Ultra-hot Jupiters present a unique opportunity to understand the physics and chemistry of planets at extreme conditions. WASP-12b stands out as an archetype of this class of exoplanets. 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 to measure the planet's tidal deformation, atmospheric properties, and orbital decay rate. The planet was modeled as a triaxial ellipsoid parameterized by the second-order fluid Love number, \(h_2\), which quantifies its radial deformation and provides insight into the interior structure. We measured the tidal deformation of WASP-12b and estimated a Love number of \(h_2=1.55_{-0.49}^{+0.45}\) (at 3.2\(\sigma\)) from its phase curve. We measured occultation depths of \(333\pm24\)ppm and \(493\pm29\)ppm in the CHEOPS and TESS bands, respectively, while the dayside emission spectrum indicates that CHEOPS and TESS probe similar pressure levels in the atmosphere at a temperature of 2900K. We also estimated low geometric albedos of \(0.086\pm0.017\) and \(0.01\pm0.023\) in the CHEOPS and TESS passbands, respectively, suggesting the absence of reflective clouds in the dayside of the WASP-12b. The CHEOPS occultations do not show strong evidence for variability in the dayside atmosphere of the planet. Finally, we refine the orbital decay rate by 12% to a value of -30.23\(\pm\)0.82 ms/yr. WASP-12b becomes the second exoplanet, after WASP-103b, for which the Love number has been measured (at 3\(sigma\)) from the effect of tidal deformation in the light curve. However, constraining the core mass fraction of the planet requires measuring \(h_2\) 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.