Local Number Fields

The database contains extension fields of $\Q_p$ of degree $n$ up to isomorphism including all extensions for primes $p<200$ and $1\leq n \leq 15$.

Browse local number fields

The table gives for each $p$ and $n$ shown, the number of degree $n$ extension fields of $\Q_p$ up to isomorphism.

$p$ \ $n$	2	3	4	5	6	7	8	9	10	11	12	13	14	15
2	7	2	59	2	47	2	1823	3	158	2	5493	2	590	4
3	3	10	5	2	75	2	8	795	6	2	785	2	6	1172
5	3	2	7	26	7	2	11	3	258	2	17	2	6	1012
7	3	4	5	2	12	50	8	7	6	2	20	2	654	8
11	3	2	5	6	7	2	8	3	18	122	13	2	6	12
13	3	4	7	2	12	2	11	7	6	2	28	170	9	8
17	3	2	7	2	7	2	15	3	6	2	17	2	6	4
19	3	4	5	2	12	2	8	13	8	2	20	2	6	8
23	3	2	5	2	7	2	8	3	6	12	13	2	6	4

A random local number field from the database.

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a field label, e.g. 2.4.6.7

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Degree		e.g. 6, or a range like 3..5
Prime $p$ for base field $\Q_p$		e.g. 3, or a range like 3..7
Discriminant exponent $c$		e.g. 8, or a range like 2..6
Ramification index $e$		e.g. 3, or a range like 2..6
Top slope		e.g. 0, 1, 2, 4/3, 3.5, or a range like 3..5
Galois group $G$		e.g. 5T3, C4, or a list of labels
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