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Bielliptic modular curves X-0*(N) with square-free levels

Author
Bars, F.; Gonzalez, J.
Type of activity
Journal article
Journal
Mathematics of computation
Date of publication
2019-11-01
Volume
88
Number
320
First page
2939
Last page
2957
DOI
10.1090/mcom/3424
Repository
http://hdl.handle.net/2117/168794 Open in new window
https://arxiv.org/abs/1812.11746 Open in new window
URL
https://www.ams.org/journals/mcom/2019-88-320/S0025-5718-2019-03424-5/ Open in new window
Abstract
Let N=1 be a square-free integer such that the modular curve X*0(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(X*0(N)) when the genus of X*0(N) is =3. Moreover, we prove that the set of all quadratic points over Q for the modular curve X*0(N) with genus =2 and N square-free is not finite exactly for 51 values of N.

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