Isomorphism classes of ordinary elliptic curves over fields of characteristic 3

Abstract

Ordinary elliptic curves over fields of characteristic 3 can be represented by y 2 = x 3 + ax 2 + b where a, b ≠ 0 ∈ . In this paper we count the number of different isomorphism classes of ordinary elliptic curves over finite fields of characteristic three. We show there are (2q−2) different isomorphism classes.