Multiplicative dependence in the denominators of points of elliptic curves

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.