# Curve - non singular curve and its genus

Help me please with this problem:$X \subset \mathbb{P}^{2}$ defined as $x^{3}y+y^{3}z+z^{3}x=0$

1.Prove X - non singular curve and find its genus. 2.Prove X - maximal curve over $F_{8}$ field, and find all points of X.

Thanks a lot!

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