Let $l,l'$ and $p$ be three distinct prime numbers and $\Phi_k(X,Y)$ is $k$-th modular polynomial defined over $GF(p)$. Suppose that we know $\Phi_l(X,j)$ and $\Phi_{l'}(X,j)$ have two roots. Is this claim true?
$\Phi_l(X,j)$ and $\Phi_{l'}(X,j)$ have not any common root?
