We prove a special case of the Dynamical André–Oort Conjecture formulated by Baker and DeMarco . For any integer , we show that for a rational plane curve parameterized by for some nonconstant polynomial , if there exist infinitely many points such that both and are postcritically finite maps, then for a st root of unity . As a key step in our proof, we show that the Mandelbrot set is not the filled Julia set of any polynomial .Communicated by Prof. Umberto Zannier