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Constructing elliptic curves over finite fields using double eta-quotients

Andreas Enge, Reinhard Schertz (2004)

Journal de Théorie des Nombres de Bordeaux

We examine a class of modular functions for Γ 0 ( N ) whose values generate ring class fields of imaginary quadratic orders. This fact leads to a new algorithm for constructing elliptic curves with complex multiplication. The difficulties arising when the genus of X 0 ( N ) is not zero are overcome by computing certain modular polynomials.Being a product of four η -functions, the proposed modular functions can be viewed as a natural generalisation of the functions examined by Weber and usually employed to construct...

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