We present a study of the orbits of the triple system LHS1070, with the aim to determine individual masses of its components. Sixteen new relative astrometric positions of the three components in the K band were obtained with NACO at the VLT, Omega CASS at the 3.5m telescope on Calar Alto, and other high-spatial-resolution instruments. We combine them with data from the literature and fit orbit models to the dataset. We derive an improved fit for the orbit of LHS1070B and C around each other, and an estimate for the orbit of B and C around A. The orbits are nearly coplanar, with a misalignment angle of less than 10{deg}. The masses of the three components are M_A = 0.13 - 0.16 Msun, M_B = 0.077+/-0.005 Msun, and M_C = 0.071+/-0.004 Msun. Therefore, LHS1070C is certainly, and LHS1070B probably a brown dwarf. Comparison with theoretical isochrones shows that LHS1070A is either fainter or more massive than expected. One possible explanation would be that it is a binary. However, the close companion reported previously could not be confirmed.
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