| 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 |
| 18.0.118...272.1 |
$x^{18} - 12 x^{15} - 18 x^{14} + 51 x^{12} + 72 x^{11} + 72 x^{10} + 36 x^{9} + 72 x^{8} + 90 x^{7} + 75 x^{6} + 72 x^{5} + 54 x^{4} - 18 x^{2} + 3$ |
$18$ |
[0,9] |
$-\,2^{18}\cdot 3^{37}$ |
$2$ |
$19.1328312674$ |
$21.475876974362272$ |
|
|
? |
$C_3:S_4$ (as 18T40) |
$[2]$ |
$2$ |
$8$ |
$28479.2203221$ |
| 18.0.669...000.1 |
$x^{18} - 11 x^{12} + 27 x^{6} + 27$ |
$18$ |
[0,9] |
$-\,2^{18}\cdot 3^{21}\cdot 5^{12}$ |
$3$ |
$21.0693657565$ |
$25.916910735084592$ |
|
|
? |
$C_3:S_4$ (as 18T40) |
$[3]$ |
$2$ |
$8$ |
$37400.0654203$ |
| 18.6.332...624.1 |
$x^{18} - 54 x^{15} - 180 x^{14} + 1206 x^{13} + 459 x^{12} - 7848 x^{11} + 11664 x^{10} - 556 x^{9} - 72756 x^{8} + 184356 x^{7} + 44463 x^{6} - 598968 x^{5} + 542700 x^{4} + 351114 x^{3} - 1003104 x^{2} + 458298 x - 59087$ |
$18$ |
[6,6] |
$2^{12}\cdot 3^{37}\cdot 23^{9}$ |
$3$ |
$72.8282421586$ |
$72.82824215856341$ |
|
|
|
$C_3:S_4$ (as 18T40) |
$[4]$ |
$2$ |
$11$ |
$6891398522.29$ |
| 18.6.253...632.1 |
$x^{18} - 5 x^{17} + 17 x^{16} - 26 x^{15} - 97 x^{14} + 413 x^{13} - 3516 x^{12} + 4203 x^{11} - 7019 x^{10} - 56398 x^{9} + 398451 x^{8} - 800673 x^{7} + 337971 x^{6} + 7233538 x^{5} - 17698768 x^{4} - 6903624 x^{3} + 52507872 x^{2} - 23700060 x - 30249612$ |
$18$ |
[6,6] |
$2^{12}\cdot 7^{12}\cdot 197^{9}$ |
$3$ |
$81.5301929631$ |
$81.53019296306911$ |
|
|
|
$C_3:S_4$ (as 18T40) |
$[2, 6]$ |
$2$ |
$11$ |
$14150853991.4$ |
| 18.18.652...216.1 |
$x^{18} - 9 x^{17} - 42 x^{16} + 498 x^{15} + 231 x^{14} - 8343 x^{13} + 2989 x^{12} + 59949 x^{11} - 20253 x^{10} - 226761 x^{9} + 8409 x^{8} + 452259 x^{7} + 153052 x^{6} - 375174 x^{5} - 264699 x^{4} + 1605 x^{3} + 26424 x^{2} + 2088 x + 12$ |
$18$ |
[18,0] |
$2^{20}\cdot 3^{33}\cdot 47^{9}$ |
$3$ |
$110.981094172$ |
$129.4626691961398$ |
|
|
? |
$C_3:S_4$ (as 18T40) |
$[12]$ |
$2$ |
$17$ |
$5751301540210$ |
| 18.18.562...024.1 |
$x^{18} - 9 x^{17} - 75 x^{16} + 768 x^{15} + 1986 x^{14} - 25806 x^{13} - 19822 x^{12} + 438816 x^{11} - 14037 x^{10} - 4078547 x^{9} + 1648491 x^{8} + 21086784 x^{7} - 11912402 x^{6} - 58701558 x^{5} + 36211158 x^{4} + 78699796 x^{3} - 48626967 x^{2} - 36169521 x + 22115221$ |
$18$ |
[18,0] |
$2^{12}\cdot 3^{33}\cdot 47^{11}$ |
$3$ |
$125.096898928$ |
$213.54153367766565$ |
|
|
|
$C_3:S_4$ (as 18T40) |
$[3]$ |
$2$ |
$17$ |
$15891448025500$ |
