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

Abstract

Let be an algebraic number field with θ a root of an irreducible trinomial belonging to 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 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.