The tables contain information about the maximal unramified soluble extension KH for all the 3043 real quadratic number fields K with discriminant dK smaller then 10000. These data were calculated with pari/gp, KANT and GAP. The results depend on the Generalized Riemann Hypothesis (GRH). But in any case the given KH is a subfield of the maximal unramified soluble extension of K and the length of the Hilbert class field tower is greater or equal then H.
The data is given as a list. Each entry corresponds to a number field and consists of a vector
[dK, (KH :Q), H, Poly, h, g], where
An example is: [5,2,0,X^2-5,[[1,],[1,],[1,]],[[2,1],"C2"]]
[dK=1, (KH :Q)=2, H=3, Poly=4, h=5, g=6]
Use a comma to separate higher dimensions:
|Univ. of Kaiserslautern • Dept. of Mathematics • WG Algebra & Geometry • CAS SINGULAR • KIS|