Résumé
The goal of this work is to obtain a Hubble constant estimate through the study of the quadruply lensed, variable QSO SDSSJ1433+6007. To achieve this we combine multi-filter, archival $\textit{HST}$ data for lens modelling and a dedicated time delay monitoring campaign with the 2.1m Fraunhofer telescope at the $\textit{Wendelstein Observatory}$. The lens modelling is carried out with the public $\texttt{lenstronomy}$ Python package for each of the filters individually. Through this approach, we find that the data in one of the $\textit{HST}$ filters (F160W) contain a light contaminant, that would, if remained undetected, have severely biased the lensing potentials and thus our cosmological inference. After rejecting these data we obtain a combined posterior for the Fermat potential differences from the lens modelling in the remaining filters (F475X, F814W, F105W and F140W) with a precision of $\sim6\%$. The analysis of the $\textit{g'}$-band Wendelstein light curve data is carried out with a free-knot spline fitting method implemented in the public Python $\texttt{PyCS3}$ tools. The precision of the time delays between the QSO images has a range between 7.5 and 9.8$\%$ depending on the brightness of the images and their time delay. We then combine the posteriors for the Fermat potential differences and time delays. Assuming a flat $Λ$CDM cosmology, we infer a Hubble parameter of $H_0=76.6^{+7.7}_{-7.0}\frac{\mathrm{km}}{\mathrm{Mpc\;s}}$, reaching $9.6\%$ uncertainty for a single system.