To meet the ever-growing demand for the throughput of the wireless communication technologies, one way is to use light beams multiplexed by the orbital angular momentum (OAM). However, the intensity structure is often ignored, although it can carry additional information and thus lead to increase of the throughput. Some distortions of the vortex phase also can lead to modified intensity. Here, we analyze an elliptic optical vortex embedded into an elliptic Gaussian beam. Explicit closed form expressions for the normalized orbital angular momentum (OAM) of such a beam and for its complex amplitude after propagation in a paraxial ABCD-system are derived. The resulting elliptic Gaussian vortex (EGV) is shown to have a fractional OAM, whose maximal value equals to the topological charge n of a conventional Gauss vortex is attained for a zero ellipticity vortex. As the beam propagates, the major axis of the intensity ellipse in the beam cross-section rotates, making the angle of 90° between the initial plane and the focal plane of a spherical lens. On the major axis of the intensity ellipse, there are n intensity nulls of the EGV, with the distance between them varying with propagation distance and varying ellipticity. The distance between the intensity nulls is found to be maximal in the focal plane for a given ellipticity. This distance between the nulls can be used to decoding the data encoded by the vortex ellipticity.