A new analytical solution for the luminosity distance in flat $��$CDM cosmology is derived in terms of elliptical integrals of first kind with real argument. The consequent derivation of the distance modulus allows evaluating the Hubble constant, $H_0=69.77\pm 0.33$, $\om= 0.295\pm0.008$ and the cosmological constant, $��= (1.194 \pm 0.017)10^{-52} \frac{1}{m^2}$.

12 pages and 5 figures