Aims. We perform light curve inversion for 491 asteroids to retrieve phase curve parameters, rotation periods, pole longitudes and latitudes, and convex and triaxial ellipsoid shapes by using the sparse photometric observations from Gaia Data Release 2 and the dense ground-based observations from the DAMIT database. We develop a method for the derivation of reference absolute magnitudes and phase curves from the Gaia data, allowing for comparative studies involving hundreds of asteroids. Methods. For both general convex shapes and ellipsoid shapes, we computed least-squares solutions using either the Levenberg-Marquardt optimization algorithm or the Nelder-Mead downhill simplex method. Virtual observations were generated by adding Gaussian random errors to the observations, and, later on, a Markov chain Monte Carlo method was applied to sample the spin, shape, and scattering parameters. Absolute magnitude and phase curve retrieval was developed for the reference geometry of equatorial illumination and observations based on model magnitudes averaged over rotational phase. Results. The derived photometric slope values showed wide variations within each assumed Tholen class. The computed Gaia G-band absolute magnitudes matched notably well with the V-band absolute magnitudes retrieved from the Jet Propulsion Laboratory Small-Body Database. Finally, the reference phase curves were well fitted with the H, G1, G2 phase function. The resulting G1, G2 distribution differed, in an intriguing way, from the G1, G2 distribution that is based on the phase curves corresponding to light curve brightness maxima.