Can someone verify that the elliptic curve $y^2 = x^3 + x +1$ over $\mathbb{F}_{3^2}$ is indeed supersingular?
$\textbf{My solution:}$
The characteristic of the field is 3 so we are looking for the coefficient of $x^2$ in $(x^3+x+1)^1$, obviously we can see that there is no $x^2$ term hence the curve is supersingular.
Is this correct?
Thanks