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The automorphism group of the modular curve \(X_ 0(63)\). (English) Zbl 0708.14016
The author determines the automorphism group of the (compactified) modular curve \(X_ 0(N)\) for \(N=63\). In this case not all automorphisms come from the normalizer of \(\Gamma_ 0(N)\) in \(PSL_ 2({\mathbb{R}})\). For all other values of N the automorphism group was determined by M. A. Kenku and F. Momose in Compos. Math. 65, No.1, 51-80 (1988; Zbl 0686.14035)].
Reviewer: R.Pink

MSC:
14G35 Modular and Shimura varieties
14H45 Special algebraic curves and curves of low genus
14E07 Birational automorphisms, Cremona group and generalizations
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References:
[1] Birch, B.J., Kuyk, W., ed: Modular Functions of One Variable IV , Lect. Notes Math. 476, 1975. · Zbl 0315.14014 · doi:10.1007/BFb0097580
[2] Fricke, R. : Die elliptischen Functionen und ihre Anwendungen . Leipzig-Berlin: Teubner 1922. · JFM 48.0432.01
[3] Kenku, M.A. , Momose, F. , Automorphism groups of the modular curves X0(N) . Comp. Math. 65 (1988) 51-80. · Zbl 0686.14035 · numdam:CM_1988__65_1_51_0 · eudml:89883
[4] Mazur, B. , Swinnerton- Dyer, P. , Arithmetic of Weil Curves . Inv. Math. 25 (1974) 1 - 61. · Zbl 0281.14016 · doi:10.1007/BF01389997 · eudml:142281
[5] Matzat, B.H. , Konstruktive Galoistheorie . Lect. Notes Math. 1284, 1987. · Zbl 0634.12011
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