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 4 (delta <= 20)

Degree 5 (delta <= 17)

Degree 6 (delta <= 16)

Degree 7 (delta <= 15.5)

Degree 8 (delta <= 15)

Degree 9 (delta <= 14.5)

There are no totally real fields of degree 10 and root discriminant <= 14. However, here is a (probably complete but not provably so) list of the smallest 792 totally real dectic fields found.

Degree 10