LAUSR

Abstract We investigate two families S ˜ q and R ˜ q of maximal curves over finite fields recently constructed by Skabelund as cyclic covers of the Suzuki and Ree curves. We show that S ˜ q is not Galois covered by the Hermitian curve maximal over F q 4 , and R ˜ q is not Galois covered by the Hermitian curve maximal over F q 6 . We also compute the genera of many Galois subcovers of S ˜ q and R ˜ q ; in this way, many new values in the spectrum of genera of maximal curves are obtained. The full automorphism group of both S ˜ q and R ˜ q is determined.