  The present study is a continuation of a previous one on "hyperelliptic"
axisymmetric equilibria started in [Tasso and Throumoulopoulos, Phys. Plasmas
5, 2378 (1998)].
  Specifically, some equilibria with incompressible flow nonaligned with the
magnetic field and restricted by appropriate side conditions like "isothermal"
magnetic surfaces, "isodynamicity" or P + B^2/2 constant on magnetic surfaces
are found to be reducible to elliptic integrals. The third class recovers
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.
