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We show that there exists a plane curve of degree $q^3+1$ with two innerGalois points whose smooth model is the Hermitian curve of degree $q+1$, where$q$ is a power of the characteristic $p>0$. Similar results hold for the Suzukiand Ree curves respectively.

Birational embeddings of the Hermitian, Suzuki and Ree curves with two Galois points