Left. Numerically calculated growth rates of the magneto-elliptic instability for elliptic streamlines of aspect ratio χ = 4 as a function of the dimensionless magnetic field strength q = kv_A/Ω_K and the angle θ between the wavevector of disturbances and the vertical axis. Pure k_z modes are the most unstable ones, having a critical wavelength near the predicted . Weaker destabilization exists at intermediate θ (3D disturbances) for shorter wavelengths. Pure planar disturbances (θ = π/2) are stable. Right. Growth rates of the k_z modes for different aspect ratios. For χ = 2 and χ = 3 the purely hydrodynamical elliptical instability is seen as finite (and high) growth rates as q tends to zero. For χ = 4 onwards, the instability is magnetic and has a most unstable wavelength near q = 1. The χ = 100 curve stands for an approach to the limit of pure shear flow. The growth rate curve calculated matches that of the MRI.