How much is known about the fundamental units in totally real cubic fields? For example, Daniel Shanks has a family of totally real cubic fields for which the fundamental units are known; those with defining polynomial $x^3-ax^2-(a+3)x -1$. Does anyone know of other families of totally real cubic fields for which the fundamental units are known? I'm particularly interested in cubic subfields of cyclotomic extensions.



Fundamental Units in Totally Real Cubic Fields
Here are two references that may be useful.


1. Algebraic number fields with 2 independent units, 1931, by W. E. H. Berwick.
2. The determination of units in totally real cubic fields, 1959, by H. J. Godwin.


