| 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 |
| 18.6.333...472.1 |
$x^{18} - 2 x^{17} - x^{16} + 16 x^{15} - 8 x^{14} - 48 x^{13} + 72 x^{12} + 80 x^{11} - 206 x^{10} - 100 x^{9} + 206 x^{8} + 80 x^{7} - 72 x^{6} - 48 x^{5} + 8 x^{4} + 16 x^{3} + x^{2} - 2 x - 1$ |
$18$ |
[6,6] |
$2^{51}\cdot 23^{6}$ |
$2$ |
$20.2687795753$ |
$38.36665218650175$ |
|
|
|
$F_9:C_2$ (as 18T73) |
trivial |
trivial |
$2$ |
$11$ |
$372823.571334$ |
| 18.6.738...709.1 |
$x^{18} - 6 x^{17} + 9 x^{16} + 21 x^{15} - 93 x^{14} + 60 x^{13} + 237 x^{12} - 378 x^{11} - 159 x^{10} + 617 x^{9} - 159 x^{8} - 378 x^{7} + 237 x^{6} + 60 x^{5} - 93 x^{4} + 21 x^{3} + 9 x^{2} - 6 x + 1$ |
$18$ |
[6,6] |
$3^{27}\cdot 7^{13}$ |
$2$ |
$21.1850974728$ |
$23.409140290996383$ |
|
|
? |
$F_9:C_2$ (as 18T73) |
trivial |
$[2]$ |
$2$ |
$11$ |
$165725.985152$ |
| 18.2.103...952.1 |
$x^{18} - 6 x^{17} + 10 x^{16} + 4 x^{14} - 72 x^{13} + 136 x^{12} + 24 x^{11} - 497 x^{10} + 918 x^{9} - 866 x^{8} + 504 x^{7} - 158 x^{6} - 12 x^{5} + 76 x^{4} - 96 x^{3} + 22 x^{2} + 12 x - 12$ |
$18$ |
[2,8] |
$2^{56}\cdot 3^{15}$ |
$2$ |
$21.5843418105$ |
$32.263749133641326$ |
|
|
|
$F_9:C_2$ (as 18T73) |
trivial |
$[2]$ |
$2$ |
$9$ |
$836193.102014$ |
| 18.2.211...808.1 |
$x^{18} - 4 x^{17} + 9 x^{16} - 8 x^{15} + 12 x^{14} + 32 x^{13} - 36 x^{12} - 8 x^{11} - 78 x^{10} - 232 x^{9} - 78 x^{8} - 8 x^{7} - 36 x^{6} + 32 x^{5} + 12 x^{4} - 8 x^{3} + 9 x^{2} - 4 x + 1$ |
$18$ |
[2,8] |
$2^{38}\cdot 3^{13}\cdot 13^{6}$ |
$3$ |
$22.4600020852$ |
$39.09580027952751$ |
|
|
|
$F_9:C_2$ (as 18T73) |
trivial |
$[2]$ |
$2$ |
$9$ |
$743835.121405$ |
| 18.18.769...056.1 |
$x^{18} - 6 x^{17} - 21 x^{16} + 168 x^{15} + 69 x^{14} - 1686 x^{13} + 981 x^{12} + 7680 x^{11} - 8367 x^{10} - 15946 x^{9} + 23463 x^{8} + 12744 x^{7} - 26466 x^{6} - 1932 x^{5} + 12414 x^{4} - 1392 x^{3} - 2028 x^{2} + 264 x + 76$ |
$18$ |
[18,0] |
$2^{47}\cdot 3^{19}\cdot 19^{6}$ |
$3$ |
$51.9878620502$ |
$97.8852674836209$ |
|
|
|
$F_9:C_2$ (as 18T73) |
trivial |
$[2, 2, 2]$ |
$2$ |
$17$ |
$19159199673.0$ |
| 18.18.208...000.1 |
$x^{18} - 6 x^{17} - 27 x^{16} + 200 x^{15} + 212 x^{14} - 2592 x^{13} + 148 x^{12} + 16824 x^{11} - 10240 x^{10} - 58056 x^{9} + 55696 x^{8} + 102440 x^{7} - 131080 x^{6} - 74424 x^{5} + 142808 x^{4} - 6664 x^{3} - 57197 x^{2} + 24006 x - 2177$ |
$18$ |
[18,0] |
$2^{59}\cdot 5^{12}\cdot 23^{6}$ |
$3$ |
$80.6489489381$ |
$197.84503481643182$ |
|
|
|
$F_9:C_2$ (as 18T73) |
trivial |
$[2, 2]$ |
$2$ |
$17$ |
$2479728639140$ |
