Primality proving using elliptic curves with complex multiplication by imaginary quadratic fields of class number three

Abstract: In 2015, Abatzoglou, Silverberg, Sutherland, and Wong presented a framework for primality proving algorithms for special sequences of integers using an elliptic curve with complex multiplication. For some technical reason, their framework can not be applied to an elliptic curve with complex multiplication by an imaginary quadratic field of class number greater than two. In this paper, we present a method to apply their framework to imaginary quadratic fields of class number three. As an application, we give two special sequences of integers to which our method can be applied, and a computational result for the primality of these sequences.

Has companion code repository: https://github.com/hiroshi-onuki/ecpp_cm_h3

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