This database contains 3,326,283 global number fields of degree $n\leq 22$. The data is complete in a variety of ways, see completeness of global number field data for details.

Browse global number fields

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 [2,2]
Maximum number of fields to display

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 \(\Q(\sqrt{5})\)