MODULAR POLYNOMIALS FOR MODULAR CURVES 0 (N ) X +

Abstract

We show that for all N ≥ 1, the modular function field K(X + 0 (N )) is generated by j(z)j(N z) and j(z) + j(N z) over C, where j(z) is the modular invariant. Moreover we derive the defining equation of the the modular function field K(X + 0 (N )) from the classical modular polynomial ΦN (X, Y ).

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