Hyperelliptic quotients of modular curves \(X_0(N)\)
type: Item
instance of: scholarly article
title: Hyperelliptic quotients of modular curves \(X_0(N)\)
zbMATH Open document ID: 0947.11019
author: Masahiro Furumoto
author: Yuji Hasegawa
published in: Tokyo Journal of Mathematics
publication date: 2000-05-10T00:00:00Z
review text: Let \(W'\) be any subgroup of the full group \(W\) of Atkin-Lehner involutions acting on the modular curve \(X_0(N)\). The authors determine all pairs \((N,W')\) for which the quotient \(X_0(N)/W'\) is hyperelliptic, and give explicit equations for such quotients whose genus exceeds 2. For \(W'=\{1\}\) such values of \(N\) had been classified by \textit{A. P. Ogg} [Bull. Soc. Math. Fr. 102 (1974), 449-462 (1975; Zbl 0314.10018)] and for \(W'=W\) by the second author and \textit{K. Hashimoto} [Acta Arith. 77, 179-193 (1996; Zbl 0886.11023) and Acta Arith. 81, 369-385 (1997; Zbl 0886.11024)]. The techniques of proof are similar to the ones used in these references.
reviewed by: Gunther Cornelissen
Mathematics Subject Classification ID: 11F11
Mathematics Subject Classification ID: 14H45
zbMATH DE Number: 1340491
zbMATH Keywords: modular curve
zbMATH Keywords: modular form
zbMATH Keywords: hyperelliptic
zbMATH Keywords: Atkin-Lehner involution
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.3836/tjm/1270041616
OpenAlex ID: W2022446041
DOI: 10.3836/TJM/1270041616
description: scientific article; zbMATH DE number 1340491