Context. 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. Aims. The goals are to measure the planet's tidal deformation, atmospheric properties, and also to refine its orbital decay rate. Methods. 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 was modeled as a triaxial ellipsoid parameterized by the second-order fluid Love number of the planet, h2, which quantifies its radial deformation and provides insight into the interior structure. Results. We measured the tidal deformation of WASP-12b and estimated a Love number of h2 = 1.55- 0.49+0.45 (at 3.2σ) from its phase curve. We measured occultation depths of 333 ± 24 ppm and 493 ± 29 ppm 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 ~2900 K. We also estimated low geometric albedos of Ag = 0.086 ± 0.017 and Ag = 0.01 ± 0.023 in the CHEOPS and TESS passbands, respectively, suggesting the 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 120 ppm 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 ± 0.82 ms yr- 1, resulting in a modified stellar tidal quality factor of Q′∗ = 1.70 ± 0.14 × 105. Conclusions. WASP-12 b becomes the second exoplanet, after WASP-103b, for which the Love number has been measured from the effect of tidal deformation in the light curve. However, constraining the core mass fraction of the planet requires measuring h2 with a higher precision. This can be achieved with high signal-to-noise observations with JWST since the phase curve amplitude, and consequently the induced tidal deformation effect, is higher in the infrared.