Here I report on our studies of the electronic properties of elliptical quantum dots in a perpendicular external magnetic field, and in the presence of the Rashba spin-orbit interaction. Our work indicates that the Fock-Darwin spectra, corresponding to the non-interacting electrons in an elliptical quantum dot display a strong signature of the Rashba spin-orbit coupling even in a low magnetic field, as the anisotropy of the quantum dot is increased. An explanation of this pronounced effect with respect to the anisotropy is presented. The strong spin-orbit coupling effect manifests itself prominently in the corresponding dipole-allowed optical transitions and hence is susceptible to direct experimental observation.