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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

Junsworth
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  • Page 140, theorem 4.1 a) of Silverman's AEC I agrees with you - but you knew that - so I think all looks good... (Assuming that the curve is an ell. curve, i.e., smooth over the base field - which it is.) What was/is your worry? – peter a g Mar 01 '17 at 13:30
  • Thanks for your reply, just wanted some clarification is all! – Junsworth Mar 01 '17 at 14:38

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