Global number fields

This database contains 20,931,788 global number fields of degree $n\leq 47$. Here are some further statistics. In addition, extensive data on class groups of quadratic imaginary fields is available for download.

Browse global number fields

• By degree: 1   2   3   4   5   6   7   8   9   10   11   12   13   14   15   16   17   18   19   20   21   22   23   24   25   26   27   28   29   30   31   32   33   34   35   36   37   38   39   40   41   42   43   44   45   46   47  
• By discriminant range: -10000..-1001   -1000..-101   -100..-1   0..99   100..999   1000..9999  
• By signature: [1, 0]   [2, 0]   [0, 1]   [3, 0]   [1, 1]   [4, 0]   [2, 1]   [0, 2]   [5, 0]   [3, 1]  
• By class number: 1   2   3   4   5   6..10  

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

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
Root discriminant	e.g. a range such as 1..4.3 or 3..10		CM field
Galois group	e.g. C5, or 8T12, a list of group labels		Regulator	e.g. a range such as 1..3.5
Class number	e.g. 5		Class group structure	e.g. [ ], [3], or [2,4]
Number of ramified primes	e.g. 2,3		Ramified primes	e.g. 2,3
Unramified primes	e.g. 2,3
Results to display