(abridged) Aims: RXS J113155.4-123155 (z=0.66) is a quadruply imaged lensed quasar with a resolved Einstein Ring. The goal of this paper is to provide a full characterization of this system, and more particularly accurate astrometry and photometry. Method: Visible and near-infrared imaging observations of RXS J113155.4-123155 were carried out at various epochs using several ground based telescopes and the HST. The frames have been deconvolved using the MCS algorithm. A Singular Isothermal Ellipsoid (SIE) + external shear has been used to model the lensing galaxy potential. Results: MCS deconvolution enables us to separate the flux of the QSO (point-like images) from that of its host galaxy and to accurately track the flux variations of the point-like images in various filters. The deconvolved frames unveil several multiply imaged structures in the Einstein ring and an unidentified object in the vicinity of the lensing galaxy. We discuss the lightcurves and the chromatic flux ratio variations and deduce that both intrinsic variability and microlensing took place during a span longer than one year. We demonstrate that microlensing may easily account for the so called anomalous flux ratios presented in the discovery paper. However, the observed flux ratios are still poorly reproduced when modeling the lens potential with a SIE+shear. We argue that this disagreement can hardly be explained by milli-lensing caused by substructures in the lensing galaxy. A solution proposed in Paper II consists in a more complex lens model including an octupole term to the lens gravitational potential.
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