| 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 |
Unit signature rank |
| 18.6.357...000.1 |
$x^{18} - 2 x^{17} - 11 x^{16} - 2 x^{15} + 310 x^{14} - 405 x^{13} - 3568 x^{12} + 9026 x^{11} + 14204 x^{10} - 58815 x^{9} - 15539 x^{8} + 189202 x^{7} - 64469 x^{6} - 273183 x^{5} + 156303 x^{4} + 150741 x^{3} - 81162 x^{2} - 9963 x - 729$ |
$18$ |
(6, 6) |
$2^{12}\cdot 5^{11}\cdot 17^{8}\cdot 37^{6}$ |
$4$ |
$49.8235989463$ |
$244.0966450383817$ |
|
|
? |
$C_6^2:D_6$ (as 18T156) |
trivial |
trivial |
$2$ |
$11$ |
$138117514.681$ |
$6$ |
| 18.6.362...000.1 |
$x^{18} - 6 x^{17} - 4 x^{16} - 208 x^{15} + 846 x^{14} + 1077 x^{13} - 4235 x^{12} - 10726 x^{11} + 18824 x^{10} + 74378 x^{9} - 184367 x^{8} + 117188 x^{7} - 192931 x^{6} + 789736 x^{5} - 1265474 x^{4} + 935339 x^{3} - 311297 x^{2} + 31011 x + 823$ |
$18$ |
(6, 6) |
$2^{12}\cdot 5^{10}\cdot 17^{8}\cdot 37^{9}$ |
$4$ |
$83.1707048755$ |
$244.0966450383817$ |
|
|
? |
$C_3^2:S_4$ (as 18T107) |
$[2]$ |
$[4]$ |
$2$ |
$11$ |
$13811069376.8$ |
$5$ |
| 18.18.225...000.1 |
$x^{18} - 8 x^{17} - 69 x^{16} + 742 x^{15} + 463 x^{14} - 21374 x^{13} + 45054 x^{12} + 180264 x^{11} - 794484 x^{10} + 245930 x^{9} + 3537283 x^{8} - 6602254 x^{7} + 1171173 x^{6} + 8772146 x^{5} - 10063201 x^{4} + 2750688 x^{3} + 2007202 x^{2} - 1514508 x + 284953$ |
$18$ |
(18, 0) |
$2^{18}\cdot 5^{10}\cdot 17^{11}\cdot 37^{6}$ |
$4$ |
$92.0495310406$ |
$553.543338109293$ |
|
|
? |
$C_6^2:D_6$ (as 18T156) |
trivial |
$[2, 2]$ |
$2$ |
$17$ |
$882349040481$ |
$16$ |
| 18.18.232...000.1 |
$x^{18} - 4 x^{17} - 93 x^{16} + 280 x^{15} + 3167 x^{14} - 6804 x^{13} - 51206 x^{12} + 82166 x^{11} + 437064 x^{10} - 537166 x^{9} - 2014703 x^{8} + 1824198 x^{7} + 4819487 x^{6} - 2691442 x^{5} - 5341257 x^{4} + 1244966 x^{3} + 1591608 x^{2} - 453762 x + 6291$ |
$18$ |
(18, 0) |
$2^{18}\cdot 5^{10}\cdot 17^{8}\cdot 37^{9}$ |
$4$ |
$104.788521807$ |
$851.3874403604091$ |
|
|
? |
$C_3^2:S_4$ (as 18T107) |
trivial |
$[2, 2]$ |
$2$ |
$17$ |
$2855934859360$ |
$16$ |
| 18.0.308...616.2 |
$x^{18} - 138 x^{16} - 154 x^{15} + 9639 x^{14} + 22032 x^{13} - 390286 x^{12} - 1316106 x^{11} + 9128643 x^{10} + 44723906 x^{9} - 85604112 x^{8} - 784704360 x^{7} - 656568407 x^{6} + 4674002202 x^{5} + 13799506662 x^{4} + 16407533408 x^{3} + 12523138740 x^{2} + 5929322832 x + 1715187256$ |
$18$ |
(0, 9) |
$-\,2^{24}\cdot 3^{18}\cdot 11^{9}\cdot 17^{10}$ |
$4$ |
$120.996737107$ |
|
|
|
? |
$C_3^6:(C_2\times S_4)$ (as 18T684) |
$[3]$ |
$[3]$ |
$2$ |
$8$ |
$263294759775$ |
$0$ |
| 18.2.118...944.1 |
$x^{18} - 306 x^{16} - 272 x^{15} + 39015 x^{14} + 69360 x^{13} - 2699260 x^{12} - 7074720 x^{11} + 110910975 x^{10} + 378104480 x^{9} - 2791772946 x^{8} - 11846618640 x^{7} + 42024509881 x^{6} + 228790077552 x^{5} - 301918392480 x^{4} - 2576824636736 x^{3} - 278064794880 x^{2} + 14422294027776 x + 19106141017088$ |
$18$ |
(2, 8) |
$2^{24}\cdot 3^{18}\cdot 11^{12}\cdot 17^{12}$ |
$4$ |
$247.204090799$ |
$597.0151413702765$ |
|
|
? |
$C_3^5:(C_2\times S_4)$ (as 18T580) |
$[3]$ |
$[6]$ |
$2$ |
$9$ |
$206124787864000$ |
$1$ |
