  We take advantage of new 100-hour Spitzer/IRAC observations available for
MACS0647-JD, a strongly lensed $z\approx11$ galaxy candidate, to provide
improved constraints on its physical properties. Probing the physical
properties of galaxies at $z>8$ is challenging due to the inherent faintness of
such sources and the limited wavelength coverage available. Thanks to the high
$\approx$2-6$\times$ lensing magnification of the multiple images of
MACS0647-JD, we can use the sensitive Spitzer/IRAC data to probe the rest-frame
optical fluxes of MACS0647-JD and investigate its physical properties including
the age and the stellar mass. In deriving Spitzer/IRAC fluxes for MACS0647-JD,
great care is taken in coping with the impact of three bright ($\approx$8-16
mag) stars in our field to ensure robust results. Assuming a constant star
formation rate, the age, stellar mass, and rest-frame UV slope we estimate for
MACS0647-JD based on a stack of the photometry are log$_{10}$(age/yr) =
8.6$^{+0.1}_{-2.1}$, log$_{10}$(M$_{*}$/M$_{\odot}$) = 9.1$^{+0.2}_{-1.4}$, and
$\beta = -$1.3$\pm$0.6, respectively. We compare our results with expectations
from the EAGLE simulation and find that MACS0647-JD has properties consistent
with corresponding to the most massive and rapidly star-forming galaxies in the
simulation. We also find that its radius, 105$\pm$28 pc, is a factor of
$\approx$2 smaller than the mean size in a separate simulation project DRAGONS.
Interestingly enough, the observed size is similar to the small sizes seen in
very low-luminosity $z\approx$6-10 galaxies behind lensing clusters.
