Bogomolov–Fu–Tschinkel conjecture on common torsion points of elliptic curves

Let $E_1$ and $E_2$ be elliptic curves over $\mathbb{C}$, and for each $j=1,2$ let $\iota$ be the involution of $E_j$ and choose a double cover $\pi_j:E_j\to\mathbb{P}^{1}$ satisfying $\pi_j\circ\iota=\pi_j$. Bogomolov–Fu–Tschinkel conjecture. There exists a constant $c>0$, independent of $E_j$ and $\pi_j$, such that

$$\left|\pi_1(E_1[\infty])\cap\pi_2(E_2[\infty])\right|\leq c$$

for all pairs $(E_j,\pi_j)$ for which this intersection is finite. The conjecture asserts a uniform bound on common torsion points after mapping the elliptic curves to $\mathbb{P}^{1}$; the supplied text gives no resolution status.