I suggest you also find the full multiplication table for $y^2 + y = x^3$ over $\mathbb{F}_2$ (where it has 3 points) and over $\mathbb{F}_4$ (where it has 9 points). Notice that $\mathbb{F}_2$ is a subfield of $\mathbb{F}_4$, so you’ve done part of the work already. Don’t do all the multiplications out by hand, that’s tedious. Instead, use cleverness to use just a few computations to fill out the whole table (as we did in class).