Automorphisms of elliptic curves over general rings

Question

Let $E$ be an elliptic curve over a field $k$. In this case we perfectly know how to compute $\operatorname{Aut}(E)$ depending on the $j$-invariant of $E$. Namely, for a general elliptic curve it is $\mathbb{Z}/2$ but if the $j$-invariant is either $0$ or $1728$ then it gets bigger. My question is: let us consider an elliptic curve $E$ over a ring $\mathbb{Z}/p^2$. What is $\operatorname{Aut}(E)$ depending on the $j$-invariant? I suspect that if $p > 3$ it should be the same as for char. $0$ picture but what happens for $p=2, 3?$