| Label |
Polynomial |
Degree |
Signature |
Discriminant |
Ram. prime count |
Root discriminant |
Galois root discriminant |
CM field |
Galois |
Monogenic |
Galois group |
Class group |
Narrow class group |
Unit group torsion |
Unit group rank |
Regulator |
| 14.0.572...599.1 |
$x^{14} - x^{13} - 2 x^{12} + 12 x^{11} + 81 x^{10} - 203 x^{9} + 477 x^{8} - 1135 x^{7} + 2043 x^{6} - 2402 x^{5} + 1866 x^{4} - 1049 x^{3} + 537 x^{2} - 245 x + 67$ |
$14$ |
[0,7] |
$-\,31^{7}\cdot 113^{6}$ |
$2$ |
$42.225189608639354$ |
$320.2302614292546$ |
|
|
? |
$C_7 \wr C_2$ (as 14T8) |
$[3]$ |
$[3]$ |
$2$ |
$6$ |
$59474.987942609085$ |
| 14.0.973...551.1 |
$x^{14} - 5 x^{13} + 41 x^{12} - 139 x^{11} + 954 x^{10} - 2810 x^{9} + 16990 x^{8} - 43043 x^{7} + 216460 x^{6} - 427080 x^{5} + 1779327 x^{4} - 2350647 x^{3} + 8361848 x^{2} - 5698041 x + 17394953$ |
$14$ |
[0,7] |
$-\,29^{12}\cdot 31^{7}$ |
$2$ |
$99.8078832623$ |
$99.80788326233741$ |
✓ |
✓ |
? |
$C_{14}$ (as 14T1) |
$[4, 4, 1356]$ |
$[4, 4, 1356]$ |
$2$ |
$6$ |
$6020.985100147561$ |
| 14.0.337...704.1 |
$x^{14} - 105 x^{12} - 147 x^{11} + 5271 x^{10} + 19838 x^{9} - 94150 x^{8} - 607634 x^{7} + 570164 x^{6} + 12260920 x^{5} + 42847770 x^{4} + 95169270 x^{3} + 197804880 x^{2} + 348280352 x + 336238208$ |
$14$ |
[0,7] |
$-\,2^{6}\cdot 7^{24}\cdot 31^{7}$ |
$3$ |
$210.587796028$ |
$456.46642613478804$ |
|
|
? |
$C_7^2:S_3$ (as 14T15) |
$[21]$ |
$[21]$ |
$2$ |
$6$ |
$8415941567.41$ |
| 14.0.119...791.1 |
$x^{14} - 5 x^{13} - 31 x^{12} + 309 x^{11} + 262 x^{10} - 8842 x^{9} + 67732 x^{8} - 350971 x^{7} + 1534032 x^{6} - 4949688 x^{5} + 19407809 x^{4} - 39113311 x^{3} + 126961596 x^{2} - 125321277 x + 300251687$ |
$14$ |
[0,7] |
$-\,31^{7}\cdot 113^{12}$ |
$2$ |
$320.2302614292546$ |
$320.2302614292546$ |
✓ |
✓ |
? |
$C_{14}$ (as 14T1) |
$[2, 2, 381066]$ |
$[2, 2, 381066]$ |
$2$ |
$6$ |
$222748.97284811488$ |
| 16.0.703...000.1 |
$x^{16} - 2 x^{15} - 766 x^{14} - 21882 x^{13} + 883428 x^{12} + 4750522 x^{11} - 159167190 x^{10} - 3070448446 x^{9} + 2468409535 x^{8} + 1057497307488 x^{7} + 945395140228 x^{6} - 59423341191200 x^{5} - 1080625508736060 x^{4} - 8453738972592256 x^{3} + 147821208122480424 x^{2} + 522280733343722304 x + 6389814241614089048$ |
$16$ |
[0,8] |
$2^{30}\cdot 5^{4}\cdot 7^{24}\cdot 31^{8}\cdot 283^{4}$ |
$5$ |
$2319.78779289$ |
|
|
|
? |
$C_2^6:(C_7^2:S_3)$ (as 16T1799) |
$[4, 12]$ |
$[12, 4]$ |
$2$ |
$7$ |
$27795097491200000000$ |
| 16.0.112...000.1 |
$x^{16} - 4 x^{15} + 576 x^{14} - 2884 x^{13} + 170450 x^{12} - 1101772 x^{11} + 31708600 x^{10} - 251796868 x^{9} + 3981787093 x^{8} - 35120784512 x^{7} + 352057105568 x^{6} - 3172525137768 x^{5} + 21738623269972 x^{4} - 147238076856304 x^{3} + 696198330264032 x^{2} - 2661477248616624 x + 7592536165198532$ |
$16$ |
[0,8] |
$2^{34}\cdot 5^{4}\cdot 7^{24}\cdot 31^{8}\cdot 283^{4}$ |
$5$ |
$2758.7081486$ |
|
|
|
? |
$C_2^6:(C_7^2:S_3)$ (as 16T1799) |
$[4, 12]$ |
$[12, 4]$ |
$2$ |
$7$ |
$106548265553000000000$ |
| 21.7.195...007.1 |
$x^{21} + 18 x^{19} - 20 x^{18} + 115 x^{17} - 188 x^{16} + 227 x^{15} - 571 x^{14} - 633 x^{13} + 412 x^{12} - 2156 x^{11} + 1703 x^{10} + 2628 x^{9} + 1031 x^{8} + 1528 x^{7} - 391 x^{6} + 241 x^{5} - 147 x^{4} + 21 x^{3} - 10 x^{2} - x + 1$ |
$21$ |
[7,7] |
$-\,31^{7}\cdot 577^{9}$ |
$2$ |
$47.9161181809$ |
$133.74228949737625$ |
|
|
? |
$S_3\times D_7$ (as 21T8) |
trivial |
trivial |
$2$ |
$13$ |
$3294250109.26$ |
| 21.7.127...944.1 |
$x^{21} - 3 x^{20} + x^{19} - 42 x^{18} - 157 x^{17} + 310 x^{16} + 5798 x^{15} - 3709 x^{14} - 92464 x^{13} + 474108 x^{12} - 2368117 x^{11} + 9006061 x^{10} - 20442035 x^{9} + 24167098 x^{8} + 18849199 x^{7} - 129416738 x^{6} + 120608306 x^{5} + 151200437 x^{4} - 174966569 x^{3} - 172336121 x^{2} + 129418146 x + 31235087$ |
$21$ |
[7,7] |
$-\,2^{18}\cdot 29^{6}\cdot 31^{7}\cdot 379^{6}$ |
$4$ |
$81.2322223036$ |
$29339.501842851583$ |
|
|
? |
$C_7\wr S_3$ (as 21T32) |
$[7]$ |
$[7]$ |
$2$ |
$13$ |
$105149816421$ |
| 21.3.243...488.1 |
$x^{21} - 7 x^{15} - 6 x^{14} - 343 x^{3} - 882 x^{2} - 756 x - 216$ |
$21$ |
[3,9] |
$-\,2^{12}\cdot 3^{18}\cdot 7^{21}\cdot 31^{7}$ |
$4$ |
$83.7908932986$ |
|
|
|
? |
$A_7^3.D_6$ (as 21T157) |
trivial |
trivial |
$2$ |
$11$ |
$1530405992890$ |
| 21.1.569...744.1 |
$x^{21} - 154 x^{19} - 350 x^{18} + 9422 x^{17} + 38318 x^{16} - 232820 x^{15} - 1495990 x^{14} - 59192 x^{13} + 16100140 x^{12} + 74605944 x^{11} + 291794048 x^{10} + 22521464 x^{9} - 4000275328 x^{8} - 1691077124 x^{7} + 11054922536 x^{6} - 418374125568 x^{5} - 2346556141272 x^{4} - 4154662343608 x^{3} - 3218488878808 x^{2} - 17560545695056 x - 50542023253032$ |
$21$ |
[1,10] |
$2^{18}\cdot 7^{36}\cdot 31^{10}$ |
$3$ |
$261.178511779$ |
$456.46642613478804$ |
|
|
? |
$C_7^2:S_3$ (as 21T17) |
$[7]$ |
$[7]$ |
$2$ |
$10$ |
$21312988696200000$ |
