For \\alpha a positive irrational, we consider the uniform subalgebra A_\\alpha of C(T^2) consisting of those functions f satisfying \\hat{f}(m,n)=0 whenever m+n\\alpha<0. For positive irrationals \\alpha, \\beta, we determine when A_\\alpha and A_\\beta are isometrically isomorphic. Furthermore, we describe the group Aut(A_\\alpha) of isometric automorphisms of A_\\alpha. Finally we show how an explicit representation of Aut(A_\\alpha) can be derived from Pell's equations.
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