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arXiv · 2208.10957

Bielliptic quotient modular curves of $X_0(N)$

Francesc Bars·Mohamed Kamel·Andreas Schweizer
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Abstract

Let $N\geq 1$ be a non-square free integer and let $W_N$ be a non-trivial subgroup of the group of the Atkin-Lehner involutions of $X_0(N)$ such that the modular curve $X_0(N)/W_N$ has genus at least two. We determine all pairs $(N,W_N)$ such that $X_0(N)/W_N$ is a bielliptic curve and the pairs $(N,W_N)$ such that $X_0(N)/W_N$ has an infinite number of quadratic points over $\mathbb{Q}$.

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BibTeXRIS

Francesc Bars, Mohamed Kamel, Andreas Schweizer. 2022-08-23. Bielliptic quotient modular curves of $X_0(N)$. https://doi.org/10.1090/mcom%2F3800

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