Many astronomical optical systems have the disadvantage of generating curved focal planes requiring flattening optical elements to project the corrected image on flat detectors. The use of these designs in combination with a classical flat sensor implies an overall degradation of throughput and system performances to obtain the proper corrected image. With the recent development of curved sensor this can be avoided. This new technology has been gathering more and more attention from a very broad community, as the potential applications are multiple: from low-cost commercial to high impact scientific systems, to mass-market and on board cameras, defense and security, and astronomical community. We describe here the first concave curved CMOS detector developed within a collaboration between CNRS-LAM and CEA-LETI. This fully-functional detector 20 Mpix (CMOSIS CMV20000) has been curved down to a radius of $R_c$ =150 mm over a size of 24x32 mm$^2$. We present here the methodology adopted for its characterization and describe in detail all the results obtained. We also discuss the main components of noise, such as the readout noise, the fixed pattern noise and the dark current. Finally we provide a comparison with the flat version of the same sensor in order to establish the impact of the curving process on the main characteristics of the sensor.