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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
##### Keywords:
defining equations of modular curves; cusp form
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