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We explore the influence of two different polarizations of quantum oxygen vibrations on the spacial symmetry of the bound magnetic bipolaron in the context of the tJ model by using exact diagonalization within a limited functional space. Linear as well as quadratic electron phonon coupling to transverse polarization stabilize d-wave symmetry. The existence of a magnetic background is essential for the formation of a d-wave bipolaron state. With increasing linear electron phonon coupling to longitudinal polarization the symmetry of a d-wave bipolaron state changes to a p-wave. Bipolaron develops a large anisotropic effective mass.