The electron interaction energy of two interacting electrons in a parabolic quantum dot is investigated under the influence of a magnetic field. The ground state and low-lying excited states are calculated as a function of magnetic field with the electron-electron Coulomb interaction taken into account. The binding energies of two electrons in a parabolic quantum dot are investigated. Oscillator strength of interacting electrons for different magnetic field strengths has been calculated. We find that a ground state transition (singlet-triplet state transition) occurs in the weak confinement as well as in strong confinement.