We investigate weakly coupled quarter-filled ladders with model parameters relevant for NaV_2O_5 using density-matrix renormalization group calculations on an extended Hubbard model coupled to the lattice. NaV2O5 exhibits super-antiferroelectric charge order with a zigzag pattern on each ladder. We show that this order, with a periodicity of four ladders, causes a spin dimerization along the ladder and a corresponding spin gap of the same magnitude as that observed experimentally. The spin gap

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... s destroyed again at large charge order due to a restructuring of the spins. An analysis of an effective spin model predicts a re-creation of the gap by inter-ladder singlets when the charge order increases further.