I am interested in field extensions of the rationals. About degree 3 extensions there are many refrences including the famous paper of Shanks "The Simplest Cubic Fields". In particular he gave generating polynomial for all such extensions. Later people then classified the parameters of this cubic equation.

I am interested in finding out if any similar results exist in degree 5 and higher cases. Kindly provide refrences if any.

quinticfields (a typo, I guess). $\endgroup$ – Dietrich Burde Feb 9 '14 at 13:22