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| Main Author: | |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2511.13230 |
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Table of 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.