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The database currently contains 1,393,286 $p$-adic fields, 19,585 absolute families, and 585,893 relative families. Here are some further statistics.

Browse fields

This table gives, for each $p$ and $n$ shown, the number of degree $n$ extension fields of $\Q_p$ up to isomorphism. Here are more counts for larger $p$ and $n$.

$p$ \ $n$ 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23
2 7 2 59 2 47 2 1823 3 158 2 5493 2 590 4 890111 2 2991 2 314543 6 8942 2
3 3 10 5 2 75 2 8 795 6 2 785 2 6 1172 13 2 130647 2 11 10004 6 2
5 3 2 7 26 7 2 11 3 258 2 17 2 6 1012 17 2 11 2 7587 4 6 2
7 3 4 5 2 12 50 8 7 6 2 20 2 654 8 13 2 21 2 11 3784 6 2

Browse families

This table gives the number of degree $n$ families over $\Q_p$. Here are more counts for larger $p$ and $n$, and search pages for absolute families and relative families.
$p$ \ $n$ 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23
2 3 2 10 2 8 2 49 3 10 2 43 2 12 4 389 2 19 2 78 4 16 2
3 2 4 3 2 10 2 4 28 4 2 20 2 4 16 5 2 101 2 6 20 4 2
5 2 2 3 6 4 2 4 3 16 2 6 2 4 20 5 2 6 2 34 4 4 2
7 2 2 3 2 4 8 4 3 4 2 6 2 22 4 5 2 6 2 6 28 4 2

Some interesting $p$-adic fields, a random $p$-adic field, a random absolute family, a random relative family

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Degree e.g. 6, or a range like 3..5 Residue field characteristic e.g. 3, or a range like 3..7
Ramification index e.g. 3, or a range like 2..6 Residue field degree e.g. 3, or a range like 2..6
Discriminant exponent e.g. 8, or a range like 2..6 Top Artin slope e.g. 4/3, or a range like 3..5
Galois unramified degree e.g. 3, or a range like 1..4 Galois tame degree e.g. 2, or a range like 2..3
Galois Artin slopes e.g. [2,2,3] or [3,7/2,4] Visible Artin slopes e.g. [2,2,3] or [2,3,17/4]
Indices of insep. e.g. [1,1,0] or [18,10,4,0] Assoc. Inertia e.g. [1,2,1] or [1,1,1,1]
Jump Set e.g. [1,2] or [1,3,8] Num. automorphisms e.g. 2, or a range like 2..3
Galois group e.g. 8.3, C5 or 7T2 Inertia subgroup e.g. 8.3, C5 or 7T2
Wild inertia subgroup e.g. 8.3, C5 or 7T2
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e.g. 2.1.4.6a2.1