  We investigate scaling relations between the dark matter (DM) halo model
parameters for a sample of intermediate redshift early - type galaxies (ETGs)
resorting to a combined analysis of Einstein radii and aperture velocity
dispersions. Modeling the dark halo with a Navarro - Frenk - White profile and
assuming a Salpeter initial mass function (IMF) to estimate stellar masses, we
find that the column density ${\cal{S}}$ and the Newtonian acceleration within
the halo characteristic radius $r_s$ and effective radius $R_{eff}$ are not
universal quantities, but correlate with the luminosity $L_V$, the stellar mass
$M_{\star}$ and the halo mass $M_{200}$, contrary to recent claims in the
literature. We finally discuss a tight correlation among the DM mass
$M_{DM}(R_{eff})$ within the effective radius $R_{eff}$, the stellar mass
$M_{\star}(R_{eff})$ and $R_{eff}$ itself. The slopes of the scaling relations
discussed here strongly depend, however, on the DM halo model and the IMF
adopted so that these ingredients have to be better constrained in order to
draw definitive conclusions on the DM scaling relations for ETGs.
