On the computation of the class numbers of some cubic fields

Abstract

Class numbers are calculated for cubic fields of the form x3+12Ax−12=0, A>0, for 1≤a≤17, and for some other values of A. These fields have a known unit, which under certain conditions is the fundamental unit, and are important in studying the Diophantine Equation x3+y3+z3=3.

Keywords

• class numbers
• cubic fields
• Diophantine equation.