On the ring of invariants of ordinary quartic curves in characteristic 2

The moduli space of the ordinary non-singular quartic curves over fields of characteristic 2 is isomorphic to a certain open subset of an affine variety, whose coordinate ring in turn is given as the invariant algebra of a certain module of the finite group GL3(F2). We derive a complete description of this invariant algebra by combining theoretical analysis with application of specially tailored computational techniques.