Ultra-hot Jupiters present a unique opportunity to understand the physics and chemistry of planets, their atmospheres, and interiors at extreme conditions. WASP-12 b stands out as an archetype of this class of exoplanets, with a close-in orbit around its star that results in intense stellar irradiation and tidal effects. We performed comprehensive analyses of the transits, occultations, and phase curves of WASP-12b by combining new CHEOPS observations with previous TESS and Spitzer data. The planet is modeled as a triaxial ellipsoid parameterized by the second-order fluid Love number of the planet, h_2_, which quantifies its radial deformation and provides insight into the interior structure. We measure the tidal deformation of WASP-12b and estimate a Love number of h_2_=1.55_-0.49_^+0.45^ (at 3.2{sigma}) from its phase curve. We measure occultation depths of 333+/-24}ppm and 493+/-29ppm in the CHEOPS and TESS bands, respectively, while the nightside fluxes are consistent with zero, and also marginal eastward phase offsets. Our modeling of the dayside emission spectrum indicates that CHEOPS and TESS probe similar pressure levels in the atmosphere at a temperature of ~2900K. We also estimate low geometric albedos of A_g_=0.086+/-0.017 and A_g_=0.01+/-0.023 in the CHEOPS and TESS passbands, respectively which suggest an absence of reflective clouds in the high-temperature dayside of the planet. The CHEOPS occultations do not show strong evidence for variability in the dayside atmosphere of the planet at the median occultation depth precision of 120ppm attained. Finally, combining the new CHEOPS timings with previous measurements refines the precision of the orbital decay rate by 12% to a value of ~30.23+/-0.82ms/yr, resulting in a modified stellar tidal quality factor of Q'*=1.70+/-0.14x10^^.