We report electric polarization and magnetization measurements in single crystals of double perovskite using pulsed magnetic fields and optical second harmonic generation in dc magnetic fields. We observe well-resolved magnetic field-induced changes in the electric polarization in single crystals and thereby resolve the question about whether multiferroic behavior is intrinsic to these materials or is an extrinsic feature of polycrystals. We find electric polarization along the crystalline axis, that is suppressed by applying a magnetic fields along the axis, and advance a model for the origin of magnetoelectric coupling. We furthermore map the phase diagram using both capacitance and electric polarization to identify regions of ordering and regions of magnetoelectric hysteresis. This compound is a rare example of coupled hysteretic behavior in the magnetic and electric properties. The ferromagneticlike magnetic hysteresis loop that couples to hysteretic electric polarization can be attributed not to ordinary ferromagnetic domains, but to the rich physics of magnetic frustration of Ising-like spins in the axial next-nearest-neighbor interaction model.