GENERATION OF RAY CLASS FIELDS OF IMAGINARY QUADRATIC FIELDS

Abstract

Let K be an imaginary quadratic field other than Q( and Q( −3), and let OK be its ring of integers. Let N be a positive integer such that N = 5 or N ≥ 7. In this paper, we generate the ray class field modulo N OK over K by using a single x-coordinate of an elliptic curve with complex multiplication by OK .

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