The Orders of Elliptic Curves y(2) = x(3) + b, b ∈ F(* q)

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This paper particularly deals with elliptic curves in the form of E(x, y) = y(2) － x(3) －b = 0, b ∈ F(* q) , where 3 divides q－1. In this paper, we refer to the well-known twist technique as x-twist and propose y-twist. By combining x-twist and y-twist, we can consider six elliptic curves and this paper proposes a method to obtain the orders of these six curves by counting only one order among the six curves.
Faculty of Engineering, Okayama Universityの論文