On the Resolution of Index Form Equations in Sextic Fields with an Imaginary Quadratic Subfield

We give an efficient algorithm for the resolution of index form equations, especially for determining power integral bases, in sextic fields with an imaginary quadratic subfield. The method reduces the problem to the resolution of acubic relative Thueequationover the quadratic subfield. At the end of the paper we give a table containing the generators of all power integral bases in the first 25 fields of this type with smallest discriminant (in absolute value).1991 Mathematics Subject Classification:primary 11Y50, secondary 11Y40, 11D57