  We study the total and baryonic mass distributions of the deflector SDSS
J0100+1818 through a full strong lensing analysis. The system is composed by an
ultra-massive early-type galaxy at $z=0.581$, with total stellar mass of $(1.5
\pm 0.3) 10^{12}$ M$_\odot$ and stellar velocity dispersion of ($450 \pm 40$)
km s$^{-1}$, surrounded by ten multiple images of three background sources, two
of which spectroscopically confirmed at $z=1.880$. We take advantage of
high-resolution HST photometry and VLT/X-shooter spectroscopy to measure the
positions of the multiple images and perform a strong lensing study with the
software GLEE. We test different total mass profiles for the lens and model the
background sources first as point-like and then as extended objects. We
successfully predict the positions of the observed multiple images and
reconstruct over approximately 7200 HST pixels the complex surface brightness
distributions of the sources. We measure the cumulative total mass profile of
the lens and find a total mass value of $(9.1 \pm 0.1) 10^{12}$ M$_\odot$,
within the Einstein radius of approximately 42 kpc, and stellar-over-total mass
fractions ranging from ($49 \pm 12$)%, at the half-light radius ($R_e = 9.3$
kpc) of the lens galaxy, to ($10 \pm 2$)%, in the outer regions ($R = 70$kpc).
These results suggest that the baryonic mass component of SDSS J0100+1818 is
very concentrated in its core and that the lens early-type galaxy/group is
immersed in a massive dark matter halo. This is consistent with what found in
other ultra-high mass candidates at intermediate redshift. We measure also the
physical sizes of the distant sources, resolving them down to a few hundreds of
parsec. Finally, we quantify and discuss a relevant source of systematic
uncertainties on the reconstructed sizes of background galaxies, associated to
the adopted lens total mass model.
