| 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 |
| 18.0.144...803.1 |
$x^{18} - 9 x^{17} + 39 x^{16} - 108 x^{15} + 201 x^{14} - 231 x^{13} + 99 x^{12} + 147 x^{11} - 333 x^{10} + 389 x^{9} - 333 x^{8} + 147 x^{7} + 99 x^{6} - 231 x^{5} + 201 x^{4} - 108 x^{3} + 39 x^{2} - 9 x + 1$ |
$18$ |
[0,9] |
$-\,3^{21}\cdot 7^{12}$ |
$2$ |
$13.1837863724$ |
$16.82934070487988$ |
|
|
? |
$C_3^2:C_6$ (as 18T20) |
trivial |
$6$ |
$8$ |
$1141.1139985$ |
| 18.0.328...627.1 |
$x^{18} + 3 x^{12} - 2 x^{9} + 9 x^{6} - 3 x^{3} + 1$ |
$18$ |
[0,9] |
$-\,3^{43}$ |
$1$ |
$13.7971588371$ |
$17.6123217011059$ |
|
|
? |
$C_3^2:C_6$ (as 18T20) |
trivial |
$18$ |
$8$ |
$6574.04147929$ |
| 18.18.191...664.1 |
$x^{18} - 4 x^{17} - 78 x^{16} + 284 x^{15} + 2310 x^{14} - 7399 x^{13} - 33669 x^{12} + 90384 x^{11} + 267586 x^{10} - 554078 x^{9} - 1204383 x^{8} + 1654492 x^{7} + 3046555 x^{6} - 2007012 x^{5} - 3972458 x^{4} + 183745 x^{3} + 1953503 x^{2} + 824787 x + 100591$ |
$18$ |
[18,0] |
$2^{12}\cdot 3^{9}\cdot 7^{15}\cdot 29^{8}$ |
$4$ |
$62.1513152365$ |
$131.34926787196719$ |
|
|
? |
$C_3^2:C_6$ (as 18T20) |
trivial |
$2$ |
$17$ |
$32570423525.3$ |
| 18.18.570...992.1 |
$x^{18} - 4 x^{17} - 68 x^{16} + 456 x^{15} + 154 x^{14} - 7390 x^{13} + 13879 x^{12} + 28718 x^{11} - 112571 x^{10} + 51052 x^{9} + 176585 x^{8} - 192314 x^{7} - 20421 x^{6} + 57892 x^{5} + 9156 x^{4} - 2204 x^{3} - 397 x^{2} - 4 x + 1$ |
$18$ |
[18,0] |
$2^{18}\cdot 3^{9}\cdot 7^{12}\cdot 41^{8}$ |
$4$ |
$66.0362102473$ |
$150.7226614230438$ |
|
|
|
$C_3^2:C_6$ (as 18T20) |
trivial |
$2$ |
$17$ |
$67003902454.0$ |
