liftings of automorphisms of elliptic curves

Question

Let $E$ be an elliptic curve with $j(E) = 0$ over a field $k$ where $\text{char} ~k$ is $2$ or $3$. Then $\text{Aut} (E)$ is of order $24$ and $12$ respectively. How do these groups behave under deformations of $E$? That is, if $\tilde{E}$ is an elliptic curve over $W_2(k)$ with $j(\tilde{E})=0$, what is $\text{Aut}(\tilde{E})$?