Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Bielliptic modular curves $X_0^*(N)$ with square-free levels   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 $N$.

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The categories of this paper are: quant-ph
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The categories of this paper are: chao-dyn
35
The categories of this paper are: mtrl-th
18
The categories of this paper are: econ
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The categories of this paper are: hep-lat
33
The categories of this paper are: plasm-ph
5
The categories of this paper are: gr-qc
31
The categories of this paper are: ao-sci
37
The categories of this paper are: supr-con
36
The categories of this paper are: cmp-lg
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The categories of this paper are: patt-sol
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The categories of this paper are: physics
1
The categories of this paper are: cs
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The categories of this paper are: q-fin
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The categories of this paper are: solv-int
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The categories of this paper are: bayes-an