Nesterenko's CM-point conjecture for modular values

Let $\tau\in\mathbb{H}$. The numbers

$$\tau,\quad e^{2\pi i\tau},\quad E_2(\tau),\quad E_4(\tau),\quad E_6(\tau)$$

are considered, where $E_2$, $E_4$, and $E_6$ denote the usual Eisenstein series. Nesterenko's conjecture. If at most three of these five numbers are algebraically independent, then $\tau$ is necessarily a CM point, meaning that it generates a quadratic extension over $\mathbb{Q}$. This conjecture would imply both Nesterenko's theorem and Schneider's theorem on algebraic values of the $j$-function; its resolution status is not specified in the source.