  We combine photometry of Eris from a 6-month campaign on the Palomar 60-inch
telescope in 2015, a 1-month Hubble Space Telescope WFC3 campaign in 2018, and
Dark Energy Survey data spanning 2013--2018 to determine a light curve of
definitive period $15.771\pm 0.008$~days (1-$\sigma$ formal uncertainties),
with nearly sinusoidal shape and peak-to-peak flux variation of 3\%. This is
consistent at part-per-thousand precision with the $P=15.78590\pm0.00005$~day
period of Dysnomia's orbit around Eris, strengthening the recent detection of
synchronous rotation of Eris by Szakats et al (2022) with independent data.
Photometry from Gaia is consistent with the same light curve. We detect a slope
of $0.05\pm0.01$~mag per degree of Eris' brightness with respect to
illumination phase, intermediate between Pluto's and Charon's values.
Variations of $0.3$~mag are detected in Dysnomia's brightness, plausibly
consistent with a double-peaked light curve at the synchronous period. The
synchronous rotation of Eris is consistent with simple tidal models initiated
with a giant-impact origin of the binary, but is difficult to reconcile with
gravitational capture of Dysnomia by Eris.
