Elliptic curves with isomorphic groups of points over finite field extensions

Consider a pair of ordinary elliptic curves E and E′ defined over the same finite field Fq. Suppose they have the same number of Fq-rational points, i.e. |E(Fq)|=|E′(Fq)|. In this paper we characterise for which finite field extensions Fqk, k≥1 (if any) the corresponding groups of Fqk-rational points are isomorphic, i.e. E(Fqk)≅E′(Fqk).