This research studied the nuclear deformation of the ⁶⁵Cu isotope by employing advanced shell model calculations alongside the Hartree-Fock approximation within the framework of the fp-shell model space. A detailed analysis of inelastic electron scattering was conducted, focusing on both the longitudinal and transverse form factors, as well as excitation energies. These calculations were performed using the shell model, incorporating elements of the one-body transition density matrix and leveraging the full fp-shell space to facilitate the JUN45 interaction. Various theoretical wave functions, including the harmonic oscillator (HO), Skyrme Hartree- Fock (SLy4), and Wood-Saxon (WS) potentials, were applied, and their results were meticulously compared with experimental data. Furthermore, the potential energy surfaces were explored as a function of quadrupole deformation parameters through the SLy5 parameterization within the Hartree-Fock approach. Notably, the shell model computations were executed using the NushellX@MSU code without imposing any constraints on the model space, offering a comprehensive and unconstrained insight into the nuclear structure dynamics of ⁶⁵Cu. Finally, the calculated results were compared with the available experimental data.