We present a numerical method to estimate the lensing parameters and the Hubble constant H _ { 0 } from quadruply imaged gravitational lens systems .
The lens galaxy is modeled using both separable deflection potentials and constant mass - to - light ratio profiles , while possible external perturbations have been taken into account introducing an external shear .
The model parameters are recovered inverting the lens and the time delay ratio equations and imposing a set of physically motivated selection criteria .
We investigate correlations among the model parameters and the Hubble constant .
Finally , we apply the codes to the real lensed quasars PG 1115+080 and RX J0911+0551 , and combine the results from these two systems to get H _ { 0 } = 56 { \pm } 23 { km s ^ { -1 } Mpc ^ { -1 } } .
In addition , we are able to fit to the single systems a general elliptical potential with a non fixed angular part , and then we model the two lens systems with the same potential and a shared H _ { 0 } : in this last case we estimate H _ { 0 } = 49 _ { -11 } ^ { +6 } \textrm { Km } \textrm { s } ^ { -1 } \textrm { Mpc } ^ { -1 } .