  The genus of a maximal curve over a finite field with r^2 elements is either
g_0=r(r-1)/2 or less than or equal to g_1=(r-1)^2/4. Maximal curves with genus
g_0 or g_1 have been characterized up to isomorphism. A natural genus to be
studied is g_2=(r-1)(r-3)/8, and for this genus there are two non-isomorphism
maximal curves known when r \equiv 3 (mod 4). Here, a maximal curve with genus
g_2 and a non-singular plane model is characterized as a Fermat curve of degree
(r+1)/2.
