The maximum number density of Active Galactic Nuclei (AGNs), as deduced from X-ray studies, occurs at z >= 1, with lower luminosity objects peaking at smaller redshifts. Optical studies lead to a different evolutionary behaviour, with a number density peaking at z ~ 2 independently of the intrinsic luminosity, but this result is limited to active nuclei brighter than the host galaxy. A selection based on optical variability can detect low luminosity AGNs (LLAGNs), where the host galaxy light prevents the identification by non-stellar colours. The authors collected X-ray data in a field where there existed an optically-selected sample of "variable galaxies", i.e. variable objects with diffuse appearance, in order to investigate the X-ray and optical properties of the population of AGNs, particularly of low luminosity ones, where the host galaxy is visible. They observed a field of ~ 0.2 deg² in the Selected Area 57, for 67 ks with XMM-Newton. They correlated the list of detected X-ray sources with a photographic survey of SA 57, complete to B_J ~ 23 and with the available spectroscopic data. They obtained a catalog of 140 X-ray sources to limiting fluxes of 5 x 10^-16 and 2 x 10^-15 erg/cm²/s in the 0.5 - 2 keV and 2 - 10 keV bands, respectively, 98 of which are identified in the optical bands. The X-ray detection of part of the variability-selected candidates confirms their AGN nature. Diffuse variable objects populate the low luminosity side of the sample. Only 25/44 optically-selected QSOs are detected in X-rays. 15% of all QSOs in the field have X/O < 0.1. Additional information on the likely optical counterparts of 98 of the X-ray sources is available in the reference paper, e.g., in Table 3. This table was created by the HEASARC in September 2007 based on CDS table J/A+A/469/1211 file table2.dat. This is a service provided by NASA HEASARC .