| 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 |
| 18.6.146...693.1 |
$x^{18} - 3 x^{17} - 4 x^{16} + 33 x^{15} - 73 x^{14} + 6 x^{13} + 269 x^{12} - 365 x^{11} + 9 x^{10} + 331 x^{9} + 106 x^{8} - 1784 x^{7} + 1952 x^{6} + 505 x^{5} - 976 x^{4} - 985 x^{3} + 2554 x^{2} - 1500 x - 113$ |
$18$ |
[6,6] |
$19^{16}\cdot 37^{3}$ |
$2$ |
$25.005573617$ |
$83.32411881951172$ |
|
|
? |
$C_2^2:C_{18}$ (as 18T26) |
trivial |
$2$ |
$11$ |
$290338.751062$ |
| 18.12.756...064.1 |
$x^{18} + x^{16} - 65 x^{14} + 297 x^{12} - 549 x^{10} + 433 x^{8} - 77 x^{6} - 48 x^{4} + 5 x^{2} + 1$ |
$18$ |
[12,3] |
$-\,2^{18}\cdot 19^{16}$ |
$2$ |
$27.3968015041$ |
$46.0757443483935$ |
|
|
? |
$C_2^2:C_{18}$ (as 18T26) |
trivial |
$2$ |
$14$ |
$2651499.3108$ |
| 18.12.258...864.1 |
$x^{18} - 54 x^{14} + 42 x^{12} + 603 x^{10} - 1539 x^{8} + 1368 x^{6} - 450 x^{4} + 27 x^{2} + 1$ |
$18$ |
[12,3] |
$-\,2^{18}\cdot 3^{44}$ |
$2$ |
$29.3309679999$ |
$49.32861169414063$ |
|
|
? |
$C_2^2:C_{18}$ (as 18T26) |
trivial |
$2$ |
$14$ |
$5317286.48059$ |
| 18.0.352...591.1 |
$x^{18} + 9 x^{16} - 9 x^{15} + 162 x^{14} - 99 x^{13} + 1473 x^{12} - 1404 x^{11} + 6264 x^{10} - 5939 x^{9} + 12636 x^{8} - 11961 x^{7} + 14742 x^{6} - 10530 x^{5} + 7452 x^{4} - 3267 x^{3} + 1215 x^{2} - 243 x + 27$ |
$18$ |
[0,9] |
$-\,3^{44}\cdot 71^{3}$ |
$2$ |
$29.8427924526$ |
$123.5735646798655$ |
✓ |
|
? |
$C_2^2:C_{18}$ (as 18T26) |
$[21]$ |
$2$ |
$8$ |
$40934.0329443$ |
| 18.6.416...857.1 |
$x^{18} - 8 x^{17} + 27 x^{16} - 42 x^{15} - 12 x^{14} + 242 x^{13} - 833 x^{12} + 2227 x^{11} - 5196 x^{10} + 10127 x^{9} - 15321 x^{8} + 14901 x^{7} - 1829 x^{6} - 22543 x^{5} + 46651 x^{4} - 53722 x^{3} + 41301 x^{2} - 20001 x + 4181$ |
$18$ |
[6,6] |
$19^{16}\cdot 113^{3}$ |
$2$ |
$30.1196283048$ |
$145.61599739544846$ |
|
|
? |
$C_2^2:C_{18}$ (as 18T26) |
trivial |
$2$ |
$11$ |
$1701924.22156$ |
| 18.0.383...792.1 |
$x^{18} - 2 x^{17} + 36 x^{16} - 124 x^{15} + 667 x^{14} - 2334 x^{13} + 8164 x^{12} - 20338 x^{11} + 54321 x^{10} - 96972 x^{9} + 150518 x^{8} - 244982 x^{7} + 834376 x^{6} - 2158328 x^{5} + 4885022 x^{4} - 8338866 x^{3} + 13279313 x^{2} - 14690014 x + 10525279$ |
$18$ |
[0,9] |
$-\,2^{18}\cdot 19^{16}\cdot 37^{3}$ |
$3$ |
$50.011147234$ |
$280.26781127800797$ |
✓ |
|
? |
$C_2^2:C_{18}$ (as 18T26) |
$[2, 2, 570]$ |
$2$ |
$8$ |
$22305.8950792$ |
| 18.18.383...792.1 |
$x^{18} - 2 x^{17} - 66 x^{16} + 108 x^{15} + 1544 x^{14} - 1850 x^{13} - 16889 x^{12} + 15264 x^{11} + 95078 x^{10} - 72124 x^{9} - 281919 x^{8} + 202114 x^{7} + 412283 x^{6} - 313520 x^{5} - 223063 x^{4} + 212908 x^{3} - 16553 x^{2} - 12592 x + 647$ |
$18$ |
[18,0] |
$2^{18}\cdot 19^{16}\cdot 37^{3}$ |
$3$ |
$50.011147234$ |
$235.67619781468147$ |
|
|
? |
$C_2^2:C_{18}$ (as 18T26) |
trivial |
$2$ |
$17$ |
$2587028370.07$ |
| 18.18.127...096.1 |
$x^{18} - 190 x^{16} + 15219 x^{14} - 670985 x^{12} + 17820195 x^{10} - 292417885 x^{8} + 2904860828 x^{6} - 16125600181 x^{4} + 40252586306 x^{2} - 16862569939$ |
$18$ |
[18,0] |
$2^{18}\cdot 19^{17}\cdot 31^{6}$ |
$3$ |
$101.358994709$ |
$179.64807867551454$ |
|
|
? |
$C_2^2:C_{18}$ (as 18T26) |
$[2, 2]$ |
$2$ |
$17$ |
$402218304851$ |
