We study the physical properties of 216 z ~ 2.1 LAEs discovered in an ultra-deep narrow-band MUSYC image of the ECDF-S. We fit their stacked Spectral Energy Distribution (SED) using Charlot & Bruzual templates. We consider star formation histories parametrized by the e-folding time parameter tau, allowing for exponentially decreasing (tau>0), exponentially increasing (tau<0), and constant star formation rates. These LAEs are characterized by best fit parameters and 68% confidence intervals of log(M_*/M_sun)=8.6[8.4-9.1], E(B-V)=0.22[0.00-0.31], tau=-0.02[(-4)-18] Gyr, and age_ SF=0.018[0.009-3] Gyr. Thus, we obtain robust measurements of low stellar mass and dust content, but we cannot place meaningful constraints on the age or star formation history of the LAEs. We also calculate the instantaneous SFR to be 35[0.003-170] M_sun/yr, with its average over the last 100 Myr before observation giving <SFR>_100=4[2-30] M_sun/yr. When we compare the results for the same star formation history, LAEs at z~2.1 are dustier and show higher instantaneous SFRs than z~3.1 LAEs, while the observed stellar masses of the two samples seem consistent. LAEs appear to occupy the low-mass end of the distribution of star forming galaxies at z~2. We perform SED fitting on several sub-samples selected based on photometric properties and find that LAE sub-samples at z~2.1 exhibit heterogeneous properties. The IRAC-bright, UV-bright and red LAEs have the largest stellar mass and dust reddening. The UV-faint, IRAC-faint, and high equivalent width LAE sub-samples appear less massive (<10^9 M_sun) and less dusty, with E(B-V) consistent with zero.
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