We present a multi-wavelength study of the low-mass X-ray binary Sco X-1 using Kepler K2 optical data and Fermi GBM and MAXI X-ray data. We recover a clear sinusoidal orbital modulation from the Kepler data. Optical fluxes are distributed bimodally around the mean orbital light curve, with both high and low states showing the same modulation. The high state is broadly consistent with the flaring branch of the Z diagram and the low state with the normal branch. We see both rapid optical flares and slower dips in the high state, and slow brightenings in the low state. High state flares exhibit a narrow range of amplitudes with a striking cut-off at a maximum amplitude. Optical fluxes correlate with X-ray fluxes in the high state, but in the low state they are anti-correlated. These patterns can be seen clearly in both flux-flux diagrams and cross-correlation functions and are consistent between MAXI and GBM. The high state correlation arises promptly with at most a few minutes lag. We attribute this to thermal reprocessing of X-ray flares. The low state anti-correlation is broader, consistent with optical lags of between zero and 3 ~min, and strongest with respect to high energy X-rays. We suggest that the decreases in optical flux in the low state may reflect decreasing efficiency of disc irradiation, caused by changes in the illumination geometry. These changes could reflect the vertical extent or covering factor of obscuration or the optical depth of scattering material.
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