Let \(E\) be an elliptic curve defined over a number field \(K\) and let \(H\) be a finite \(K\)-subgroup of \(E\). In this note the map from the group of homogeneous spaces of \(E/K\) to \(H^1(G_{\overline K/K},H)\) is explicitly described in the following two cases: (1) when \(K={\mathbb Q}\), there exists a \(3\)-torsion point defined over \({\mathbb Q}\) and \(H\) is the subgroup generated by this point. (2) when \(K\) is the cyclotomic field \({\mathbb Q}(\zeta_3)\) and the \(3\)-torsion subgroup \(H\) is defined over \(K\).