  We describe the invariants of plane quartic curves -- nonhyperelliptic genus
3 curves in their canonical model -- as determined by Dixmier and Ohno, with
application to the classification of curves with given structure. In
particular, we determine modular equations for the strata in the moduli space
$\Me_3$ of plane quartics which have at least seven hyperflexes, and obtain an
computational characterization of curves in these strata.
