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

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Título:	Bielliptic modular curves X-0*(N) with square-free levels
Autor/a:	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 X0(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 X*0(N) with genus =2 and N square-free is not finite exactly for 51 values of N.
Abstract:	Peer Reviewed
Materia(s):	-Àrees temàtiques de la UPC::Matemàtiques i estadística::Àlgebra -Arithmetical algebraic geometry -Curves, Modular -Geometria algebraica aritmètica -Corbes modulars
Derechos:	Attribution-NonCommercial-NoDerivs 3.0 Spain http://creativecommons.org/licenses/by-nc-nd/3.0/es/
Tipo de documento:	Artículo - Versión presentada Artículo
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