We present the JHKs light curves for the double-lined eclipsing binary 2MASS J05352184-0546085, in which both components are brown dwarfs. We analyze these light curves with the published Ic-band light curve and radial velocities to provide refined measurements of the systems physical parameters. The component masses and radii are here determined with an accuracy of ~6.5% and ~1.5%, respectively. We confirm the previous surprising finding that the primary brown dwarf has a cooler effective temperature than its companion. Next, we perform a detailed study of the variations in the out-of-eclipse phases of the light curves to ascertain the properties of any inhomogeneities on the surfaces of the brown dwarfs. Our analysis reveals two low-amplitude periodic signals, one attributable to the rotation of the primary (with a period of 3.293+/-0.001 d) and the other to that of the secondary (14.05+/-0.05 d). Finally, we explore the effects on the derived physical parameters of the system when spots are included in the modeling. The observed low-amplitude rotational modulations are well fit by cool spots covering a small fraction of their surfaces. To mimic the observed ~200 K suppression of the primarys temperature, our model requires that the primary possess a very large spot coverage fraction of ~65%. Altogether, a spot configuration in which the primary is heavily spotted while the secondary is lightly spotted can explain the apparent temperature reversal and can bring the temperatures of the brown dwarfs into agreement with the predictions of theoretical models.
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