| 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 |
| 18.0.328...363.1 |
$x^{18} + 6 x^{16} - 6 x^{15} + 27 x^{14} - 21 x^{13} + 53 x^{12} - 9 x^{11} + 57 x^{10} + x^{9} + 18 x^{8} + 18 x^{7} + 4 x^{6} + 27 x^{5} + 18 x^{4} + 10 x^{3} + 9 x^{2} + 3 x + 1$ |
$18$ |
[0,9] |
$-\,3^{21}\cdot 11^{12}$ |
$2$ |
$17.8198175824$ |
$21.761357200260658$ |
|
|
? |
$\SOPlus(4,2)$ (as 18T36) |
trivial |
$6$ |
$8$ |
$33659.9437841$ |
| 18.0.184...448.1 |
$x^{18} - 3 x^{17} - 3 x^{16} + 10 x^{15} + 21 x^{14} - 45 x^{13} - 17 x^{12} + 18 x^{11} + 126 x^{10} - 184 x^{9} + 162 x^{8} - 318 x^{7} + 523 x^{6} - 471 x^{5} + 309 x^{4} - 138 x^{3} + 45 x^{2} - 9 x + 1$ |
$18$ |
[0,9] |
$-\,2^{44}\cdot 3^{21}$ |
$2$ |
$19.6106759933$ |
$24.23672593327708$ |
|
|
|
$\SOPlus(4,2)$ (as 18T36) |
trivial |
$6$ |
$8$ |
$110226.745818$ |
| 18.2.490...528.1 |
$x^{18} - 6 x^{16} + 24 x^{14} - 60 x^{12} - 18 x^{10} + 24 x^{8} - 72 x^{6} - 180 x^{4} + 33 x^{2} - 2$ |
$18$ |
[2,8] |
$2^{47}\cdot 3^{20}$ |
$2$ |
$20.7089220753$ |
$24.987759659239007$ |
|
|
|
$\SOPlus(4,2)$ (as 18T36) |
trivial |
$2$ |
$9$ |
$279130.496866$ |
| 18.2.215...104.1 |
$x^{18} - 6 x^{17} + 9 x^{16} + 18 x^{15} - 54 x^{14} - 24 x^{13} + 135 x^{12} + 78 x^{11} - 303 x^{10} - 104 x^{9} + 321 x^{8} + 180 x^{7} + 9 x^{6} - 762 x^{5} + 354 x^{4} + 660 x^{3} - 720 x^{2} + 216 x - 43$ |
$18$ |
[2,8] |
$2^{18}\cdot 3^{20}\cdot 11^{9}$ |
$3$ |
$22.4833523029$ |
$24.638891793904754$ |
|
|
|
$\SOPlus(4,2)$ (as 18T36) |
trivial |
$2$ |
$9$ |
$171597.947651$ |
| 18.18.244...016.1 |
$x^{18} - 6 x^{17} - 33 x^{16} + 222 x^{15} + 441 x^{14} - 3228 x^{13} - 3519 x^{12} + 23940 x^{11} + 20004 x^{10} - 95540 x^{9} - 76188 x^{8} + 196728 x^{7} + 156600 x^{6} - 190776 x^{5} - 145320 x^{4} + 67824 x^{3} + 44124 x^{2} - 2688 x - 1756$ |
$18$ |
[18,0] |
$2^{24}\cdot 3^{20}\cdot 11^{15}$ |
$3$ |
$62.9992374377$ |
$69.0391438702834$ |
|
|
? |
$\SOPlus(4,2)$ (as 18T36) |
trivial |
$2$ |
$17$ |
$126944040549$ |
| 18.18.287...744.1 |
$x^{18} - 6 x^{17} - 39 x^{16} + 186 x^{15} + 516 x^{14} - 2286 x^{13} - 2829 x^{12} + 14238 x^{11} + 4938 x^{10} - 47130 x^{9} + 10971 x^{8} + 77838 x^{7} - 51087 x^{6} - 48144 x^{5} + 54420 x^{4} - 5076 x^{3} - 9012 x^{2} + 2568 x - 100$ |
$18$ |
[18,0] |
$2^{33}\cdot 3^{24}\cdot 17^{9}$ |
$3$ |
$63.5732565836$ |
$67.57424396297215$ |
|
|
? |
$\SOPlus(4,2)$ (as 18T36) |
$[2]$ |
$2$ |
$17$ |
$105925015490$ |
