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!
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!