Let a module M in an integral domain D_1 for R(sqrt(D)) be expressed using a two-element basis as M = [ξ_1, ξ_2], where ξ_1 and ξ_2 are in D_1. Then the different of the module is defined as Δ = Δ(M) = left bracketing bar ξ_1 | ξ_2 ξ_1^, | ξ_2^, right bracketing bar = ξ_1 ξ_2^, - ξ_1^, ξ_2 and the discriminant is defined as the square of the different. For imaginary quadratic fields Q(sqrt(n)) (with n<0), the discriminants are given in the following table.

different | fundamental discriminant | module