I'm taking a course on electrodynamics and I'm confused when we start talking about potentials. The electromagnetic field seems to have 6 independent components to me. It's described by six dynamical equations (and 2 non-dynamical constraint equations). The EM field tensor has 6 independent components as well.
However, when describing the field in terms of the EM four-potential, the EM field seems to be completely determined by four independent components. What am I missing here?