1. Introduction. Let k be a perfect field of characteristic p > 0 and E/k an elliptic curve over k. Ifk denotes the algebraic closure of k, then E(k) is an Abelian group and its p-torsion, denoted by E[p], is either 0 or Z/pZ. (See, for instance, Theorem V.3.1 in [7].) E is then called supersingular if E[p] = 0, and ordinary otherwise. (As observed by Silverman in Remark V.3.2.2 of [7], there are other characterizations of supersingular elliptic curves relevant to various applications.)It is a known fact that, for a fixed characteristic p > 0, there are (up to isomorphism) finitely many supersingular elliptic curves. (See, for instance, Theorem V.4