| 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 |
| 18.10.394...289.1 |
$x^{18} - 7 x^{17} + 13 x^{16} + 14 x^{15} - 64 x^{14} + 25 x^{13} + 62 x^{12} - 6 x^{11} - 16 x^{10} - 110 x^{9} + 40 x^{8} + 67 x^{7} + 43 x^{6} - 53 x^{5} - 20 x^{4} + 14 x^{3} - 4 x^{2} - x + 1$ |
$18$ |
[10,4] |
$19^{16}\cdot 37^{2}$ |
$2$ |
$20.4604180731$ |
$83.32411881951172$ |
|
|
? |
$C_2^8:C_9$ (as 18T368) |
trivial |
$[2]$ |
$2$ |
$13$ |
$135813.9354$ |
| 18.10.394...289.2 |
$x^{18} - 8 x^{17} + 21 x^{16} + 7 x^{15} - 171 x^{14} + 414 x^{13} - 353 x^{12} - 237 x^{11} + 757 x^{10} - 490 x^{9} - 127 x^{8} + 306 x^{7} - 159 x^{6} + 12 x^{5} + 57 x^{4} - 27 x^{3} - 9 x^{2} + 4 x + 1$ |
$18$ |
[10,4] |
$19^{16}\cdot 37^{2}$ |
$2$ |
$20.4604180731$ |
$83.32411881951172$ |
|
|
? |
$C_2^8:C_9$ (as 18T368) |
trivial |
$[2]$ |
$2$ |
$13$ |
$139723.055343$ |
| 18.6.394...289.2 |
$x^{18} - x^{17} + 4 x^{16} - 10 x^{15} + 4 x^{14} - 13 x^{13} + 12 x^{12} + 93 x^{11} - 167 x^{10} + 125 x^{9} - 305 x^{8} + 577 x^{7} - 322 x^{6} - 145 x^{5} + 154 x^{4} + 44 x^{3} - 64 x^{2} + 15 x - 1$ |
$18$ |
[6,6] |
$19^{16}\cdot 37^{2}$ |
$2$ |
$20.4604180731$ |
$83.32411881951172$ |
|
|
? |
$C_2^8:C_9$ (as 18T368) |
trivial |
$[2]$ |
$2$ |
$11$ |
$59372.2035473$ |
| 18.6.368...689.1 |
$x^{18} - 2 x^{17} - 2 x^{16} - 10 x^{15} + 2 x^{14} + 41 x^{13} - 25 x^{12} + 68 x^{11} - 57 x^{10} + 61 x^{9} - 304 x^{8} - 53 x^{7} - 104 x^{6} - 99 x^{5} + 46 x^{4} + 6 x^{3} + 4 x^{2} + 7 x + 1$ |
$18$ |
[6,6] |
$19^{16}\cdot 113^{2}$ |
$2$ |
$23.1627273219$ |
$145.61599739544846$ |
|
|
? |
$C_2^8:C_9$ (as 18T368) |
trivial |
$[2]$ |
$2$ |
$11$ |
$156587.347558$ |
| 18.10.368...689.2 |
$x^{18} - 6 x^{17} + 12 x^{16} - 12 x^{15} + 16 x^{14} + 18 x^{13} - 83 x^{12} - 249 x^{11} + 765 x^{10} + 80 x^{9} - 1195 x^{8} - 185 x^{7} + 1318 x^{6} + 65 x^{5} - 644 x^{4} + 7 x^{3} + 96 x^{2} - 4 x - 1$ |
$18$ |
[10,4] |
$19^{16}\cdot 113^{2}$ |
$2$ |
$23.1627273219$ |
$145.61599739544846$ |
|
|
? |
$C_2^8:C_9$ (as 18T368) |
trivial |
$[2]$ |
$2$ |
$13$ |
$439599.498559$ |
| 18.10.105...561.1 |
$x^{18} - 8 x^{17} + 25 x^{16} - 32 x^{15} - 39 x^{14} + 260 x^{13} - 446 x^{12} + 9 x^{11} + 1102 x^{10} - 1402 x^{9} - 171 x^{8} + 1641 x^{7} - 880 x^{6} - 473 x^{5} + 402 x^{4} + 104 x^{3} - 90 x^{2} - 3 x + 1$ |
$18$ |
[10,4] |
$19^{16}\cdot 191^{2}$ |
$2$ |
$24.5537607294$ |
$189.31566492031587$ |
|
|
? |
$C_2^8:C_9$ (as 18T368) |
trivial |
$[2]$ |
$2$ |
$13$ |
$694739.500993$ |
| 18.10.105...561.2 |
$x^{18} - 4 x^{17} - 4 x^{16} + 24 x^{15} + 4 x^{13} - 61 x^{12} - 507 x^{11} + 1367 x^{10} + 281 x^{9} - 3913 x^{8} + 3502 x^{7} + 1372 x^{6} - 3492 x^{5} + 1273 x^{4} + 442 x^{3} - 319 x^{2} + 34 x - 1$ |
$18$ |
[10,4] |
$19^{16}\cdot 191^{2}$ |
$2$ |
$24.553760729393655$ |
$189.31566492031587$ |
|
|
? |
$C_2^8:C_9$ (as 18T368) |
trivial |
$[2]$ |
$2$ |
$13$ |
$736905.887804417$ |
| 18.2.756...064.1 |
$x^{18} + 14 x^{16} + 66 x^{14} + 134 x^{12} + 91 x^{10} - 78 x^{8} - 159 x^{6} - 87 x^{4} - 18 x^{2} - 1$ |
$18$ |
[2,8] |
$2^{18}\cdot 19^{16}$ |
$2$ |
$27.3968015041$ |
|
|
|
✓ |
$C_2^8:C_9$ (as 18T368) |
trivial |
trivial |
$2$ |
$9$ |
$344079.988637$ |
| 18.10.756...064.2 |
$x^{18} - 6 x^{16} - 3 x^{14} + 68 x^{12} - 68 x^{10} - 151 x^{8} + 198 x^{6} + 33 x^{4} - 34 x^{2} - 1$ |
$18$ |
[10,4] |
$2^{18}\cdot 19^{16}$ |
$2$ |
$27.3968015041$ |
|
|
|
? |
$C_2^8:C_9$ (as 18T368) |
trivial |
trivial |
$2$ |
$13$ |
$2067125.20635$ |
| 18.14.756...064.2 |
$x^{18} - 9 x^{16} + 17 x^{14} + 49 x^{12} - 178 x^{10} + 83 x^{8} + 160 x^{6} - 131 x^{4} + 28 x^{2} - 1$ |
$18$ |
[14,2] |
$2^{18}\cdot 19^{16}$ |
$2$ |
$27.3968015041$ |
|
|
|
? |
$C_2^8:C_9$ (as 18T368) |
trivial |
trivial |
$2$ |
$15$ |
$4692013.12703$ |
| 18.10.756...064.3 |
$x^{18} - 4 x^{16} - 14 x^{14} + 49 x^{12} + 37 x^{10} - 160 x^{8} + 65 x^{6} + 41 x^{4} - 13 x^{2} - 1$ |
$18$ |
[10,4] |
$2^{18}\cdot 19^{16}$ |
$2$ |
$27.3968015041$ |
|
|
|
? |
$C_2^8:C_9$ (as 18T368) |
trivial |
trivial |
$2$ |
$13$ |
$1872250.75632$ |
| 18.14.756...064.3 |
$x^{18} - 7 x^{16} + 7 x^{14} + 45 x^{12} - 119 x^{10} + 63 x^{8} + 75 x^{6} - 82 x^{4} + 17 x^{2} - 1$ |
$18$ |
[14,2] |
$2^{18}\cdot 19^{16}$ |
$2$ |
$27.3968015041$ |
|
|
|
? |
$C_2^8:C_9$ (as 18T368) |
trivial |
trivial |
$2$ |
$15$ |
$4505742.50348$ |
| 18.10.258...864.1 |
$x^{18} - 18 x^{14} + 9 x^{12} + 81 x^{10} - 54 x^{8} - 90 x^{6} + 81 x^{4} - 9$ |
$18$ |
[10,4] |
$2^{18}\cdot 3^{44}$ |
$2$ |
$29.330967999939233$ |
|
|
|
? |
$C_2^8:C_9$ (as 18T368) |
trivial |
trivial |
$2$ |
$13$ |
$6765640.006566327$ |
| 18.2.258...864.2 |
$x^{18} + 9 x^{16} + 9 x^{14} - 96 x^{12} - 333 x^{10} - 450 x^{8} - 306 x^{6} - 108 x^{4} - 18 x^{2} - 1$ |
$18$ |
[2,8] |
$2^{18}\cdot 3^{44}$ |
$2$ |
$29.3309679999$ |
|
|
|
✓ |
$C_2^8:C_9$ (as 18T368) |
trivial |
trivial |
$2$ |
$9$ |
$1164023.95238$ |
| 18.10.103...616.1 |
$x^{18} + 13 x^{16} - 41 x^{14} - 825 x^{12} + 483 x^{10} + 14023 x^{8} - 12551 x^{6} - 19822 x^{4} + 20239 x^{2} - 1369$ |
$18$ |
[10,4] |
$2^{18}\cdot 19^{16}\cdot 37^{2}$ |
$3$ |
$40.9208361463$ |
|
|
|
? |
$C_2^8:C_9$ (as 18T368) |
trivial |
$[2, 2]$ |
$2$ |
$13$ |
$71766297.0337$ |
| 18.6.103...616.1 |
$x^{18} + 21 x^{16} + 158 x^{14} + 457 x^{12} - 25 x^{10} - 2275 x^{8} - 1736 x^{6} + 3394 x^{4} + 1147 x^{2} - 1369$ |
$18$ |
[6,6] |
$2^{18}\cdot 19^{16}\cdot 37^{2}$ |
$3$ |
$40.9208361463$ |
|
|
|
? |
$C_2^8:C_9$ (as 18T368) |
trivial |
$[2, 2]$ |
$2$ |
$11$ |
$27370209.3427$ |
| 18.14.103...616.1 |
$x^{18} - 24 x^{16} + 218 x^{14} - 892 x^{12} + 1307 x^{10} + 1214 x^{8} - 4624 x^{6} + 2098 x^{4} + 2072 x^{2} - 1369$ |
$18$ |
[14,2] |
$2^{18}\cdot 19^{16}\cdot 37^{2}$ |
$3$ |
$40.9208361463$ |
|
|
|
? |
$C_2^8:C_9$ (as 18T368) |
trivial |
$[2, 2]$ |
$2$ |
$15$ |
$176686536.915$ |
| 18.14.103...616.2 |
$x^{18} - 16 x^{16} + 42 x^{14} + 229 x^{12} - 1282 x^{10} + 1517 x^{8} + 2387 x^{6} - 7316 x^{4} + 5920 x^{2} - 1369$ |
$18$ |
[14,2] |
$2^{18}\cdot 19^{16}\cdot 37^{2}$ |
$3$ |
$40.9208361463$ |
|
|
|
? |
$C_2^8:C_9$ (as 18T368) |
trivial |
$[2, 2]$ |
$2$ |
$15$ |
$200559300.784$ |
| 18.6.103...616.2 |
$x^{18} + 13 x^{16} + 16 x^{14} - 255 x^{12} - 581 x^{10} + 894 x^{8} + 2592 x^{6} - 252 x^{4} - 2960 x^{2} - 1369$ |
$18$ |
[6,6] |
$2^{18}\cdot 19^{16}\cdot 37^{2}$ |
$3$ |
$40.9208361463$ |
|
|
|
? |
$C_2^8:C_9$ (as 18T368) |
trivial |
$[2, 2]$ |
$2$ |
$11$ |
$31043587.8029$ |
| 18.10.103...616.2 |
$x^{18} - 4 x^{16} - 128 x^{14} - 217 x^{12} + 2279 x^{10} + 5730 x^{8} - 5939 x^{6} - 9877 x^{4} + 8917 x^{2} - 1369$ |
$18$ |
[10,4] |
$2^{18}\cdot 19^{16}\cdot 37^{2}$ |
$3$ |
$40.9208361463$ |
|
|
|
? |
$C_2^8:C_9$ (as 18T368) |
trivial |
$[2, 2]$ |
$2$ |
$13$ |
$77763714.8539$ |
| 18.18.103...616.2 |
$x^{18} - 36 x^{16} + 500 x^{14} - 3571 x^{12} + 14453 x^{10} - 34157 x^{8} + 46714 x^{6} - 34967 x^{4} + 12395 x^{2} - 1369$ |
$18$ |
[18,0] |
$2^{18}\cdot 19^{16}\cdot 37^{2}$ |
$3$ |
$40.9208361463$ |
|
|
|
? |
$C_2^8:C_9$ (as 18T368) |
trivial |
$[2, 2]$ |
$2$ |
$17$ |
$448497656.217$ |
| 18.6.103...616.3 |
$x^{18} - 5 x^{16} - 48 x^{14} + 58 x^{12} + 756 x^{10} + 853 x^{8} - 2268 x^{6} - 6053 x^{4} - 4958 x^{2} - 1369$ |
$18$ |
[6,6] |
$2^{18}\cdot 19^{16}\cdot 37^{2}$ |
$3$ |
$40.9208361463$ |
|
|
|
? |
$C_2^8:C_9$ (as 18T368) |
trivial |
$[2, 2]$ |
$2$ |
$11$ |
$31418398.4612$ |
| 18.18.103...616.3 |
$x^{18} - 36 x^{16} + 538 x^{14} - 4331 x^{12} + 20381 x^{10} - 56900 x^{8} + 91269 x^{6} - 76824 x^{4} + 27158 x^{2} - 1369$ |
$18$ |
[18,0] |
$2^{18}\cdot 19^{16}\cdot 37^{2}$ |
$3$ |
$40.9208361463$ |
|
|
|
? |
$C_2^8:C_9$ (as 18T368) |
trivial |
$[2, 2]$ |
$2$ |
$17$ |
$439032095.645$ |
| 18.10.103...616.3 |
$x^{18} - 7 x^{16} - 12 x^{14} + 159 x^{12} - 81 x^{10} - 1020 x^{8} + 854 x^{6} + 2350 x^{4} - 1332 x^{2} - 1369$ |
$18$ |
[10,4] |
$2^{18}\cdot 19^{16}\cdot 37^{2}$ |
$3$ |
$40.92083614629157$ |
|
|
|
? |
$C_2^8:C_9$ (as 18T368) |
trivial |
$[2, 2]$ |
$2$ |
$13$ |
$88217241.68322437$ |
| 18.18.103...616.4 |
$x^{18} - 30 x^{16} + 362 x^{14} - 2311 x^{12} + 8629 x^{10} - 19542 x^{8} + 26713 x^{6} - 21037 x^{4} + 8547 x^{2} - 1369$ |
$18$ |
[18,0] |
$2^{18}\cdot 19^{16}\cdot 37^{2}$ |
$3$ |
$40.92083614629157$ |
|
|
|
? |
$C_2^8:C_9$ (as 18T368) |
trivial |
$[2, 2]$ |
$2$ |
$17$ |
$456779996.291431$ |
| 18.10.103...616.4 |
$x^{18} + 13 x^{16} - 79 x^{14} - 331 x^{12} + 2041 x^{10} - 740 x^{8} - 7478 x^{6} + 8830 x^{4} - 851 x^{2} - 1369$ |
$18$ |
[10,4] |
$2^{18}\cdot 19^{16}\cdot 37^{2}$ |
$3$ |
$40.92083614629157$ |
|
|
|
? |
$C_2^8:C_9$ (as 18T368) |
trivial |
$[2, 2]$ |
$2$ |
$13$ |
$79712785.40285014$ |
| 18.6.103...616.4 |
$x^{18} + 8 x^{16} - 94 x^{14} - 373 x^{12} + 1884 x^{10} + 5500 x^{8} - 8741 x^{6} - 23716 x^{4} - 12543 x^{2} - 1369$ |
$18$ |
[6,6] |
$2^{18}\cdot 19^{16}\cdot 37^{2}$ |
$3$ |
$40.9208361463$ |
|
|
|
? |
$C_2^8:C_9$ (as 18T368) |
trivial |
$[2, 2]$ |
$2$ |
$11$ |
$27584471.2575$ |
| 18.6.103...616.5 |
$x^{18} + 2 x^{16} - 108 x^{14} - 37 x^{12} + 1799 x^{10} + 1905 x^{8} - 7322 x^{6} - 15017 x^{4} - 8695 x^{2} - 1369$ |
$18$ |
[6,6] |
$2^{18}\cdot 19^{16}\cdot 37^{2}$ |
$3$ |
$40.92083614629157$ |
|
|
|
? |
$C_2^8:C_9$ (as 18T368) |
trivial |
$[2, 2]$ |
$2$ |
$11$ |
$30732212.91288549$ |
