Hyperelliptic quotients of modular curves \(X_0(N)\)
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.
scientific article; zbMATH DE number 1340491