  The theoretical concept that braided magnetic field lines in the solar corona
may dissipate a sufficient amount of energy to account for the brightening
observed in the active-region corona, has been substantiated by high-resolution
observations only recently. From the analysis of coronal images obtained with
the High Resolution Coronal Imager, first observational evidence of the
braiding of magnetic field lines was reported by Cirtain et al. 2013 (hereafter
CG13). We present nonlinear force-free reconstructions of the associated
coronal magnetic field based on vector SDO/HMI magnetograms. We deliver
estimates of the free magnetic energy associated to a braided coronal
structure. Our model results suggest (~100 times) more free energy at the
braiding site than analytically estimated by CG13, strengthening the
possibility of the active-region corona being heated by field line braiding. We
were able to assess the coronal free energy appropriately by using vector field
measurements and attribute the lower energy estimate of CG13 to the
underestimated (by a factor of 10) azimuthal field strength. We also quantify
the increase of the overall twist of a flare-related flux rope which had been
claimed by CG13. From our models we find that the overall twist of the flux
rope increased by about half a turn within twelve minutes. Unlike another
method, to which we compare our results to, we evaluate the winding of the flux
rope's constituent field lines around each other purely based on their modeled
coronal 3D field line geometry -- to our knowledge for the first time.
