  We investigate the coronal magnetic energy and helicity budgets of ten solar
ARs, around the times of large flares. In particular, we are interested in a
possible relation of the derived quantities to the particular type of the
flares that the AR produces, i.e., whether they are associated with a CME or
they are confined. Using an optimization approach, we employ time series of 3D
nonlinear force-free magnetic field models of ten ARs, covering a time span of
several hours around the time of occurrence of large solar flares (GOES class
M1.0 and larger). We subsequently compute the 3D magnetic vector potentials
associated to the model 3D coronal magnetic field using a finite-volume method.
This allows us to correspondingly compute the coronal magnetic energy and
helicity budgets, as well as related (intensive) quantities such as the
relative contribution of free magnetic energy, $E_{\mathrm{F}}/{E}$ (energy
ratio), the fraction of non-potential (current-carrying) helicity,
$|H_{\mathrm{J}}|/|{H_{V}}|$ (helicity ratio), and the normalized
current-carrying helicity, $|H_{\mathrm{J}}|/{\phi^{\prime}}^{2}$. The total
energy and helicity budgets of flare-productive ARs (extensive parameters)
cover a broad range of magnitudes, with no obvious relation to the eruptive
potential of the individual ARs, i.e., whether or not a CME is produced in
association with the flare. The intensive eruptivity proxies,
$E_{\mathrm{F}}/{E}$ and $|H_{\mathrm{J}}|/|{H_{V}}|$, and
$|H_{\mathrm{J}}|/{\phi^{\prime}}^{2}$, however, seem to be distinctly
different for ARs that produced CME-associated large flares compared to those
which produced confined flares. For the majority of ARs in our sample, we are
able to identify characteristic pre-flare magnitudes of the intensive
quantities, clearly associated to subsequent CME-productivity.
