| 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 |
| 18.6.866...168.1 |
$x^{18} - 6 x^{17} + 15 x^{16} - 20 x^{15} + 8 x^{14} + 20 x^{13} - 14 x^{12} - 60 x^{11} + 122 x^{10} - 64 x^{9} - 136 x^{8} + 252 x^{7} - 40 x^{6} - 140 x^{5} + 6 x^{4} + 36 x^{3} + 45 x^{2} - 18 x + 1$ |
$18$ |
[6,6] |
$2^{33}\cdot 3^{6}\cdot 7^{12}$ |
$3$ |
$18.8073426477$ |
$22.58643281430495$ |
|
|
? |
$C_3\times S_3^2$ (as 18T43) |
trivial |
$2$ |
$11$ |
$40342.6255514$ |
| 18.0.914...883.2 |
$x^{18} - 27 x^{15} + 279 x^{12} - 1296 x^{9} + 2241 x^{6} + 162 x^{3} + 27$ |
$18$ |
[0,9] |
$-\,3^{31}\cdot 23^{6}$ |
$2$ |
$18.863318871$ |
$31.810664815402767$ |
|
|
? |
$C_3\times S_3^2$ (as 18T43) |
trivial |
$18$ |
$8$ |
$124809.299104$ |
| 18.6.932...968.1 |
$x^{18} - 6 x^{17} + 12 x^{16} - 12 x^{15} + 21 x^{14} - 24 x^{13} - 45 x^{12} + 120 x^{11} - 87 x^{10} + 52 x^{9} - 174 x^{8} + 240 x^{7} + 66 x^{6} - 336 x^{5} + 249 x^{4} + 270 x^{3} - 3 x^{2} - 12 x + 1$ |
$18$ |
[6,6] |
$2^{24}\cdot 3^{33}$ |
$2$ |
$18.8840711416$ |
$20.48509314595983$ |
|
|
? |
$C_3\times S_3^2$ (as 18T43) |
trivial |
$2$ |
$11$ |
$44983.5370214$ |
| 18.0.117...128.1 |
$x^{18} - 3 x^{15} + 2 x^{12} + x^{9} + 4 x^{6} - 12 x^{3} + 8$ |
$18$ |
[0,9] |
$-\,2^{6}\cdot 3^{18}\cdot 7^{15}$ |
$3$ |
$19.1299111659$ |
$36.949063875717606$ |
|
|
? |
$C_3\times S_3^2$ (as 18T43) |
trivial |
$14$ |
$8$ |
$65236.1886784$ |
| 18.18.686...125.1 |
$x^{18} - 5 x^{17} - 24 x^{16} + 107 x^{15} + 258 x^{14} - 810 x^{13} - 1373 x^{12} + 2760 x^{11} + 3408 x^{10} - 4525 x^{9} - 3273 x^{8} + 4002 x^{7} + 1008 x^{6} - 1719 x^{5} + 109 x^{4} + 274 x^{3} - 72 x^{2} + 1$ |
$18$ |
[18,0] |
$3^{9}\cdot 5^{6}\cdot 7^{15}\cdot 19^{6}$ |
$4$ |
$39.9990978088$ |
$111.72897058338793$ |
|
|
? |
$C_3\times S_3^2$ (as 18T43) |
trivial |
$2$ |
$17$ |
$365898661.102$ |
| 18.18.123...000.1 |
$x^{18} - 56 x^{16} - 80 x^{15} + 1022 x^{14} + 2520 x^{13} - 5980 x^{12} - 21000 x^{11} + 11144 x^{10} + 75280 x^{9} + 9856 x^{8} - 129080 x^{7} - 57476 x^{6} + 99680 x^{5} + 62440 x^{4} - 24800 x^{3} - 19600 x^{2} + 1000$ |
$18$ |
[18,0] |
$2^{33}\cdot 3^{12}\cdot 5^{9}\cdot 7^{12}$ |
$4$ |
$60.6530797034$ |
$126.16348990930013$ |
|
|
? |
$C_3\times S_3^2$ (as 18T43) |
$[2]$ |
$2$ |
$17$ |
$14691002887.3$ |
