Automorphism groups of superspecial curves of genus 4 over [formula omitted

Abstract

In this paper, we explicitly determine the automorphism group of every nonhyperelliptic superspecial curve of genus 4 over F11. Our algorithm determining automorphism groups works for any nonhyperelliptic curve of genus 4 over finite fields. With this computation, we show the compatibility between the enumeration of superspecial curves of genus 4 over F11 obtained computationally by the first and second authors in 2017 and an enumeration by Galois cohomology theory.