Elliptic and hyperelliptic magnetohydrodynamic equilibria*

We construct three classes of axisymmetric equilibria with incompressible flow nonaligned with the magnetic field reducible to elliptic integrals and having similar magnetic field characteristics. They are restricted by appropriate side conditions like ``isothermal'' magnetic surfaces, ``isodynamicity'' or $P+B^{2}/2$ constant on magnetic surfaces. The third class is closely related to recent equilibria found in Schief, Phys. Plasmas 10, 2677 (2003). In contrast to field aligned flows, all solutions found here have nonzero toroidal magnetic field on and elliptic surfaces near the magnetic axis.