Number fields

This database contains 22,175,416 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.

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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:	-10000..-1001   -1000..-101   -100..-1   0..99   100..999   1000..9999   10000..99999   100000..999999   $\cdots$
By signature:	[1,0]   [2,0]   [0,1]   [3,0]   [1,1]   [4,0]   [2,1]   [0,2]   [5,0]   [3,1]   [1,2]   [6,0]   [4,1]   [2,2]   [0,3]   [7,0]   $\cdots$
By class number:	1  2  3  4  5  6  7  8  9  10  11  12  13  14  15  16  17  18  19  20  21  22  23  24  $\cdots$
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Degree		e.g. 3	Signature		e.g. [1,1]
Discriminant		e.g. -3 or 1000-2000	Root discriminant		e.g. a range such as 1..4.3 or 3-10
Galois group		e.g. [8,3], 8.3, C5 or 7T2	Field is
Ramified prime count		e.g. 2	Galois root discriminant		e.g. a range such as 1..4.3 or 3-10
Class number		e.g. 5	Class group structure		e.g. [ ], [3], or [2,4]
Ramified		e.g. 2,3	Unramified primes		e.g. 2,3
Regulator		e.g. a range such as 1..3.5	CM field
$p$-adic completions		e.g. 2.4.10.7 or 2.4.10.7,3.2.1.2	Relative class number		e.g. 3
Index		e.g. 2	Intermediate field		e.g. 2.2.5.1 or x^2-5 or a field nickname
Monogenic			Inessential primes		e.g. 2,3
Results to display			Minimal sibling

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Label, name, or polynomial
	e.g. 2.2.5.1, Qsqrt5, x^2-5, or x^2-x-1 for $\Q(\sqrt{5})$