The gravitational lens SDSS J1148+1930 , also known as the Cosmic Horseshoe , is one of the biggest and of the most detailed Einstein rings ever observed .
We use the forward reconstruction method implemented in the lens fitting code Lensed to investigate with great detail the properties of the lens and of the background source .
We model the lens with different mass distributions , focusing in particular on the determination of the slope of the dark matter component .
The inherent degeneracy between the lens slope and the source size can be broken when we can isolate separate components of each lensed image , as in this case .
For an elliptical power law model , \kappa ( r ) \sim r ^ { - t } , the results favour a flatter-than-isothermal slope with a maximum-likelihood value t = 0.08 .
Instead , when we consider the contribution of the baryonic matter separately , the maximum-likelihood value of the slope of the dark matter component is t = 0.31 or t = 0.44 , depending on the assumed Initial Mass Function .
We discuss the origin of this result by analysing in detail how the images and the sources change when the slope t changes .
We also demonstrate that these slope values at the Einstein radius are not inconsistent with recent forecast from the theory of structure formation in the \Lambda CDM model .