Tetragonal modular quotients $X_0^{+d}(N)$

Petar Orlić

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arXiv · 2404.08014

Tetragonal modular quotients $X_0^{+d}(N)$

Petar Orlić

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Abstract

Let $N$ be a positive integer. For every $d | N$ such that $(d, N/d) = 1$ there exists an Atkin-Lehner involution $w_d$ of the modular curve $X_0(N)$. In this paper we determine all quotient curves $X_0(N)/w_d$ whose $\mathbb{Q}$-gonality is equal to $4$ and all quotient curves $X_0(N)/w_d$ whose $\mathbb{C}$-gonality is equal to $4$.

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Petar Orlić. 2024-04-10. Tetragonal modular quotients $X_0^{+d}(N)$. https://arxiv.org/abs/2404.08014

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