Learn more about

This database contains 5,025,155 global number fields of degree $n\leq 23$. In addition, extensive data on class groups of quadratic imaginary fields is available for download.

Browse global number fields

A random global number field from the database

Go to a specific field by label, nickname, or polynomial

Field:  
e.g., 2.2.5.1, Qsqrt5, x^2-5, or x^2-x-1 for \(\Q(\sqrt{5})\)

Search for fields

Enter values into one or more boxes to restrict the search.

degree e.g. 3 signature e.g. [1,1]
discriminant e.g. -3, or a range such as 1000..2000 or 1000-2000 or -1000..-1
Galois group e.g. C5, or 8T12, a list of group labels
unramified primes e.g. 2,3 ramified primes e.g. 2,3
class number e.g. 5 class group structure e.g. [ ], [3], or [2,4]
Maximum number of fields to display