A characterization of the Ree curve

Abstract

Let $q=3q_0^2$, where $q_0=3^s$ and $s\ge 3$. We prove that a smooth, projective, geometrically irreducible curve over $\F_q$ with $q^3+1$ rational points and genus \[ \frac32q_0(q-1)(q+q_0+1) \] is $\F_q$-isomorphic to the Ree curve.