Upper panel: Kepler light curve of LHS 6343 phased with a period of 12.71 days (black dots). The transits have been removed leaving a gap centred on phase 0. The sinusoidal best fit applied to calculate the phase lead (~98°) is plotted as a red solid line. Lower panel: the vertical scale is zoomed in and the Kepler data are plotted in 0.025 phase bins to highlight the deviations from a sinusoidal shape which cause the appearance of harmonics of the main frequency in the periodogram of Fig. 2. Error bars are 1-σ deviations of the binned flux values.