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Defining equations of modular curves \(X_ 0(N)\). (English) Zbl 0865.11052
Given a positive integer \(N\), let \(X_0(N)\) be the modular curve determined by the congruence subgroup \(\Gamma_0(N) \subset \text{SL} (2,\mathbb{Z})\). In this paper, the author describes a general method of calculating defining equations of modular curves \(X_0(N)\) using the Fourier expansion of a certain cusp form of weight two for \(\Gamma_0(N)\). He also lists defining equations of all modular curves \(X_0(N)\) of genus two to six.

MSC:
11G18 Arithmetic aspects of modular and Shimura varieties
14G35 Modular and Shimura varieties
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