Global Number Fields

This database contains 1,214,934 global number fields of degree $n\leq 15$. The data is complete in a variety of ways, see completeness of global number field data for details.

Browse global number fields

• By degree: 1   2   3   4   5   6   7   8   9   10   11   12   13   14   15  
• 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  

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