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~ { } { L _ { [ 2 - 10 ] keV } } \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 \alpha _ { ox } 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 \alpha _ { ox } and L _ { 2500 \text { \AA } } is found , in agreement with previous investigations of optically selected samples .
We calculate bolometric corrections , k _ { bol } , for the whole sample using hard X-ray luminosities ( { L _ { [ 2 - 10 ] keV } } ) , 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 \alpha _ { ox } and k _ { bol } , which can be used to estimate accurate bolometric corrections using only optical and X-ray data .
We find a significant correlation between \alpha _ { ox } and Eddington ratio , in which \alpha _ { ox } increases for increasing Eddington ratios .