Discriminant and integral basis of sextic fields defined by x(6) + ax plus b

Abstract

Let K=Q(θ) be an algebraic number field with θ a root of an irreducible trinomial f(x)=x6+ax+b belonging to Z[x]. In this paper, for each prime number p we compute the highest power of p dividing the discriminant of K in terms of the prime powers dividing a, b and discriminant of f(x). An explicit p-integral basis of K is also given for each prime p and a method is described to obtain an integral basis of K from these p-integral bases which is illustrated with examples.