  We take advantage of the largest high-resolution simulation of cosmic
structure growth ever carried out -- the Millennium Simulation of the
concordance LambdaCDM cosmogony -- to study how the star formation histories,
ages and metallicities of elliptical galaxies depend on environment and on
stellar mass. We concentrate on a galaxy formation model which is tuned to fit
the joint luminosity/colour/morphology distribution of low redshift galaxies.
Massive ellipticals in this model have higher metal abundances, older
luminosity-weighted ages, shorter star formation timescales, but lower assembly
redshifts than less massive systems. Within clusters the typical masses, ages
and metal abundances of ellipticals are predicted to decrease, on average, with
increasing distance from the cluster centre. We also quantify the effective
number of progenitors of ellipticals as a function of present stellar mass,
finding typical numbers below 2 for M* < 10^{11} Msun, rising to about 5 for
the most massive systems. These findings are consistent with recent
observational results that suggest ``down-sizing'' or ``anti-hierarchical''
behaviour for the star formation history of the elliptical galaxy population,
despite the fact that our model includes all the standard elements of
hierarchical galaxy formation and is implemented on the standard, LambdaCDM
cosmogony.
