We use the Legendre invariant formalism of geometrothermodynamics toinvestigate the geometric properties of the equilibrium space of a sphericallysymmetric phantom black hole with electric charge and dilaton. We find that atcertain points of the equilibrium space, the thermodynamic curvature ischaracterized by the presence of singularities that are interpreted as phasetransitions. We also investigate the phase transition structure by using thestandard approach of black hole thermodynamics based upon the analysis of theheat capacity and response functions. We show compatibility between the twoapproaches. In addition, a new type of phase transition is found which is dueto the presence of phantom energy and corresponds to a transition between blackhole states with different stability properties.
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