NumberFieldClassNumber

NumberFieldClassNumber[θ] gives the class number for the algebraic number field ℚ[θ] generated by θ.

Examples

Class number for a quadratic field:

NumberFieldClassNumber[Sqrt[-5]]
(* 2 *)

A field with class number 1:

NumberFieldClassNumber[Sqrt[2]]
(* 1 *)

Cyclotomic field:

NumberFieldClassNumber[Exp[2 Pi I/7]]

Please visit the official Wolfram Language Reference for more details.