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Core ellipticals, which are massive early-type galaxies with almost constant inner surface brightness profiles, are the result of dry mergers. During these events, a binary black hole (BBH) is formed, destroying the original cuspy central regions of the merging objects and scattering stars that are not on tangential orbits. The size of the emerging core correlates with the mass of the finally merged black hole (BH). Therefore, the determination of the size of the core of massive early-type galaxies provides key insights not only into the mass of the black hole, but also into the origin and evolution of these objects. In this work, we report the first Euclid-based dynamical mass determination of a supermassive black hole (SMBH). To this end, we study the center of NGC 1272, the second most luminous elliptical galaxy in the Perseus cluster, combining the Euclid Visible Camera (VIS) photometry coming from the Early Release Observations (EROs) of the Perseus cluster with the Visible Integral-field Replicable Unit Spectrograph (VIRUS) spectroscopic observations at the Hobby-Eberly Telescope (HET). The core of NGC 1272 is detected on the Euclid VIS image. Its size is 1.​​″29 ± 0.​​″07 or 0.45 kpc, which was determined by fitting PSF-convolved core-Sérsic and Nuker-law functions. We deproject the surface brightness profile of the galaxy, finding that the galaxy is axisymmetric and nearly spherical. The two-dimensional stellar kinematics of the galaxy is measured from the VIRUS spectra by deriving optimally regularized non-parametric line-of-sight velocity distributions. Dynamical models of the galaxy are constructed using our axisymmetric and triaxial Schwarzschild codes. We measure a BH mass of (5 ± 3)×109 M⊙, which is in line with the expectation from the MBH − rb correlation, but is eight times larger than predicted by the MBH − σ correlation (at 1.8σ significance). The core size, rather than the velocity dispersion, allows one to select galaxies harboring the most massive BHs. The spatial resolution, wide area coverage, and depth of the Euclid (Wide and Deep) surveys allow us to find cores of passive galaxies that are larger than 2 kpc at a redshift of up to 1.