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The database currently contains 21,582 $p$-adic fields, including all with $p < 200$ and degree $n < 16$. Here are some further statistics.

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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

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e.g. 2.4.6.7