In this article we recall how to describe the twists of a curve over a finite field and we show how to compute the number of rational points on such a twist by methods of linear algebra We illustrate this in the case of plane quartic curves with at least 16 automorphisms In particular we treat the twists of the Dyck-Fermat and Klein quartics. Our methods show how in special cases non-Abelian cohomology can be explicitly computed They also show how questions which appear difficult from a function field perspective can be resolved by using the theory of the Jacobian variety (C) 2010 Elsevier Inc. All rights reserved.
- Non-Abelian Galois cohomology
- Dyck–Fermat quartic
- Klein quartic