see paper for full list of authors ; International audience ; Shape parameters of a weakly deformed ground-state band and highly deformed slightly triaxial sideband in Ca42 were determined from E2 matrix elements measured in the first low-energy Coulomb excitation experiment performed with AGATA. The picture of two coexisting structures is well reproduced by new state-of-the-art large-scale shell model and beyond-mean-field calculations. Experimental evidence for superdeformation of the band built on 0+2 has been obtained and the role of triaxiality in the A∼40 mass region is discussed. Furthermore, the potential of Coulomb excitation as a tool to study superdeformation has been demonstrated for the first time.