Summary: We compute the partition function of four-dimensional abelian gauge theory on a general four-torus \(T^4\) with flat metric using Dirac quantization. In addition to an \(\mathrm{ SL}(4,\mathcal Z)\) symmetry, it possesses \(\mathrm{ SL}(2,\mathcal Z)\) symmetry that is electromagnetic S-duality. We show explicitly how this \(\mathrm{ SL}(2,\mathcal Z)\) S-duality of the \(4d\) abelian gauge theory has its origin in symmetries of the \(6d\) \((2,0)\) tensor theory, by computing the partition function of a single fivebrane compactified on \(T^2\) times \(T^4\), which has \(\mathrm{ SL}(2,\mathcal Z)\times\mathrm{ SL}(4,\mathcal Z)\) symmetry. If we identify the couplings of the abelian gauge theory \(\tau=\frac{\theta}{2\pi}+i\frac{4\pi} {e^2}\) with the complex modulus of the \(T^2\) torus \(\tau=\beta^2+i\frac{R_1} {R_2}\), then in the small \(T^2\) limit, the partition function of the fivebrane tensor field can be factorized, and contains the partition function of the \(4d\) gauge theory. In this way the \(\mathrm{ SL}(2,\mathcal Z)\) symmetry of the 6d tensor partition function is identified with the \(S\)-duality symmetry of the 4d gauge partition function. Each partition function is the product of zero mode and oscillator contributions, where the \(\mathrm{ SL}(2,\mathcal Z)\) acts suitably. For the 4d gauge theory, which has a Lagrangian, this product redistributes when using path integral quantization.