In 1894, Henry Wente discovered the Wente torus, an immersed torus of constant (but not zero) mean curvature. Such constant mean curvature (CMC) surfaces are counterexamples to Hopf's conjecture that a sphere is the only closed surface with constant mean curvature that is compact [1]. The set of all symmetric tori is in one-to-one correspondence with the set of reduced fractions ; each corresponds to a symmetric Wente torus labeled as [2].