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

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dc.contributor.author	Bars Cortina, Francesc
dc.contributor.author	González Rovira, Josep
dc.date	2019-11-01
dc.identifier.citation	Bars, F.; Gonzalez, J. Bielliptic modular curves X-0*(N) with square-free levels. "Mathematics of computation", 1 Novembre 2019, vol. 88, núm. 320, p. 2939-2957.
dc.identifier.citation	0025-5718
dc.identifier.citation	https://arxiv.org/abs/1812.11746
dc.identifier.citation	10.1090/mcom/3424
dc.identifier.uri	http://hdl.handle.net/2117/168794
dc.language.iso	eng
dc.relation	https://www.ams.org/journals/mcom/2019-88-320/S0025-5718-2019-03424-5/
dc.rights	Attribution-NonCommercial-NoDerivs 3.0 Spain
dc.rights	info:eu-repo/semantics/openAccess
dc.rights	http://creativecommons.org/licenses/by-nc-nd/3.0/es/
dc.subject	Àrees temàtiques de la UPC::Matemàtiques i estadística::Àlgebra
dc.subject	Arithmetical algebraic geometry
dc.subject	Curves, Modular
dc.subject	Geometria algebraica aritmètica
dc.subject	Corbes modulars
dc.title	Bielliptic modular curves X-0*(N) with square-free levels
dc.type	info:eu-repo/semantics/submittedVersion
dc.type	info:eu-repo/semantics/article
dc.description.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.
dc.description.abstract	Peer Reviewed

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