Do there exist any elliptic curves $E\mathbb{F}_8$ satisfying either $\# E(\mathbb{F}_8) = 7$ or $\#E(\mathbb{F}_8) = 11$?

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As the question title suggests, do there exist any elliptic curves $E(\mathbb{F}_8)$ satisfying either $\# E(\mathbb{F}_8) = 7$ or $\#E(\mathbb{F}_8) = 11$?