The database contains 18,683,673 number fields.

Distribution by signature

There is one row for each degree $n$, and the column is indexed by $r_2$, the number of non-real embeddings, so the signature is $(n-2r_2, r_2)$. Percentages for individual entries are taken with the degree. Percentages for the column All give the proportion of fields of a given degree among all fields in the database.
$n \backslash r_2$ 0 1 2 3 4 5 6 7 8 9 10 11 All
1 1 1
100.00% 0.00%
2 684,216 684,128 1,368,344
50.00% 50.00% 7.32%
3 201,440 657,369 858,809
23.46% 76.54% 4.60%
4 672,184 595,920 1,070,120 2,338,224
28.75% 25.49% 45.77% 12.51%
5 274,956 312,070 675,285 1,262,311
21.78% 24.72% 53.50% 6.76%
6 828,871 436,909 2,086,754 2,170,066 5,522,600
15.01% 7.91% 37.79% 39.29% 29.56%
7 932 18,303 369,331 574,035 962,601
0.10% 1.90% 38.37% 59.63% 5.15%
8 107,694 330,500 607,204 540,440 1,492,204 3,078,042
3.50% 10.74% 19.73% 17.56% 48.48% 16.47%
9 8,378 2,945 8,918 92,873 121,668 234,782
3.57% 1.25% 3.80% 39.56% 51.82% 1.26%
10 261,472 8,909 79,025 451,369 1,120,951 817,265 2,738,991
9.55% 0.33% 2.89% 16.48% 40.93% 29.84% 14.66%
11 35 2 3 14 599 748 1,401
2.50% 0.14% 0.21% 1.00% 42.76% 53.39% 0.01%
12 1,564 846 4,604 10,091 37,595 51,836 105,826 212,362
0.74% 0.40% 2.17% 4.75% 17.70% 24.41% 49.83% 1.14%
13 19 2 2 2 10 23 58 116
16.38% 1.72% 1.72% 1.72% 8.62% 19.83% 50.00% 0.00%
14 144 18 53 47 122 39 153 560 1,136
12.68% 1.58% 4.67% 4.14% 10.74% 3.43% 13.47% 49.30% 0.01%
15 206 13 68 38 88 82 193 125 813
25.34% 1.60% 8.36% 4.67% 10.82% 10.09% 23.74% 15.38% 0.00%
16 3,991 115 2,685 511 12,511 1,451 12,608 2,141 25,639 61,652
6.47% 0.19% 4.36% 0.83% 20.29% 2.35% 20.45% 3.47% 41.59% 0.33%
17 10 2 2 1 2 2 7 8 28 62
16.13% 3.23% 3.23% 1.61% 3.23% 3.23% 11.29% 12.90% 45.16% 0.00%
18 1,988 90 783 588 1,449 498 2,720 754 1,552 4,680 15,102
13.16% 0.60% 5.18% 3.89% 9.59% 3.30% 18.01% 4.99% 10.28% 30.99% 0.08%
19 9 2 2 2 1 2 2 2 3 17 42
21.43% 4.76% 4.76% 4.76% 2.38% 4.76% 4.76% 4.76% 7.14% 40.48% 0.00%
20 1,548 99 1,004 260 2,730 949 3,073 847 4,248 917 8,968 24,643
6.28% 0.40% 4.07% 1.06% 11.08% 3.85% 12.47% 3.44% 17.24% 3.72% 36.39% 0.13%
21 152 19 36 49 48 26 96 80 54 121 68 749
20.29% 2.54% 4.81% 6.54% 6.41% 3.47% 12.82% 10.68% 7.21% 16.15% 9.08% 0.00%
22 71 15 38 27 110 69 140 50 99 31 82 118 850
8.35% 1.76% 4.47% 3.18% 12.94% 8.12% 16.47% 5.88% 11.65% 3.65% 9.65% 13.88% 0.00%
23 7 0 2 2 2 2 2 2 2 2 4 13 40
17.50% 0.00% 5.00% 5.00% 5.00% 5.00% 5.00% 5.00% 5.00% 5.00% 10.00% 32.50% 0.00%
Total 3,049,888 3,048,276 4,905,919 3,840,415 2,790,090 872,992 124,878 4,569 31,625 5,768 9,122 131

Distribution by Galois group

For each degree $3\leq n\leq 7$, we give the breakdown of fields in the database by Galois group. Columns are indexed by $t$, the $t$-number. Degrees $1$ and $2$ are omitted because there is only one possible Galois group for each. Percentages show the proportions are with respect to the number of fields in the database of that degree.
$n \backslash t$ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 All
3 1,822 856,987 858,809
0.21% 99.79%
4 11,945 99,475 1,477,849 28,787 720,168 2,338,224
0.51% 4.25% 63.20% 1.23% 30.80%
5 983 15,955 26,984 113,768 1,104,621 1,262,311
0.08% 1.26% 2.14% 9.01% 87.51%
6 15,542 24,493 236,290 5,261 14,611 177,913 244,006 46,108 64,234 2,312 476,289 110,104 1,946,055 1,011,145 9,721 1,138,516 5,522,600
0.28% 0.44% 4.28% 0.10% 0.26% 3.22% 4.42% 0.83% 1.16% 0.04% 8.62% 1.99% 35.24% 18.31% 0.18% 20.62%
7 118 2,101 86 1,423 40,860 56,883 861,130 962,601
0.01% 0.22% 0.01% 0.15% 4.24% 5.91% 89.46%

Four families of groups have a representative which appears as a Galois group in every degree $n$, $C_n$, the cyclic group of order $n$, $D_n$, the dihedral group of order $2n$, $A_n$, the alternating group on $n$ letters, and $S_n$, the symmetric group on $n$ letters. Percentages are based on the number of fields in the database of the degree.
$n$ 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23
$C_n$ $=A_3$ 11,945 983 15,542 118 5,817 218 1,461 18 1,059 5 38 20 117 4 143 3 69 6 43 2
0.51% 0.08% 0.28% 0.01% 0.19% 0.09% 0.05% 1.28% 0.50% 4.31% 3.35% 2.46% 0.19% 6.45% 0.95% 7.14% 0.28% 0.80% 5.06% 5.00%
$D_n$ $=S_3$ 1,477,849 15,955 236,290 2,101 30,358 706 885 56 158 41 33 53 86 12 10 11 9 3 8 10
63.20% 1.26% 4.28% 0.22% 0.99% 0.30% 0.03% 4.00% 0.07% 35.34% 2.90% 6.52% 0.14% 19.35% 0.07% 26.19% 0.04% 0.40% 0.94% 25.00%
$A_n$ 1,822 28,787 113,768 9,721 56,883 122 633 1,209 76 9 5 5 5 6 3 2 1 1 2 1 2
0.21% 1.23% 9.01% 0.18% 5.91% 0.00% 0.27% 0.04% 5.42% 0.00% 4.31% 0.44% 0.62% 0.01% 4.84% 0.01% 2.38% 0.00% 0.27% 0.12% 5.00%
$S_n$ 856,987 720,168 1,104,621 1,138,516 861,130 4,099 3,230 4,977 968 16 48 16 28 25 28 19 18 20 22 22 20
99.79% 30.80% 87.51% 20.62% 89.46% 0.13% 1.38% 0.18% 69.09% 0.01% 41.38% 1.41% 3.44% 0.04% 45.16% 0.13% 42.86% 0.08% 2.94% 2.59% 50.00%

Distribution by class number

Class numbers have been computed for 98.76% of the fields in the database. Some of these class numbers have been computed under the assumption of the Generalized Riemann Hypothesis.

For main table entries, the percentage is out of fields of that degree for which we have computed the class number. For row totals, the percentage is the number of fields of that degree for which we have computed the class number divided by the total number of fields of that degree. For column totals, percentages are based on the total number of fields for which we have computed the class number. Finally, the lower right corner gives the percentage of fields in the database for which we have computed the class number.
$n$ $h=1$ $1<h\leq 10$ $10<h\leq 10^2$ $10^{2}<h\leq 10^{3}$ $10^{3}<h\leq 10^{4}$ $10^{4}<h\leq 10^{5}$ $10^{5}<h\leq 10^{6}$ $10^{6}<h\leq 10^{7}$ $10^{7}<h\leq 10^{8}$ $10^{8}<h\leq 10^{9}$ $10^{9}<h\leq 10^{10}$ $10^{10}<h\leq 10^{11}$ Total
$2$ 177,168 424,902 123,439 584,569 58,266 1,368,344
12.95% 31.05% 9.02% 42.72% 4.26% 100.00%
$3$ 477,929 317,809 54,005 6,735 1,873 280 24 858,655
55.66% 37.01% 6.29% 0.78% 0.22% 0.03% 0.00% 99.98%
$4$ 1,005,495 732,240 309,601 232,927 46,527 9,735 1,518 88 1 2,338,132
43.00% 31.32% 13.24% 9.96% 1.99% 0.42% 0.06% 0.00% 0.00% 100.00%
$5$ 1,106,102 148,317 7,351 428 19 1 1,262,218
87.63% 11.75% 0.58% 0.03% 0.00% 0.00% 99.99%
$6$ 2,813,009 2,017,772 575,013 56,969 7,290 1,342 6 5,471,401
51.41% 36.88% 10.51% 1.04% 0.13% 0.02% 0.00% 99.07%
$7$ 939,643 22,726 217 5 962,591
97.62% 2.36% 0.02% 0.00% 100.00%
$8$ 1,165,321 1,045,374 537,178 167,742 38,150 10,766 4,571 2,060 652 154 31 4 2,972,007
39.21% 35.17% 18.07% 5.64% 1.28% 0.36% 0.15% 0.07% 0.02% 0.01% 0.00% 0.00% 96.56%
$9$ 168,720 61,390 4,441 128 234,679
71.89% 26.16% 1.89% 0.05% 99.96%
$10$ 1,725,294 804,020 120,773 37,931 1,015 470 60 2,689,563
64.15% 29.89% 4.49% 1.41% 0.04% 0.02% 0.00% 98.20%
$11$ 1,165 58 12 1,235
94.33% 4.70% 0.97% 88.15%
$12$ 65,248 103,159 37,821 5,216 264 160 24 2 211,894
30.79% 48.68% 17.85% 2.46% 0.12% 0.08% 0.01% 0.00% 99.78%
$13$ 116 116
100.00% 100.00%
$14$ 640 407 52 18 10 1,127
56.79% 36.11% 4.61% 1.60% 0.89% 99.21%
$15$ 653 83 2 2 740
88.24% 11.22% 0.27% 0.27% 91.02%
$16$ 24,560 15,700 3,929 1,926 948 180 62 39 16 12 6 2 47,380
51.84% 33.14% 8.29% 4.07% 2.00% 0.38% 0.13% 0.08% 0.03% 0.03% 0.01% 0.00% 76.85%
$17$ 55 5 60
91.67% 8.33% 96.77%
$18$ 8,158 3,155 1,011 801 261 55 29 13,470
60.56% 23.42% 7.51% 5.95% 1.94% 0.41% 0.22% 89.19%
$19$ 41 41
100.00% 97.62%
$20$ 11,135 4,036 1,716 560 270 100 45 13 1 17,876
62.29% 22.58% 9.60% 3.13% 1.51% 0.56% 0.25% 0.07% 0.01% 72.54%
$21$ 320 16 336
95.24% 4.76% 44.86%
$22$ 424 39 6 2 3 4 6 1 485
87.42% 8.04% 1.24% 0.41% 0.62% 0.82% 1.24% 0.21% 57.06%
$23$ 20 20
100.00% 50.00%
Total 9,691,217 5,701,203 1,776,572 1,095,959 154,896 23,092 6,346 2,203 670 166 37 6 18,452,371
52.52% 30.90% 9.63% 5.94% 0.84% 0.13% 0.03% 0.01% 0.00% 0.00% 0.00% 0.00% 98.76%

Distribution of class number one fields by signature

A number field has class number one if and only if its ring of integers is a unique factorization domain.
The table below has one row for each degree $n$, and the columns are indexed by $r_2$, as above. Percentages for individual entries are with respect to all fields in the database with that signature for which we have computed the class number. An entry is not shown if we have not computed the class number for any fields with that combination of degree and signature.
$n \backslash r_2$ 0 1 2 3 4 5 6 7 8 9 10 11
1 1
100.00%
2 177,159 9
25.89% 0.00%
3 155,974 321,955
77.43% 48.99%
4 441,079 352,625 211,791
65.62% 59.18% 19.79%
5 255,061 293,560 557,481
92.76% 94.07% 82.57%
6 440,352 317,987 847,635 1,207,035
54.24% 72.78% 40.63% 56.49%
7 885 18,296 358,551 561,911
95.16% 99.96% 97.08% 97.89%
8 74,513 272,200 280,784 200,726 337,098
69.93% 82.97% 47.04% 39.57% 23.52%
9 5,443 2,749 8,133 57,091 95,304
65.01% 93.34% 91.21% 61.49% 78.38%
10 183,228 5,109 41,028 292,280 715,416 488,233
84.02% 57.37% 51.93% 64.78% 63.91% 60.05%
11 32 2 3 14 473 641
100.00% 100.00% 100.00% 100.00% 96.33% 92.50%
12 973 608 3,070 6,198 18,864 21,746 13,789
65.97% 71.87% 66.74% 61.48% 50.25% 42.00% 13.06%
13 19 2 2 2 10 23 58
100.00% 100.00% 100.00% 100.00% 100.00% 100.00% 100.00%
14 125 18 48 47 109 37 127 129
89.29% 100.00% 96.00% 100.00% 89.34% 94.87% 84.11% 23.04%
15 152 12 48 31 71 70 170 99
87.36% 100.00% 88.89% 96.88% 87.65% 90.91% 89.95% 81.82%
16 2,525 107 1,929 435 6,764 933 5,411 889 5,567
81.43% 94.69% 81.91% 94.57% 67.44% 80.99% 55.73% 58.10% 29.41%
17 7 2 2 1 2 2 7 8 24
87.50% 100.00% 100.00% 100.00% 100.00% 100.00% 100.00% 100.00% 85.71%
18 1,198 83 527 476 998 422 1,812 565 1,006 1,071
73.45% 94.32% 79.85% 91.19% 79.71% 89.03% 76.42% 82.24% 73.48% 24.25%
19 9 2 2 2 1 2 2 2 2 17
100.00% 100.00% 100.00% 100.00% 100.00% 100.00% 100.00% 100.00% 100.00% 100.00%
20 732 75 588 210 1,654 736 1,976 641 2,148 599 1,776
83.47% 96.15% 95.77% 98.13% 91.23% 96.08% 88.45% 92.63% 75.98% 82.73% 25.24%
21 71 4 13 23 13 10 40 29 21 68 28
91.03% 100.00% 100.00% 100.00% 100.00% 100.00% 100.00% 85.29% 100.00% 95.77% 96.55%
22 29 9 19 14 56 52 71 25 43 22 40 44
90.62% 90.00% 90.48% 93.33% 90.32% 98.11% 87.65% 100.00% 89.58% 100.00% 90.91% 61.11%
23 1 1 2 2 1 1 2 2 8
100.00% 100.00% 100.00% 100.00% 100.00% 100.00% 100.00% 100.00% 100.00%