2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/76641The 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)/2.18 pages, Latex2eAlgebraic GeometryPC: 11G20, 11G, 11; SC: 14G15, 14G, 14text