Abstract
Let Fq be a finite field of q elements, where q is a power of a prime number p greater than or equal to 5. In this paper, we study the elliptic curve denoted Ea,b(Fq[e]) over the ring Fq[e] where e3 = e2 and (a,b) ∈ (Fq[e])2. In a first time, we study the arithmetic of the ring Fq[e], e3 = e2. In addition, using the Weierstrass equation, we define the elliptic curve Ea,b(Fq[e]). The study of this elliptic curve helped us to define two elliptic curve over the finite field Fq. We finish this paper by given a classification of the elements in Ea,b(Fq[e])
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