| 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 |
| 18.12.516...871.1 |
$x^{18} - 2 x^{17} - 8 x^{16} + 24 x^{15} - 8 x^{14} - 8 x^{13} - 30 x^{12} - 9 x^{11} + 103 x^{10} - 10 x^{9} - 41 x^{8} - 96 x^{7} + 41 x^{6} + 99 x^{5} - 44 x^{4} - 27 x^{3} + 13 x^{2} + 2 x - 1$ |
$18$ |
[12,3] |
$-\,37^{4}\cdot 191\cdot 229^{6}$ |
$3$ |
$18.2736446529$ |
$2322.2140099608105$ |
|
|
? |
$C_2\times A_4^3.S_4$ (as 18T764) |
trivial |
$2$ |
$14$ |
$61415.7107975$ |
| 18.12.581...123.1 |
$x^{18} - 6 x^{17} + 4 x^{16} + 30 x^{15} - 31 x^{14} - 62 x^{13} + 33 x^{12} + 91 x^{11} + 4 x^{10} - 85 x^{9} + 4 x^{8} + 91 x^{7} + 33 x^{6} - 62 x^{5} - 31 x^{4} + 30 x^{3} + 4 x^{2} - 6 x + 1$ |
$18$ |
[12,3] |
$-\,7^{12}\cdot 13^{4}\cdot 43^{5}$ |
$3$ |
$18.3942844514$ |
$464.7841483677139$ |
|
|
? |
$C_6\wr C_3$ (as 18T188) |
trivial |
$2$ |
$14$ |
$66429.7907366$ |
| 18.12.904...183.1 |
$x^{18} - 7 x^{17} + 9 x^{16} + 44 x^{15} - 129 x^{14} - 27 x^{13} + 439 x^{12} - 291 x^{11} - 576 x^{10} + 632 x^{9} + 345 x^{8} - 462 x^{7} - 230 x^{6} + 207 x^{5} + 126 x^{4} - 60 x^{3} - 27 x^{2} + 6 x + 1$ |
$18$ |
[12,3] |
$-\,7^{15}\cdot 138041^{2}$ |
$2$ |
$18.8521278962$ |
$1880.4094066508408$ |
|
|
? |
$S_4^3.C_6$ (as 18T768) |
trivial |
$2$ |
$14$ |
$88570.7345752$ |
| 18.12.959...831.1 |
$x^{18} - 3 x^{17} - 7 x^{16} + 34 x^{15} - 34 x^{14} - 21 x^{13} + 134 x^{12} - 245 x^{11} + 115 x^{10} + 105 x^{9} - 10 x^{8} - 106 x^{7} + 17 x^{6} + 82 x^{5} - 131 x^{4} + 66 x^{3} + 14 x^{2} - 11 x - 1$ |
$18$ |
[12,3] |
$-\,7^{12}\cdot 13^{4}\cdot 43^{4}\cdot 71$ |
$4$ |
$18.9139543581$ |
$2092.3567752939575$ |
|
|
? |
$C_2\times A_4^3.A_4$ (as 18T696) |
trivial |
$2$ |
$14$ |
$88418.0840893$ |
| 18.12.105...647.1 |
$x^{18} - 8 x^{17} + 21 x^{16} - 15 x^{15} - 25 x^{14} + 82 x^{13} - 132 x^{12} + 80 x^{11} + 56 x^{10} - 131 x^{9} + 153 x^{8} - 99 x^{7} + 61 x^{6} - 93 x^{5} + 21 x^{4} + 62 x^{3} - 37 x^{2} + 3 x + 1$ |
$18$ |
[12,3] |
$-\,7^{15}\cdot 53^{6}$ |
$2$ |
$19.0110887763$ |
$36.8456567103712$ |
|
|
? |
$C_6\times S_4$ (as 18T61) |
trivial |
$2$ |
$14$ |
$91563.2420757$ |
| 18.12.136...607.1 |
$x^{18} - 8 x^{17} + 19 x^{16} - 45 x^{14} + 6 x^{13} + 59 x^{12} + 58 x^{11} - 104 x^{10} - 155 x^{9} + 212 x^{8} + 122 x^{7} - 270 x^{6} + 20 x^{5} + 169 x^{4} - 62 x^{3} - 41 x^{2} + 19 x + 1$ |
$18$ |
[12,3] |
$-\,7^{15}\cdot 169457^{2}$ |
$2$ |
$19.2865691756$ |
$2083.426210338043$ |
|
|
? |
$S_4^3.C_6$ (as 18T768) |
trivial |
$2$ |
$14$ |
$106654.385237$ |
| 18.12.153...731.1 |
$x^{18} - 9 x^{17} + 27 x^{16} - 12 x^{15} - 94 x^{14} + 154 x^{13} + 70 x^{12} - 316 x^{11} + 80 x^{10} + 304 x^{9} - 188 x^{8} - 154 x^{7} + 168 x^{6} + 28 x^{5} - 78 x^{4} + 5 x^{3} + 15 x^{2} - x - 1$ |
$18$ |
[12,3] |
$-\,167\cdot 173\cdot 2307632671^{2}$ |
$3$ |
$19.4165469044$ |
$8165158.632743212$ |
|
|
✓ |
$C_2^9.S_9$ (as 18T968) |
trivial |
$2$ |
$14$ |
$114002.533972$ |
| 18.12.161...639.1 |
$x^{18} - 9 x^{17} + 24 x^{16} + 9 x^{15} - 141 x^{14} + 170 x^{13} + 115 x^{12} - 266 x^{11} + 55 x^{10} - 308 x^{9} + 704 x^{8} + 18 x^{7} - 980 x^{6} + 858 x^{5} - 242 x^{4} - 41 x^{3} + 44 x^{2} - 11 x + 1$ |
$18$ |
[12,3] |
$-\,7^{12}\cdot 22679^{3}$ |
$2$ |
$19.468657736$ |
$551.0749169202542$ |
|
|
? |
$S_3\wr C_3$ (as 18T207) |
trivial |
$2$ |
$14$ |
$110975.912853$ |
| 18.12.165...896.1 |
$x^{18} - 4 x^{17} + x^{16} + 20 x^{15} - 42 x^{14} + 7 x^{13} + 114 x^{12} - 130 x^{11} - 66 x^{10} + 203 x^{9} - 109 x^{8} - 134 x^{7} + 169 x^{6} + 49 x^{5} - 83 x^{4} - 11 x^{3} + 16 x^{2} + x - 1$ |
$18$ |
[12,3] |
$-\,2^{12}\cdot 37^{6}\cdot 59\cdot 16361^{2}$ |
$4$ |
$19.4985507404$ |
$9486.771800045728$ |
|
|
? |
$C_2\times S_4^3.S_4$ (as 18T912) |
trivial |
$2$ |
$14$ |
$122127.16932$ |
| 18.12.221...399.1 |
$x^{18} - 6 x^{17} + 4 x^{16} + 33 x^{15} - 60 x^{14} + 17 x^{13} + 44 x^{12} - 240 x^{11} + 290 x^{10} + 272 x^{9} - 41 x^{8} - 992 x^{7} - 415 x^{6} + 2830 x^{5} - 1547 x^{4} - 1504 x^{3} + 2040 x^{2} - 850 x + 125$ |
$18$ |
[12,3] |
$-\,7^{12}\cdot 113^{3}\cdot 223^{3}$ |
$3$ |
$19.8135628918$ |
$580.8852469488014$ |
|
|
? |
$S_3\wr C_3$ (as 18T207) |
trivial |
$2$ |
$14$ |
$136529.514651$ |
| 18.12.244...827.1 |
$x^{18} - 10 x^{16} - 8 x^{15} + 28 x^{14} + 52 x^{13} - 82 x^{12} - 73 x^{11} + 312 x^{10} - 112 x^{9} - 460 x^{8} + 429 x^{7} + 171 x^{6} - 365 x^{5} + 62 x^{4} + 91 x^{3} - 36 x^{2} + 1$ |
$18$ |
[12,3] |
$-\,257^{6}\cdot 947^{3}$ |
$2$ |
$19.9236714284$ |
$493.33457207051686$ |
|
|
? |
$S_3\wr S_3$ (as 18T314) |
trivial |
$2$ |
$14$ |
$146650.558663$ |
| 18.12.250...584.1 |
$x^{18} - 3 x^{16} - 27 x^{14} + 113 x^{12} + 15 x^{10} - 465 x^{8} + 366 x^{6} + 102 x^{4} - 39 x^{2} + 1$ |
$18$ |
[12,3] |
$-\,2^{6}\cdot 3^{24}\cdot 7^{12}$ |
$3$ |
$19.9481992835$ |
$31.66579252742446$ |
|
|
|
$C_6\times A_4$ (as 18T25) |
trivial |
$2$ |
$14$ |
$180334.192107$ |
| 18.12.264...328.1 |
$x^{18} - 4 x^{17} - 3 x^{16} + 40 x^{15} - 54 x^{14} - 116 x^{13} + 358 x^{12} + 8 x^{11} - 904 x^{10} + 556 x^{9} + 1244 x^{8} - 1152 x^{7} - 1146 x^{6} + 1076 x^{5} + 690 x^{4} - 512 x^{3} - 169 x^{2} + 104 x - 1$ |
$18$ |
[12,3] |
$-\,2^{16}\cdot 37^{6}\cdot 1163^{3}$ |
$3$ |
$20.0099534742$ |
$384.12532239440077$ |
|
|
? |
$S_3\wr S_3$ (as 18T314) |
trivial |
$2$ |
$14$ |
$181638.102013$ |
| 18.12.301...608.1 |
$x^{18} - 6 x^{17} + 8 x^{16} + 16 x^{15} - 65 x^{14} + 90 x^{13} + 17 x^{12} - 278 x^{11} + 321 x^{10} + 90 x^{9} - 394 x^{8} + 194 x^{7} + 108 x^{6} - 154 x^{5} + 31 x^{4} + 36 x^{3} - 15 x^{2} - 2 x + 1$ |
$18$ |
[12,3] |
$-\,2^{12}\cdot 37^{6}\cdot 107\cdot 16361^{2}$ |
$4$ |
$20.1541835204$ |
$12775.68917038369$ |
|
|
? |
$C_2\times S_4^3.S_4$ (as 18T912) |
trivial |
$2$ |
$14$ |
$166990.357156$ |
| 18.12.429...367.1 |
$x^{18} - 3 x^{17} - 7 x^{16} + 34 x^{15} - 35 x^{14} - 42 x^{13} + 146 x^{12} + 32 x^{11} - 240 x^{10} - 164 x^{9} + 112 x^{8} + 146 x^{7} + 105 x^{6} + 174 x^{5} + 108 x^{4} - 27 x^{3} - 45 x^{2} - 13 x - 1$ |
$18$ |
[12,3] |
$-\,7^{15}\cdot 67^{6}$ |
$2$ |
$20.5560643036$ |
$48.72037301447419$ |
|
|
? |
$C_6\times S_4$ (as 18T61) |
trivial |
$2$ |
$14$ |
$254333.220281$ |
| 18.12.496...487.1 |
$x^{18} - 9 x^{17} + 33 x^{16} - 60 x^{15} + 27 x^{14} + 90 x^{13} - 110 x^{12} + 3 x^{11} - 132 x^{10} + 210 x^{9} + 198 x^{8} - 261 x^{7} - 139 x^{6} + 111 x^{5} + 75 x^{4} - 24 x^{3} - 18 x^{2} + 3 x + 1$ |
$18$ |
[12,3] |
$-\,3^{24}\cdot 7^{12}\cdot 127$ |
$3$ |
$20.7223188015$ |
|
|
|
? |
$C_2^9:C_3^2$ (as 18T459) |
trivial |
$2$ |
$14$ |
$244676.881686$ |
| 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 |
$2$ |
$14$ |
$263090.025524$ |
| 18.12.755...599.1 |
$x^{18} - 6 x^{16} - 2 x^{15} - 5 x^{14} + 50 x^{13} + 48 x^{12} - 137 x^{11} - 110 x^{10} - 151 x^{9} + 393 x^{8} + 748 x^{7} - 519 x^{6} - 661 x^{5} + 256 x^{4} + 180 x^{3} - 38 x^{2} - 7 x + 1$ |
$18$ |
[12,3] |
$-\,7^{12}\cdot 13^{5}\cdot 43^{5}$ |
$3$ |
$21.2113661095$ |
$712.7029119734025$ |
|
|
? |
$C_6\wr C_3$ (as 18T188) |
trivial |
$2$ |
$14$ |
$275520.322473$ |
| 18.12.755...599.2 |
$x^{18} - 3 x^{17} - 4 x^{16} + 26 x^{15} - 38 x^{14} + 14 x^{13} + 29 x^{12} - 84 x^{11} + 246 x^{10} - 483 x^{9} + 496 x^{8} - 218 x^{7} - 122 x^{6} + 284 x^{5} - 162 x^{4} - 2 x^{3} + 24 x^{2} - 2 x - 1$ |
$18$ |
[12,3] |
$-\,7^{12}\cdot 13^{5}\cdot 43^{5}$ |
$3$ |
$21.2113661095$ |
$712.7029119734025$ |
|
|
? |
$C_2\times A_4^3.A_4$ (as 18T696) |
trivial |
$2$ |
$14$ |
$286892.983454$ |
| 18.12.987...691.1 |
$x^{18} - 3 x^{17} - 12 x^{16} + 46 x^{15} + 15 x^{14} - 165 x^{13} + 11 x^{12} + 321 x^{11} - 9 x^{10} - 405 x^{9} - 60 x^{8} + 297 x^{7} + 126 x^{6} - 90 x^{5} - 93 x^{4} - 10 x^{3} + 21 x^{2} + 9 x + 1$ |
$18$ |
[12,3] |
$-\,3^{27}\cdot 73^{3}\cdot 577^{2}$ |
$3$ |
$21.5294534389$ |
|
|
|
? |
$D_6\wr C_3$ (as 18T472) |
trivial |
$2$ |
$14$ |
$318063.575479$ |
| 18.12.987...691.2 |
$x^{18} - 6 x^{17} + 3 x^{16} + 41 x^{15} - 48 x^{14} - 153 x^{13} + 249 x^{12} + 276 x^{11} - 624 x^{10} - 165 x^{9} + 774 x^{8} - 90 x^{7} - 472 x^{6} + 132 x^{5} + 135 x^{4} - 38 x^{3} - 18 x^{2} + 3 x + 1$ |
$18$ |
[12,3] |
$-\,3^{27}\cdot 73^{3}\cdot 577^{2}$ |
$3$ |
$21.5294534389$ |
|
|
|
? |
$C_2\times S_4^3.A_4$ (as 18T879) |
trivial |
$2$ |
$14$ |
$309730.934527$ |
| 18.12.987...691.3 |
$x^{18} - 6 x^{16} - 4 x^{15} - 6 x^{14} + 51 x^{13} + 105 x^{12} - 186 x^{11} - 318 x^{10} + 237 x^{9} + 552 x^{8} + 18 x^{7} - 613 x^{6} - 237 x^{5} + 384 x^{4} + 112 x^{3} - 99 x^{2} + 9 x + 1$ |
$18$ |
[12,3] |
$-\,3^{27}\cdot 73^{3}\cdot 577^{2}$ |
$3$ |
$21.5294534389$ |
|
|
|
? |
$C_2\times S_4^3.A_4$ (as 18T879) |
trivial |
$2$ |
$14$ |
$334605.67531$ |
| 18.12.100...967.1 |
$x^{18} - 4 x^{17} - 12 x^{16} + 54 x^{15} + 63 x^{14} - 307 x^{13} - 186 x^{12} + 961 x^{11} + 307 x^{10} - 1779 x^{9} - 187 x^{8} + 1893 x^{7} - 151 x^{6} - 988 x^{5} + 200 x^{4} + 161 x^{3} - 13 x^{2} - 11 x - 1$ |
$18$ |
[12,3] |
$-\,23^{3}\cdot 5569^{3}\cdot 21817^{2}$ |
$3$ |
$21.5446369005$ |
$115766.25967503864$ |
|
|
? |
$C_2^9.S_9$ (as 18T968) |
trivial |
$2$ |
$14$ |
$297575.6426$ |
| 18.12.110...176.1 |
$x^{18} - 10 x^{16} + 26 x^{14} + 29 x^{12} - 188 x^{10} + 125 x^{8} + 158 x^{6} - 81 x^{4} + 3 x^{2} + 1$ |
$18$ |
[12,3] |
$-\,2^{12}\cdot 37^{4}\cdot 229^{6}$ |
$3$ |
$21.6664502136$ |
$657.7159307568076$ |
|
|
? |
$C_2\times A_4^3.S_4$ (as 18T764) |
trivial |
$2$ |
$14$ |
$382025.335018$ |
| 18.12.110...176.2 |
$x^{18} - 10 x^{16} + 32 x^{14} - 18 x^{12} - 92 x^{10} + 150 x^{8} + 13 x^{6} - 150 x^{4} + 72 x^{2} + 1$ |
$18$ |
[12,3] |
$-\,2^{12}\cdot 37^{4}\cdot 229^{6}$ |
$3$ |
$21.6664502136$ |
$616.3349549315699$ |
|
|
? |
$C_2\times A_4^3.S_4$ (as 18T764) |
trivial |
$2$ |
$14$ |
$321587.49409$ |
| 18.12.110...176.3 |
$x^{18} - 6 x^{16} + 4 x^{14} + 43 x^{12} - 114 x^{10} + 96 x^{8} - 6 x^{6} - 22 x^{4} + 4 x^{2} + 1$ |
$18$ |
[12,3] |
$-\,2^{12}\cdot 37^{4}\cdot 229^{6}$ |
$3$ |
$21.6664502136$ |
$657.7159307568076$ |
|
|
? |
$C_2\times A_4^3.S_4$ (as 18T764) |
trivial |
$2$ |
$14$ |
$372335.492177$ |
| 18.12.125...184.1 |
$x^{18} - x^{16} - 25 x^{14} + 90 x^{12} - 97 x^{10} - 14 x^{8} + 81 x^{6} - 34 x^{4} - x^{2} + 1$ |
$18$ |
[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 |
$2$ |
$14$ |
$404681.718697$ |
| 18.12.125...184.2 |
$x^{18} + 7 x^{16} - 16 x^{14} - 74 x^{12} + 230 x^{10} - 172 x^{8} - 45 x^{6} + 97 x^{4} - 30 x^{2} + 1$ |
$18$ |
[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 |
$2$ |
$14$ |
$345466.150734$ |
| 18.12.125...184.3 |
$x^{18} - 6 x^{16} - 3 x^{14} + 50 x^{12} - 12 x^{10} - 89 x^{8} + 58 x^{6} + 8 x^{4} - 9 x^{2} + 1$ |
$18$ |
[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 |
$2$ |
$14$ |
$393002.389776$ |
| 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 |
$2$ |
$14$ |
$349463.693227$ |
| 18.12.132...816.1 |
$x^{18} - 13 x^{16} - 5 x^{15} + 71 x^{14} + 33 x^{13} - 193 x^{12} - 65 x^{11} + 247 x^{10} + 50 x^{9} - 114 x^{8} - 53 x^{7} - x^{6} + 69 x^{5} + 7 x^{4} - 34 x^{3} + 3 x^{2} + 5 x - 1$ |
$18$ |
[12,3] |
$-\,2^{12}\cdot 11^{3}\cdot 101^{6}\cdot 479^{2}$ |
$4$ |
$21.8863980213$ |
$1158.0077074022477$ |
|
|
? |
$D_6\wr S_3$ (as 18T556) |
trivial |
$2$ |
$14$ |
$457172.031967$ |
| 18.12.209...159.1 |
$x^{18} - 2 x^{17} - 6 x^{16} + 14 x^{15} - 3 x^{14} - 32 x^{13} + 34 x^{12} + 19 x^{11} - 10 x^{10} - 51 x^{9} + 15 x^{8} + 90 x^{7} - 57 x^{6} - 57 x^{5} + 44 x^{4} + 14 x^{3} - 12 x^{2} - x + 1$ |
$18$ |
[12,3] |
$-\,7^{12}\cdot 4591\cdot 181607^{2}$ |
$3$ |
$22.4484341158$ |
$105661.95255575814$ |
|
|
? |
$C_2\times S_4^3.A_4$ (as 18T879) |
trivial |
$2$ |
$14$ |
$507360.579561$ |
| 18.12.246...211.1 |
$x^{18} - 3 x^{17} - 15 x^{16} + 32 x^{15} + 78 x^{14} - 133 x^{13} - 147 x^{12} + 275 x^{11} - 27 x^{10} - 233 x^{9} + 400 x^{8} - 152 x^{7} - 378 x^{6} + 406 x^{5} - 6 x^{4} - 171 x^{3} + 90 x^{2} - 17 x + 1$ |
$18$ |
[12,3] |
$-\,7^{17}\cdot 13^{9}$ |
$2$ |
$22.6526922589$ |
$53.26406107867856$ |
|
|
? |
$C_6^2.C_6$ (as 18T92) |
trivial |
$2$ |
$14$ |
$606102.254632$ |
| 18.12.246...211.2 |
$x^{18} - 3 x^{17} - 8 x^{16} + 11 x^{15} + 36 x^{14} + 21 x^{13} - 56 x^{12} - 369 x^{11} - 20 x^{10} + 1104 x^{9} + 92 x^{8} - 1279 x^{7} - 70 x^{6} + 651 x^{5} + 29 x^{4} - 143 x^{3} - 8 x^{2} + 11 x + 1$ |
$18$ |
[12,3] |
$-\,7^{17}\cdot 13^{9}$ |
$2$ |
$22.6526922589$ |
$53.26406107867856$ |
|
|
? |
$C_6^2.C_6$ (as 18T92) |
trivial |
$2$ |
$14$ |
$599704.249482$ |
| 18.12.251...136.1 |
$x^{18} - 9 x^{16} - 18 x^{13} + 138 x^{12} + 144 x^{11} - 207 x^{10} - 324 x^{9} - 99 x^{8} + 450 x^{7} + 369 x^{6} - 432 x^{5} - 351 x^{4} + 162 x^{3} + 153 x^{2} + 18 x - 3$ |
$18$ |
[12,3] |
$-\,2^{24}\cdot 3^{36}$ |
$2$ |
$22.6785788981$ |
$30.883428090661386$ |
|
|
? |
$S_3^2:C_6$ (as 18T93) |
trivial |
$2$ |
$14$ |
$810029.648073$ |
| 18.12.288...559.1 |
$x^{18} - 3 x^{17} - 3 x^{16} + 29 x^{15} - 26 x^{14} - 87 x^{13} + 156 x^{12} + 36 x^{11} - 300 x^{10} + 229 x^{9} + 15 x^{8} - 525 x^{7} + 630 x^{6} + 677 x^{5} - 678 x^{4} - 533 x^{3} + 175 x^{2} + 177 x + 29$ |
$18$ |
[12,3] |
$-\,3^{9}\cdot 7^{12}\cdot 13^{9}$ |
$3$ |
$22.8523568346$ |
$47.53481777030535$ |
|
|
? |
$S_3^2:C_6$ (as 18T93) |
trivial |
$2$ |
$14$ |
$625728.498159$ |
| 18.12.300...000.1 |
$x^{18} - 6 x^{17} + 9 x^{16} + 14 x^{15} - 93 x^{14} + 246 x^{13} - 139 x^{12} - 840 x^{11} + 1350 x^{10} + 902 x^{9} - 2604 x^{8} - 276 x^{7} + 2352 x^{6} - 72 x^{5} - 1104 x^{4} + 32 x^{3} + 240 x^{2} - 16$ |
$18$ |
[12,3] |
$-\,2^{12}\cdot 3^{24}\cdot 5^{9}\cdot 11^{3}$ |
$4$ |
$22.9033382172$ |
$83.00104733220466$ |
|
|
? |
$C_3\wr D_4$ (as 18T189) |
trivial |
$2$ |
$14$ |
$826735.916468$ |
| 18.12.408...856.1 |
$x^{18} - 9 x^{16} + 33 x^{14} - 44 x^{12} - 48 x^{10} + 211 x^{8} - 229 x^{6} + 103 x^{4} - 18 x^{2} + 1$ |
$18$ |
[12,3] |
$-\,2^{24}\cdot 101^{6}\cdot 479^{2}$ |
$3$ |
$23.2967591165$ |
|
|
|
? |
$D_6\wr S_3$ (as 18T556) |
trivial |
$2$ |
$14$ |
$729299.636172$ |
| 18.12.585...512.1 |
$x^{18} - 3 x^{17} - 6 x^{16} + 24 x^{15} - 15 x^{14} + 27 x^{13} - 12 x^{12} - 261 x^{11} + 222 x^{10} + 508 x^{9} - 384 x^{8} - 534 x^{7} + 258 x^{6} + 330 x^{5} - 63 x^{4} - 102 x^{3} + 12 x + 1$ |
$18$ |
[12,3] |
$-\,2^{6}\cdot 3^{31}\cdot 23^{6}$ |
$3$ |
$23.7662925164$ |
|
|
|
? |
$C_2^4:(A_4\times D_6)$ (as 18T366) |
trivial |
$2$ |
$14$ |
$1230959.50166$ |
| 18.12.673...408.1 |
$x^{18} - 7 x^{17} + 11 x^{16} + 30 x^{15} - 110 x^{14} + 58 x^{13} + 159 x^{12} - 212 x^{11} + 115 x^{10} - 264 x^{9} + 351 x^{8} + 98 x^{7} - 587 x^{6} + 506 x^{5} - 98 x^{4} - 109 x^{3} + 74 x^{2} - 16 x + 1$ |
$18$ |
[12,3] |
$-\,2^{6}\cdot 7^{15}\cdot 53^{6}$ |
$3$ |
$23.9524709306$ |
$104.21525486870038$ |
|
|
? |
$C_2^4:(A_4\times D_6)$ (as 18T366) |
trivial |
$2$ |
$14$ |
$909450.396577$ |
| 18.12.675...768.1 |
$x^{18} - 15 x^{16} + 72 x^{14} - 93 x^{12} - 225 x^{10} + 675 x^{8} - 297 x^{6} - 378 x^{4} + 162 x^{2} + 27$ |
$18$ |
[12,3] |
$-\,2^{6}\cdot 3^{27}\cdot 7^{12}$ |
$3$ |
$23.9565297087$ |
$53.7805908144551$ |
|
|
? |
$C_2^3:A_4^2$ (as 18T263) |
trivial |
$2$ |
$14$ |
$868588.19407$ |
| 18.12.780...859.1 |
$x^{18} - 15 x^{16} - x^{15} + 60 x^{14} + 48 x^{13} - 40 x^{12} - 375 x^{11} + 87 x^{10} + 729 x^{9} - 756 x^{8} + 336 x^{7} + 108 x^{6} - 279 x^{5} + 108 x^{4} + 28 x^{3} - 21 x^{2} + 1$ |
$18$ |
[12,3] |
$-\,3^{27}\cdot 73^{2}\cdot 577^{3}$ |
$3$ |
$24.1498103348$ |
|
|
|
? |
$D_6\wr C_3$ (as 18T472) |
trivial |
$2$ |
$14$ |
$987631.658974$ |
| 18.12.101...104.1 |
$x^{18} - 3 x^{16} - 4 x^{14} - 23 x^{12} + 79 x^{10} + 139 x^{8} - 303 x^{6} + 135 x^{4} - 21 x^{2} + 1$ |
$18$ |
[12,3] |
$-\,2^{18}\cdot 7^{12}\cdot 52879^{2}$ |
$3$ |
$24.5040537923$ |
|
|
|
? |
$D_6\wr C_3$ (as 18T472) |
trivial |
$2$ |
$14$ |
$973728.615269$ |
| 18.12.101...104.2 |
$x^{18} - 8 x^{16} + 17 x^{14} + 12 x^{12} - 87 x^{10} + 121 x^{8} - 88 x^{6} + 43 x^{4} - 11 x^{2} + 1$ |
$18$ |
[12,3] |
$-\,2^{18}\cdot 7^{12}\cdot 52879^{2}$ |
$3$ |
$24.5040537923$ |
|
|
|
? |
$C_2\times S_4^3.A_4$ (as 18T879) |
trivial |
$2$ |
$14$ |
$1286173.79101$ |
| 18.12.101...104.3 |
$x^{18} - 11 x^{16} + 43 x^{14} - 74 x^{12} + 58 x^{10} - 24 x^{8} - 9 x^{6} + 45 x^{4} - 29 x^{2} + 1$ |
$18$ |
[12,3] |
$-\,2^{18}\cdot 7^{12}\cdot 52879^{2}$ |
$3$ |
$24.5040537923$ |
|
|
|
? |
$C_2\times S_4^3.A_4$ (as 18T879) |
trivial |
$2$ |
$14$ |
$1279705.87581$ |
| 18.12.101...104.4 |
$x^{18} - 6 x^{16} + 6 x^{14} + 12 x^{12} - 3 x^{10} - 17 x^{8} - 16 x^{6} + 34 x^{4} - 13 x^{2} + 1$ |
$18$ |
[12,3] |
$-\,2^{18}\cdot 7^{12}\cdot 52879^{2}$ |
$3$ |
$24.504053792335927$ |
|
|
|
? |
$C_2\times S_4^3.A_4$ (as 18T879) |
trivial |
$2$ |
$14$ |
$1087101.6843840005$ |
| 18.12.101...104.5 |
$x^{18} - 9 x^{16} + 21 x^{14} - 6 x^{12} + 6 x^{10} - 34 x^{8} + 6 x^{6} + 23 x^{4} - 10 x^{2} + 1$ |
$18$ |
[12,3] |
$-\,2^{18}\cdot 7^{12}\cdot 52879^{2}$ |
$3$ |
$24.504053792335927$ |
|
|
|
? |
$C_2\times S_4^3.A_4$ (as 18T879) |
trivial |
$2$ |
$14$ |
$1016965.3857325111$ |
| 18.12.101...584.1 |
$x^{18} - 10 x^{16} + 36 x^{14} - 48 x^{12} - 27 x^{10} + 158 x^{8} - 180 x^{6} + 88 x^{4} - 18 x^{2} + 1$ |
$18$ |
[12,3] |
$-\,2^{18}\cdot 7^{12}\cdot 52919^{2}$ |
$3$ |
$24.5061126495$ |
|
|
|
? |
$D_6\wr C_3$ (as 18T472) |
trivial |
$2$ |
$14$ |
$1197133.31669$ |
| 18.12.101...584.2 |
$x^{18} - 14 x^{16} + 76 x^{14} - 200 x^{12} + 257 x^{10} - 128 x^{8} - 38 x^{6} + 96 x^{4} - 50 x^{2} + 1$ |
$18$ |
[12,3] |
$-\,2^{18}\cdot 7^{12}\cdot 52919^{2}$ |
$3$ |
$24.5061126495$ |
|
|
|
? |
$C_2\times S_4^3.A_4$ (as 18T879) |
trivial |
$2$ |
$14$ |
$1147445.07488$ |
