Let $E$ be an elliptic curve over a finite field $K$. In Silverman's The Arithmetic of Elliptic Curves, it is shown in Proposition 5.4. on page 343 that if the characteristic of $K$ is not equal to $2$ or $3$, then the equations of all twists of $E$ can be described explicitly:
Question: Is there a general description of the equations of an elliptic curve in Weierstrass form if $char(K)$ is $2$ or $3$?
In this paper by Kronberg, Soomro, Top, I can see how many twists an elliptic curve over a finite field with characteristic $2$ or $3$ has but I did not see (yet?) how these equations would look like.