  We present a study of the X-ray to optical properties of a sample of 545
X-ray selected Type 1 AGN, from the XMM-COSMOS survey, over a wide range of
redshifts ($0.04<\z<4.25$) and X-ray luminosities ($40.6 \leq \Log \Lhard \leq
45.3$). About 60% of them are spectroscopically identified Type 1 AGN, while
the others have a reliable photometric redshift and are classified as Type 1
AGN on the basis of their multi-band Spectral Energy Distributions. We discuss
the relationship between UV and X-ray luminosity, as parameterized by the
$\alphaox$ spectral slope, and its dependence on redshift and luminosity. We
compare our findings with previous investigations of optically selected
broad-line AGN (mostly from SDSS). A highly significant correlation between
$\alphaox$ and $\lo$ is found, in agreement with previous investigations of
optically selected samples. We calculate bolometric corrections, $\kbol$, for
the whole sample using hard X-ray luminosities ($\Lhard$), and the Eddington
ratios for a subsample of 150 objects for which black hole mass estimates are
available. We confirm the trend of increasing bolometric correction with
increasing Eddington ratio as proposed in previous works. A tight correlation
is found between $\alphaox$ and $\kbol$, which can be used to estimate accurate
bolometric corrections using only optical and X-ray data. We find a significant
correlation between $\alphaox$ and Eddington ratio, in which $\alphaox$
increases for increasing Eddington ratios.
