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As part of the mm-Wave Interferometric Survey of Dark Object Masses (WISDOM)project, we present an estimate of the mass of the supermassive black hole(SMBH) in the nearby fast-rotating early-type galaxy NGC4697. This estimate isbased on Atacama Large Millimeter/submillimeter Array (ALMA) cycle-3observations of the 12CO(2-1) emission line with a linear resolution of 29 pc(0.53"). We find that NGC4697 hosts a small relaxed central molecular gas discwith a mass of 1.6x10^7 Msun, co-spatial with the obscuring dust disc visiblein optical Hubble Space Telescope (HST) imaging. We also resolve thermal 1mmcontinuum emission from the dust in this disc. NGC4697 is found to have a verylow molecular gas velocity dispersion, $\sigma_{gas}=1.65^{+0.68}_{-0.65}$km/s. This seems to be partially because the giant molecular cloud massfunction is not fully sampled, but other mechanisms such as chemicaldifferentiation in a hard radiation field or morphological quenching also seemto be required. We detect a Keplerian increase of the rotation of the moleculargas in the very centre of NGC4697, and use forward modelling of the ALMA datacube in a Bayesian framework with the KINematic Molecular Simulation (KinMS)code to estimate a SMBH mass of ($1.3_{-0.17}^{+0.18})\times10^8$ Msun and ani-band mass-to-light ratio of $2.14_{-0.05}^{+0.04}$ Msun/Lsun (at the 99%confidence level). Our estimate of the SMBH mass is entirely consistent withprevious measurements from stellar kinematics. This increases confidence in thegrowing number of SMBH mass estimates being obtained in the ALMA era.

WISDOM Project - II: Molecular gas measurement of the supermassive black hole mass in NGC4697