Integral bases and monogenity of the simplest sextic fields
István Gaál, László Remete · Acta Arithmetica · 2018
Let $m$ be an integer, $m eq -8,-3,0,5$ such that $m^2+3m+9$ is square free. Let $\alpha$ be a root of \[ f=x^6-2mx^5-(5m+15)x^4-20x^3+5mx^2+(2m+6)x+1. \] The totally real cyclic fields $K=\mathbb Q(\alpha)$ are called simplest sextic fields and are