Analytic and numerical study of electromagnetic oscillations of isotropic relativistic plasma with fast electron distribution is presented. Different analytic formulas for the long-wavelength and short-wavelength branches are obtained. The numerical study gives the dispersion curve in the whole wavenumber range. It is shown that analytical dispersion curves in the long-wavelength and short-wavelength regions are coincident with the numerical ones. Furthermore, the approximate expression of the dispersion law for the different parameters is given by fitting numerical curves with the polynomial regression method, which provides a reference for further study.