Let \(E_1, \ldots , E_s \) be s, not necessary distinct, elliptic curves over \({\mathbb {Q}}\) . We give upper bounds on the frequency of s-tuples of points in \(E_1({\mathbb {Q}})\times \ldots \times E_s({\mathbb {Q}})\) whose denominators or x-coordinates are multiplicatively dependent. More precisely, we give such bounds in two scenarios: one in which we fix s non-torsion \({\mathbb {Q}}\) -rational points \(P_i \in E_i({\mathbb {Q}})\) and arbitrary \({\mathbb {Q}}\) -rational points \(Q_i \in E_i({\mathbb {Q}})\) , \(i =1, \ldots , s\) , and we count s-tuples \( (n_1P_1+Q_1,\ldots , n_sP_s+Q_s) \in E_1({\mathbb {Q}}) \times \ldots \times E_s({\mathbb {Q}}) \) with \(n_1, \ldots , n_s\) in an arbitrary interval of length N, and the second in which we count points \((P_1,\ldots ,P_s) \in E_1({\mathbb {Q}}) \times \ldots \times E_s({\mathbb {Q}})\) of bounded canonical height.
