We present spectroscopic observations of the quiescent black hole binary A0620-00 with the the 6.5-m Magellan Clay telescope at Las Campanas Observatory. We measure absorption-line radial velocities of the secondary and make the most precise determination to date (K2 = 435.4 +/- 0.5 km/s). By fitting the rotational broadening of the secondary, we refine the mass ratio to q = 0.060 +/- 0.004; these results, combined with the orbital period, imply a minimum mass for the compact object of 3.10 +/- 0.04 Msun. Although quiescence implies little accretion activity, we find that the disc contributes 56 +/- 7 per cent of the light in B and V, and is subject to significant flickering. Doppler maps of the Balmer lines reveal bright emission from the gas stream-disc impact point and unusual crescent-shaped features. We also find that the disc centre of symmetry does not coincide with the predicted black hole velocity. By comparison with SPH simulations, we identify this source with an eccentric disc. With high S/N, we pursue modulation tomography of H-alpha and find that the aforementioned bright regions are strongly modulated at the orbital period. We interpret this modulation in the context of disc precession, and discuss cases for the accretion disc evolution.
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