| Label |
Polynomial |
Degree |
Signature |
Discriminant |
Ram. prime count |
Root discriminant |
Galois root discriminant |
CM field |
Galois |
Monogenic |
Galois group |
Class group |
Unit group torsion |
Unit group rank |
Regulator |
| 18.0.119...867.1 |
$x^{18} - 4 x^{17} + 9 x^{16} - 14 x^{15} + 17 x^{14} - 16 x^{13} + 15 x^{12} - 23 x^{11} + 45 x^{10} - 65 x^{9} + 62 x^{8} - 40 x^{7} + 29 x^{6} - 39 x^{5} + 49 x^{4} - 41 x^{3} + 22 x^{2} - 7 x + 1$ |
$18$ |
[0,9] |
$-\,31^{6}\cdot 67^{5}$ |
$2$ |
$10.1009812596$ |
$185.1014620777746$ |
|
|
? |
$C_6\wr S_3$ (as 18T284) |
trivial |
$2$ |
$8$ |
$22.3834819773$ |
| 18.0.322...824.1 |
$x^{18} + 5 x^{16} + 11 x^{14} + 25 x^{12} + 51 x^{10} + 65 x^{8} + 59 x^{6} + 40 x^{4} + 13 x^{2} + 1$ |
$18$ |
[0,9] |
$-\,2^{18}\cdot 31^{6}\cdot 61^{4}$ |
$3$ |
$15.6635617531$ |
$290.2038898343469$ |
|
|
? |
$C_6\wr S_3$ (as 18T284) |
trivial |
$2$ |
$8$ |
$1373.9911442$ |
| 18.6.356...797.1 |
$x^{18} - 2 x^{17} - 5 x^{16} + 26 x^{15} - 33 x^{14} - 64 x^{13} + 213 x^{12} - 159 x^{11} - 271 x^{10} + 761 x^{9} - 287 x^{8} - 735 x^{7} + 1010 x^{6} - 19 x^{5} - 1218 x^{4} + 81 x^{3} + 744 x^{2} + 209 x - 79$ |
$18$ |
[6,6] |
$31^{9}\cdot 67^{5}$ |
$2$ |
$17.9029190379$ |
$185.1014620777746$ |
|
|
? |
$C_6\wr S_3$ (as 18T284) |
trivial |
$2$ |
$11$ |
$17837.0993026$ |
| 18.6.196...264.1 |
$x^{18} - x^{16} - 9 x^{14} - 29 x^{12} + 84 x^{10} + 22 x^{8} + 202 x^{6} + 61 x^{4} + 61 x^{2} - 61$ |
$18$ |
[6,6] |
$2^{18}\cdot 31^{6}\cdot 61^{5}$ |
$3$ |
$19.6822849245$ |
$484.1731512360628$ |
|
|
? |
$C_6\wr S_3$ (as 18T284) |
trivial |
$2$ |
$11$ |
$41674.6324449$ |
| 18.12.640...008.1 |
$x^{18} - 6 x^{17} + 3 x^{16} + 34 x^{15} - 74 x^{14} + 68 x^{13} - 8 x^{12} - 160 x^{11} + 395 x^{10} - 474 x^{9} + 187 x^{8} + 270 x^{7} - 312 x^{6} + 6 x^{5} + 101 x^{4} - 24 x^{3} - 13 x^{2} + 4 x + 1$ |
$18$ |
[12,3] |
$-\,2^{6}\cdot 37^{5}\cdot 229^{6}$ |
$3$ |
$21.0168076429$ |
$613.4547123181493$ |
|
|
? |
$C_6\wr S_3$ (as 18T284) |
trivial |
$2$ |
$14$ |
$255224.243058$ |
| 18.12.640...008.2 |
$x^{18} - 9 x^{17} + 30 x^{16} - 22 x^{15} - 145 x^{14} + 446 x^{13} - 269 x^{12} - 972 x^{11} + 1981 x^{10} - 378 x^{9} - 2497 x^{8} + 2227 x^{7} + 548 x^{6} - 1285 x^{5} + 199 x^{4} + 193 x^{3} - 43 x^{2} - 5 x + 1$ |
$18$ |
[12,3] |
$-\,2^{6}\cdot 37^{5}\cdot 229^{6}$ |
$3$ |
$21.0168076429$ |
$613.4547123181493$ |
|
|
? |
$C_6\wr S_3$ (as 18T284) |
trivial |
$2$ |
$14$ |
$263090.025524$ |
| 18.6.776...973.1 |
$x^{18} - 3 x^{17} + 3 x^{16} + 4 x^{15} - 47 x^{14} + 80 x^{13} + 63 x^{12} - 192 x^{11} - 99 x^{10} + 528 x^{9} - 529 x^{8} + 209 x^{7} - 75 x^{6} + 44 x^{5} + 112 x^{4} - 114 x^{3} + 21 x^{2} - 4 x - 1$ |
$18$ |
[6,6] |
$11^{6}\cdot 37^{5}\cdot 43^{6}$ |
$3$ |
$21.243788562$ |
$440.82411107236106$ |
|
|
? |
$C_6\wr S_3$ (as 18T284) |
trivial |
$2$ |
$11$ |
$66391.2727424$ |
| 18.0.110...176.1 |
$x^{18} + 17 x^{16} + 115 x^{14} + 404 x^{12} + 802 x^{10} + 911 x^{8} + 568 x^{6} + 176 x^{4} + 24 x^{2} + 1$ |
$18$ |
[0,9] |
$-\,2^{12}\cdot 37^{4}\cdot 229^{6}$ |
$3$ |
$21.6664502136$ |
$475.2592197863912$ |
✓ |
|
? |
$C_6\wr S_3$ (as 18T284) |
$[2]$ |
$2$ |
$8$ |
$11357.1143117$ |
| 18.6.136...093.1 |
$x^{18} - 4 x^{17} + 2 x^{16} + 16 x^{15} + 7 x^{14} - 90 x^{13} - 30 x^{12} + 193 x^{11} + 38 x^{10} - 358 x^{9} - 279 x^{8} + 759 x^{7} - 276 x^{6} - 456 x^{5} + 597 x^{4} - 263 x^{3} + 26 x^{2} + 24 x - 8$ |
$18$ |
[6,6] |
$37^{7}\cdot 229^{6}$ |
$2$ |
$24.9154108775$ |
$306.72735615907465$ |
|
|
? |
$C_6\wr S_3$ (as 18T284) |
trivial |
$2$ |
$11$ |
$409939.057176$ |
| 18.18.233...669.1 |
$x^{18} - 4 x^{17} - 14 x^{16} + 71 x^{15} + 53 x^{14} - 472 x^{13} + 33 x^{12} + 1522 x^{11} - 555 x^{10} - 2661 x^{9} + 1098 x^{8} + 2705 x^{7} - 839 x^{6} - 1574 x^{5} + 194 x^{4} + 435 x^{3} + 27 x^{2} - 22 x + 1$ |
$18$ |
[18,0] |
$3^{9}\cdot 7^{5}\cdot 643^{6}$ |
$3$ |
$25.6673130347$ |
$292.54642426075026$ |
|
|
? |
$C_6\wr S_3$ (as 18T284) |
trivial |
$2$ |
$17$ |
$5484058.78058$ |
| 18.0.631...063.1 |
$x^{18} - 2 x^{17} - 9 x^{16} + 30 x^{15} + 26 x^{14} - 97 x^{13} + 184 x^{12} + 231 x^{11} - 384 x^{10} + 978 x^{9} + 1461 x^{8} - 279 x^{7} + 2232 x^{6} + 2772 x^{5} - 243 x^{4} + 405 x^{3} + 4050 x^{2} - 2970 x + 1431$ |
$18$ |
[0,9] |
$-\,3^{12}\cdot 7^{5}\cdot 643^{6}$ |
$3$ |
$30.8248247635$ |
$292.54642426075026$ |
✓ |
|
? |
$C_6\wr S_3$ (as 18T284) |
$[2, 2]$ |
$2$ |
$8$ |
$164073.537426$ |
| 18.18.560...928.1 |
$x^{18} - 5 x^{17} - 29 x^{16} + 174 x^{15} + 257 x^{14} - 2275 x^{13} - 342 x^{12} + 14348 x^{11} - 5814 x^{10} - 48471 x^{9} + 33485 x^{8} + 89506 x^{7} - 78846 x^{6} - 84548 x^{5} + 90666 x^{4} + 30849 x^{3} - 45350 x^{2} + 1420 x + 4973$ |
$18$ |
[18,0] |
$2^{12}\cdot 37^{7}\cdot 229^{6}$ |
$3$ |
$39.5507494372$ |
$613.4547123181493$ |
|
|
? |
$C_6\wr S_3$ (as 18T284) |
trivial |
$2$ |
$17$ |
$223462442.496$ |
