| 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 |
| 18.0.105...387.2 |
$x^{18} - 3 x^{17} + 9 x^{16} - 21 x^{15} + 30 x^{14} - 9 x^{13} - 72 x^{12} + 123 x^{11} - 15 x^{10} - 363 x^{9} + 999 x^{8} - 1638 x^{7} + 2205 x^{6} - 2385 x^{5} + 2106 x^{4} - 1422 x^{3} + 648 x^{2} - 162 x + 21$ |
$18$ |
[0,9] |
$-\,3^{27}\cdot 7^{12}$ |
$2$ |
$19.0143102306$ |
$23.409140290996383$ |
|
|
? |
$F_9:C_2$ (as 18T68) |
trivial |
trivial |
$6$ |
$8$ |
$72896.500231$ |
| 18.0.524...432.1 |
$x^{18} - 6 x^{17} + 9 x^{16} + 6 x^{14} - 12 x^{13} - 18 x^{12} + 39 x^{10} + 62 x^{9} + 39 x^{8} - 18 x^{6} - 12 x^{5} + 6 x^{4} + 9 x^{2} - 6 x + 1$ |
$18$ |
[0,9] |
$-\,2^{36}\cdot 3^{27}$ |
$2$ |
$20.7846096908$ |
$25.87494436115978$ |
|
|
|
$F_9:C_2$ (as 18T68) |
trivial |
trivial |
$6$ |
$8$ |
$209199.360218$ |
| 18.2.330...464.1 |
$x^{18} - 2 x^{17} + 5 x^{16} - 16 x^{14} + 8 x^{13} + 16 x^{12} - 48 x^{11} - 80 x^{10} + 72 x^{9} - 272 x^{8} - 512 x^{7} + 320 x^{6} + 72 x^{5} - 1408 x^{4} + 1040 x^{3} - 515 x^{2} - 18 x - 135$ |
$18$ |
[2,8] |
$2^{61}\cdot 3^{15}$ |
$2$ |
$26.1672602119$ |
$32.263749133641326$ |
|
|
? |
$F_9:C_2$ (as 18T68) |
trivial |
$[2]$ |
$2$ |
$9$ |
$2305205.59363$ |
| 18.2.387...848.1 |
$x^{18} - x^{17} - 9 x^{16} - 10 x^{15} + 56 x^{14} + 142 x^{13} + 108 x^{12} - 242 x^{11} - 416 x^{10} - 14 x^{9} + 160 x^{8} - 190 x^{7} - 132 x^{6} + 350 x^{5} + 488 x^{4} + 346 x^{3} + 207 x^{2} + 79 x + 9$ |
$18$ |
[2,8] |
$2^{36}\cdot 3^{12}\cdot 13^{9}$ |
$3$ |
$29.9993955251$ |
$39.09580027952751$ |
|
|
|
$F_9:C_2$ (as 18T68) |
trivial |
trivial |
$2$ |
$9$ |
$4001343.87654$ |
| 18.18.659...888.1 |
$x^{18} - 6 x^{17} - 30 x^{16} + 228 x^{15} + 219 x^{14} - 3102 x^{13} + 594 x^{12} + 19704 x^{11} - 12069 x^{10} - 62950 x^{9} + 43176 x^{8} + 102192 x^{7} - 51936 x^{6} - 82080 x^{5} + 15264 x^{4} + 26880 x^{3} + 912 x^{2} - 2976 x - 512$ |
$18$ |
[18,0] |
$2^{44}\cdot 3^{19}\cdot 19^{9}$ |
$3$ |
$75.6581803827$ |
$97.8852674836209$ |
|
|
|
$F_9:C_2$ (as 18T68) |
trivial |
$[2, 2]$ |
$2$ |
$17$ |
$1466293758730$ |
| 18.18.506...000.1 |
$x^{18} - 6 x^{17} - 66 x^{16} + 424 x^{15} + 1516 x^{14} - 11440 x^{13} - 11464 x^{12} + 145584 x^{11} - 58798 x^{10} - 844908 x^{9} + 1206908 x^{8} + 1398224 x^{7} - 4364740 x^{6} + 2938936 x^{5} + 405472 x^{4} - 1079664 x^{3} + 209026 x^{2} + 92052 x - 26332$ |
$18$ |
[18,0] |
$2^{60}\cdot 5^{12}\cdot 23^{9}$ |
$3$ |
$141.343955152$ |
$197.84503481643182$ |
|
|
? |
$F_9:C_2$ (as 18T68) |
trivial |
$[2, 2, 2]$ |
$2$ |
$17$ |
$291707409256000$ |
