Furumoto, Masahiro; Hasegawa, Yuji Hyperelliptic quotients of modular curves \(X_0(N)\). (English) Zbl 0947.11019 Tokyo J. Math. 22, No. 1, 105-125 (1999). 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 A. P. Ogg [Bull. Soc. Math. Fr. 102 (1974), 449-462 (1975; Zbl 0314.10018)] and for \(W'=W\) by the second author and 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. Reviewer: Gunther Cornelissen (Bonn) Cited in 1 ReviewCited in 17 Documents MSC: 11F11 Holomorphic modular forms of integral weight 14H45 Special algebraic curves and curves of low genus Keywords:modular curve; modular form; hyperelliptic; Atkin-Lehner involution Citations:Zbl 0314.10018; Zbl 0886.11023; Zbl 0886.11024 PDFBibTeX XMLCite \textit{M. Furumoto} and \textit{Y. Hasegawa}, Tokyo J. Math. 22, No. 1, 105--125 (1999; Zbl 0947.11019) Full Text: DOI