| 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 |
| 12.8.1012071104000000.1 |
$x^{12} - 3 x^{10} - 2 x^{8} + 5 x^{6} + 19 x^{4} - 32 x^{2} + 11$ |
$12$ |
[8,2] |
$2^{12}\cdot 5^{6}\cdot 11^{3}\cdot 109^{2}$ |
$4$ |
$17.800584052206354$ |
$303.0731045220067$ |
|
|
? |
$S_4^2:D_4$ (as 12T260) |
trivial |
$[2]$ |
$2$ |
$9$ |
$1317.6300516836802$ |
| 12.2.7340688973975552.1 |
$x^{12} + 13 x^{10} + 52 x^{8} + 78 x^{6} + 26 x^{4} - 26 x^{2} - 13$ |
$12$ |
[2,5] |
$-\,2^{12}\cdot 13^{11}$ |
$2$ |
$20.9963950402$ |
$41.092971181713175$ |
|
|
? |
$C_2\wr C_6$ (as 12T134) |
trivial |
$[2]$ |
$2$ |
$6$ |
$864.466347181$ |
| 16.6.635...000.1 |
$x^{16} - x^{14} + 3 x^{12} - 13 x^{8} - 13 x^{6} + 4 x^{4} + 4 x^{2} - 1$ |
$16$ |
[6,5] |
$-\,2^{12}\cdot 5^{8}\cdot 251^{4}$ |
$3$ |
$14.968418922$ |
$138.66749394298347$ |
|
|
? |
$C_2^6.(D_4\times S_4)$ (as 16T1759) |
trivial |
trivial |
$2$ |
$10$ |
$1411.38797393$ |
| 16.0.211...296.1 |
$x^{16} + 3 x^{14} + 6 x^{12} + 23 x^{10} + 44 x^{8} + 32 x^{6} + 11 x^{4} + 6 x^{2} + 1$ |
$16$ |
[0,8] |
$2^{16}\cdot 7537^{4}$ |
$2$ |
$18.6350097571$ |
|
|
|
? |
$C_2^4.C_2^6:S_4$ (as 16T1815) |
trivial |
trivial |
$2$ |
$7$ |
$2633.76681168$ |
| 16.8.159...000.1 |
$x^{16} - 20 x^{14} + 157 x^{12} - 660 x^{10} + 1658 x^{8} - 2575 x^{6} + 2427 x^{4} - 1255 x^{2} + 251$ |
$16$ |
[8,4] |
$2^{12}\cdot 5^{8}\cdot 251^{5}$ |
$3$ |
$21.142460938$ |
$551.941560654592$ |
|
|
|
$C_2^6.(D_4\times S_4)$ (as 16T1759) |
trivial |
trivial |
$2$ |
$11$ |
$58905.4486548$ |
| 16.6.246...000.2 |
$x^{16} - 10 x^{14} + 30 x^{12} - 35 x^{10} + 35 x^{8} - 25 x^{4} - 25$ |
$16$ |
[6,5] |
$-\,2^{12}\cdot 5^{14}\cdot 9929^{2}$ |
$3$ |
$21.7262333313$ |
$1594.792971918202$ |
|
|
? |
$C_2^8.S_4\wr C_2$ (as 16T1905) |
trivial |
$[2]$ |
$2$ |
$10$ |
$32599.2432104$ |
| 16.4.309...632.1 |
$x^{16} + 14 x^{14} + 51 x^{12} - 30 x^{10} - 390 x^{8} - 289 x^{6} + 657 x^{4} + 731 x^{2} + 43$ |
$16$ |
[4,6] |
$2^{16}\cdot 43^{3}\cdot 2777^{4}$ |
$3$ |
$29.3899807098$ |
$3463.714482798763$ |
|
|
? |
$C_2^7.C_2\wr S_4$ (as 16T1851) |
trivial |
$[2]$ |
$2$ |
$9$ |
$638682.568045$ |
| 16.12.309...632.1 |
$x^{16} - 14 x^{14} + 59 x^{12} + 9 x^{10} - 734 x^{8} + 2103 x^{6} - 2343 x^{4} + 860 x^{2} + 43$ |
$16$ |
[12,2] |
$2^{16}\cdot 43^{3}\cdot 2777^{4}$ |
$3$ |
$29.3899807098$ |
$3463.714482798763$ |
|
|
? |
$C_2^7.C_2\wr S_4$ (as 16T1851) |
trivial |
$[2]$ |
$2$ |
$13$ |
$1587081.65977$ |
| 16.4.391...272.1 |
$x^{16} + 8 x^{14} + 26 x^{12} + 44 x^{10} + 33 x^{8} - 12 x^{6} - 41 x^{4} - 26 x^{2} + 3$ |
$16$ |
[4,6] |
$2^{18}\cdot 3\cdot 163^{8}$ |
$3$ |
$29.8244625163$ |
$289.21696148670196$ |
|
|
? |
$C_4^4.C_2\wr A_4$ (as 16T1845) |
trivial |
$[2]$ |
$2$ |
$9$ |
$1297582.1317$ |
| 16.0.824...000.1 |
$x^{16} + 18 x^{14} + 93 x^{12} + 214 x^{10} + 382 x^{8} + 1059 x^{6} + 1636 x^{4} + 971 x^{2} + 151$ |
$16$ |
[0,8] |
$2^{12}\cdot 3^{8}\cdot 5^{8}\cdot 151^{5}$ |
$4$ |
$31.2426901924$ |
$992.0020193894018$ |
|
|
? |
$C_2^8.A_4\wr C_2$ (as 16T1862) |
$[2]$ |
$[2]$ |
$2$ |
$7$ |
$124132.010182$ |
| 16.16.292...912.1 |
$x^{16} - 20 x^{14} + 164 x^{12} - 713 x^{10} + 1774 x^{8} - 2542 x^{6} + 2003 x^{4} - 772 x^{2} + 112$ |
$16$ |
[16,0] |
$2^{12}\cdot 3^{12}\cdot 7\cdot 61^{8}$ |
$4$ |
$33.8140338278$ |
$365.81596492664835$ |
|
|
? |
$C_2\wr \SL(2,3)$ (as 16T1670) |
trivial |
$[2, 2]$ |
$2$ |
$15$ |
$12115649.4701$ |
| 16.8.161...000.2 |
$x^{16} - 7 x^{14} - 41 x^{12} + 72 x^{10} + 396 x^{8} + 60 x^{6} - 845 x^{4} - 625 x^{2} + 25$ |
$16$ |
[8,4] |
$2^{16}\cdot 3^{12}\cdot 5^{10}\cdot 83^{4}$ |
$4$ |
$37.6267504013$ |
|
|
|
|
$C_2^6:(C_2\times S_4)$ (as 16T1521) |
trivial |
$[2, 2, 2]$ |
$2$ |
$11$ |
$6773937.72845$ |
| 16.16.652...000.1 |
$x^{16} - 20 x^{14} + 166 x^{12} - 740 x^{10} + 1912 x^{8} - 2870 x^{6} + 2354 x^{4} - 895 x^{2} + 101$ |
$16$ |
[16,0] |
$2^{16}\cdot 3^{12}\cdot 5^{8}\cdot 83^{4}\cdot 101$ |
$5$ |
$41.0577879906$ |
|
|
|
? |
$C_2^6.(D_4\times S_4)$ (as 16T1759) |
trivial |
$[2, 2]$ |
$2$ |
$15$ |
$58164674.5398$ |
| 16.12.860...064.1 |
$x^{16} - 2 x^{15} - 35 x^{14} + 72 x^{13} + 448 x^{12} - 984 x^{11} - 2681 x^{10} + 6698 x^{9} + 8782 x^{8} - 26594 x^{7} - 20622 x^{6} + 62972 x^{5} + 44263 x^{4} - 74042 x^{3} - 55712 x^{2} + 32314 x + 25763$ |
$16$ |
[12,2] |
$2^{16}\cdot 43^{3}\cdot 2777^{5}$ |
$3$ |
$48.2417210948$ |
$3463.714482798763$ |
|
|
? |
$C_2^7.C_2\wr S_4$ (as 16T1850) |
trivial |
$[2, 2]$ |
$2$ |
$13$ |
$83571859.9339$ |
| 16.12.860...064.3 |
$x^{16} - 17 x^{14} - 61 x^{12} + 2237 x^{10} - 8301 x^{8} - 26241 x^{6} + 184736 x^{4} - 289089 x^{2} + 119411$ |
$16$ |
[12,2] |
$2^{16}\cdot 43^{3}\cdot 2777^{5}$ |
$3$ |
$48.2417210948$ |
$3463.714482798763$ |
|
|
? |
$C_2^7.C_2\wr S_4$ (as 16T1850) |
trivial |
$[2, 2]$ |
$2$ |
$13$ |
$246901537.585$ |
| 16.4.860...064.5 |
$x^{16} - 2 x^{15} + 15 x^{14} - 50 x^{13} + 29 x^{12} - 468 x^{11} - 1512 x^{10} - 1862 x^{9} - 14783 x^{8} - 14000 x^{7} - 51763 x^{6} - 66054 x^{5} - 28254 x^{4} - 95978 x^{3} - 74035 x^{2} - 37612 x + 724$ |
$16$ |
[4,6] |
$2^{16}\cdot 43^{3}\cdot 2777^{5}$ |
$3$ |
$48.24172109482252$ |
$3463.714482798763$ |
|
|
? |
$C_2^7.C_2\wr S_4$ (as 16T1850) |
trivial |
$[2, 2]$ |
$2$ |
$9$ |
$34912824.712430105$ |
| 18.12.125...184.4 |
$x^{18} - 6 x^{16} - 3 x^{14} + 62 x^{12} - 60 x^{10} - 119 x^{8} + 218 x^{6} - 106 x^{4} + 13 x^{2} + 1$ |
$18$ |
[12,3] |
$-\,2^{12}\cdot 7^{12}\cdot 53^{6}$ |
$3$ |
$21.8194591003$ |
$104.27721702727186$ |
|
|
? |
$C_2^5.(A_4\times S_4)$ (as 18T544) |
trivial |
$[2]$ |
$2$ |
$14$ |
$349463.693227$ |
| 18.8.804...776.9 |
$x^{18} + 7 x^{16} - 4 x^{14} - 116 x^{12} - 193 x^{10} + 132 x^{8} + 284 x^{6} - 39 x^{4} - 32 x^{2} + 1$ |
$18$ |
[8,5] |
$-\,2^{18}\cdot 7^{12}\cdot 53^{6}$ |
$3$ |
$27.4907958178$ |
|
|
|
? |
$C_2^4:(C_6\times S_4)$ (as 18T367) |
trivial |
$[2, 2]$ |
$2$ |
$12$ |
$1334022.78276$ |
| 18.10.804...776.7 |
$x^{18} + 5 x^{16} - 12 x^{14} - 50 x^{12} + 53 x^{10} + 83 x^{8} - 96 x^{6} + 5 x^{4} + 13 x^{2} - 1$ |
$18$ |
[10,4] |
$2^{18}\cdot 7^{12}\cdot 53^{6}$ |
$3$ |
$27.4907958178$ |
|
|
|
? |
$C_2^4:(A_4\times S_4)$ (as 18T463) |
trivial |
$[2]$ |
$2$ |
$13$ |
$2059276.93656$ |
| 18.4.577...000.1 |
$x^{18} + 18 x^{14} - 24 x^{13} + 8 x^{12} - 243 x^{10} + 648 x^{9} - 648 x^{8} + 288 x^{7} - 3693 x^{6} + 14580 x^{5} - 24300 x^{4} + 21600 x^{3} - 10800 x^{2} + 2880 x - 320$ |
$18$ |
[4,7] |
$-\,2^{12}\cdot 3^{18}\cdot 5^{6}\cdot 13^{12}$ |
$4$ |
$45.0222112573$ |
|
|
|
? |
$C_3^6.C_2\wr (C_2\times A_4)$ (as 18T926) |
trivial |
trivial |
$2$ |
$10$ |
$85355267.4723$ |
| 18.6.119...552.2 |
$x^{18} + 19 x^{16} - 190 x^{14} - 3413 x^{12} + 1360 x^{10} + 119305 x^{8} + 129268 x^{6} - 1050725 x^{4} - 1160117 x^{2} - 148877$ |
$18$ |
[6,6] |
$2^{18}\cdot 7^{12}\cdot 53^{9}$ |
$3$ |
$53.28029537487781$ |
$104.27721702727186$ |
|
|
? |
$C_2^4:(A_4\times S_4)$ (as 18T462) |
$[2]$ |
$[2, 2]$ |
$2$ |
$11$ |
$153372772.8347557$ |
| 18.6.404...616.1 |
$x^{18} + 20 x^{16} + 108 x^{14} + 15 x^{12} - 618 x^{10} - 72 x^{8} + 913 x^{6} - 255 x^{4} - 107 x^{2} - 4$ |
$18$ |
[6,6] |
$2^{16}\cdot 13^{8}\cdot 229^{8}$ |
$3$ |
$64.7864111249$ |
|
|
|
? |
$C_2^2:A_4^2.S_4$ (as 18T588) |
$[2]$ |
$[2, 2]$ |
$2$ |
$11$ |
$5381447049.46$ |
| 18.2.162...000.1 |
$x^{18} - 45 x^{16} - 120 x^{15} + 540 x^{14} + 3528 x^{13} + 46085 x^{12} - 14040 x^{11} - 1308840 x^{10} - 3484520 x^{9} + 5090553 x^{8} + 46327320 x^{7} - 388795420 x^{6} + 175220280 x^{5} + 7783408815 x^{4} + 20416450776 x^{3} + 22893231735 x^{2} + 12197248200 x - 21024071250125$ |
$18$ |
[2,8] |
$2^{18}\cdot 3^{18}\cdot 5^{15}\cdot 13^{16}\cdot 53^{4}$ |
$5$ |
$541.964123205$ |
|
|
|
|
$S_6\wr C_3$ (as 18T974) |
trivial |
trivial |
$2$ |
$9$ |
$1121302705480000000$ |
| 20.2.294...176.1 |
$x^{20} + 3 x^{18} + 4 x^{16} + x^{14} - 3 x^{12} - 6 x^{10} - 9 x^{8} - 13 x^{6} - 12 x^{4} - 6 x^{2} - 1$ |
$20$ |
[2,9] |
$-\,2^{12}\cdot 41^{2}\cdot 4549^{4}$ |
$3$ |
$11.8434865297$ |
$1690.4514439867726$ |
|
|
? |
$C_2^9.C_2^6:S_5$ (as 20T1015) |
trivial |
trivial |
$2$ |
$10$ |
$265.437747416$ |
| 20.4.237...360.1 |
$x^{20} + 10 x^{18} + 28 x^{16} - 16 x^{14} - 199 x^{12} - 298 x^{10} - 19 x^{8} + 332 x^{6} + 309 x^{4} + 98 x^{2} + 10$ |
$20$ |
[4,8] |
$2^{21}\cdot 5\cdot 31^{8}\cdot 113^{8}$ |
$4$ |
$58.7227047162$ |
|
|
|
|
$C_2^{10}.C_2\wr A_5$ (as 20T995) |
$[2]$ |
$[2]$ |
$2$ |
$11$ |
$24300039683.2$ |
| 21.1.156...232.1 |
$x^{21} + 21 x^{15} - 18 x^{14} + 196 x^{9} - 336 x^{8} + 144 x^{7} + 343 x^{3} - 882 x^{2} + 756 x - 216$ |
$21$ |
[1,10] |
$2^{18}\cdot 3^{18}\cdot 7^{21}\cdot 31^{7}$ |
$4$ |
$102.142243029$ |
|
|
|
? |
$A_7^3.D_6$ (as 21T157) |
trivial |
trivial |
$2$ |
$10$ |
$12409722755200$ |
| 21.3.105...992.1 |
$x^{21} + 21 x^{15} - 18 x^{14} - 1029 x^{3} + 2646 x^{2} - 2268 x + 648$ |
$21$ |
[3,9] |
$-\,2^{18}\cdot 3^{50}\cdot 7^{21}$ |
$3$ |
$173.431003904$ |
|
|
|
? |
$A_7^3.C_6$ (as 21T154) |
trivial |
trivial |
$2$ |
$11$ |
$3726037898960000$ |
