atkin-Lehner involutions. |
| title | Tetragonal modular quotients of $X_0(N)$ |
| topic | Number Theory |
| url | https://arxiv.org/abs/2511.13230 |