Bielliptic modular curves X0* (N) with square-free levels

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Title:	Bielliptic modular curves X0* (N) with square-free levels
Author:	Bars Cortina, Francesc; González Rovira, Josep
Abstract:	Let N ≥ 1 be a square-free integer such that the modular curve X0(N) has genus ≥ 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(X0(N)) when the genus of X0(N) is ≥ 3. Moreover, we prove that the set of all quadratic points over ℚ for the modular curve X0*(N) with genus ≥ 2 and N square-free is not finite exactly for 50 values of N.
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Document type:	Article
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Uri:	https://ddd.uab.cat/record/222678