When is an elliptic curve of $j$-invariant $j=0,1728$ supersingular over $\mathbb{F}_p$?

Question

Sorry for my bad English.

Let $p$ be a prime, $E$ be an elliptic curve over $\mathbb{F}_p$ of $j$-invariant is 0 or 1728.

Now I want to know if there is a criterion of when $E$ is supersingular.

In Wikipedia,there is a table for small $p$, but I don't know the regularity of connection of $p$ and supersingular.