Tables of Totally Real Number Fields

Information: In these tables, we list all totally real fields F of fixed degree n and bounded root discriminant delta_F. Each file consists of a computer-readable array A consisting of elements [d, f] where d is the discriminant of F and f is a minimal polynomial for a primitive element of F, where we take the convention:

[a[0],a[1],...,a[d]] corresponds to a[d]*x^d + ... + a[1]*x + a[0].

Degree 2 (delta <= 30)

Degree 3 (delta <= 25)     Degree 3 (delta <= 100)      Degree 3 (delta <= 300)

Degree 4 (delta <= 20)     Degree 4 (delta <= 21)        Degree 4 (delta <= 57)     Degree 4 (delta <= 100)

Degree 5 (delta <= 17)     Degree 5 (delta <= 21.5)     Degree 5 (delta <= 35)

Degree 6 (delta <= 16)     Degree 6 (delta <= 20.5)     Degree 6 (delta <= 28)

Degree 7 (delta <= 15.5)

Degree 8 (delta <= 15)     Degree 8 (delta <= 17)

Degree 9 (delta <= 14.5)  Degree 9 (delta <= 15)

There are no totally real fields of degree 10 and root discriminant <= 14. However, here is a list of the smallest 792 totally real dectic fields found. Ken Yamamura compared this list with the tables of Klueners and Malle and found that several were missing, so this list is not complete.

Degree 10