An integer d is a fundamental discriminant if it is not equal to 1, not divisible by any square of any odd prime, and satisfies or . FundamentalDiscriminant[d] in the Mathematica package NumberTheory`NumberTheoryFunctions` (available starting with Version 5.0 and which can be loaded using the command <<NumberTheory`) will test if an integer d is a fundamental discriminant.

The first few positive fundamental discriminants are 5, 8, 12, 13, 17, 21, 24, 28, 29, 33, ... (Sloane's A003658). Similarly, the first few negative fundamental discriminants are -3, -4, -7, -8, -11, -15, -19, -20, -23, -24, -31, ... (Sloane's A003657).

 

Class Number, Dirichlet L-Series, Discriminant