| 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 |
Max $p$ |
| 18.4.390...896.1 |
$x^{18} - 3 x^{16} - 2 x^{14} + 12 x^{12} - 7 x^{10} - 11 x^{8} + 5 x^{6} + x^{4} - 5 x^{2} + 1$ |
$18$ |
(4, 7) |
$-\,2^{24}\cdot 13^{12}$ |
$2$ |
$13.9316395358$ |
$18.59650768627035$ |
|
|
? |
$S_3\times A_4$ (as 18T32) |
trivial |
trivial |
$2$ |
$10$ |
$1241.30215537$ |
$4$ |
$13$ |
| 18.4.242...752.1 |
$x^{18} - 6 x^{16} + 18 x^{14} - 38 x^{12} + 57 x^{10} - 60 x^{8} + 37 x^{6} + 6 x^{4} - 24 x^{2} + 8$ |
$18$ |
(4, 7) |
$-\,2^{33}\cdot 3^{24}$ |
$2$ |
$15.4187795211$ |
$20.58160140743025$ |
|
|
? |
$S_3\times A_4$ (as 18T32) |
trivial |
trivial |
$2$ |
$10$ |
$3365.40255182$ |
$4$ |
$3$ |
| 18.0.608...871.1 |
$x^{18} + x^{16} - 8 x^{15} + 6 x^{14} - 14 x^{13} + 40 x^{12} - 39 x^{11} + 68 x^{10} - 183 x^{9} + 24 x^{8} - 152 x^{7} + 728 x^{6} + 336 x^{5} + 96 x^{4} - 704 x^{3} + 256 x + 512$ |
$18$ |
(0, 9) |
$-\,19^{12}\cdot 31^{7}$ |
$2$ |
$27.0692605722$ |
$39.64452763115264$ |
|
|
|
$S_3\times A_4$ (as 18T32) |
trivial |
trivial |
$2$ |
$8$ |
$569373.693221$ |
$0$ |
$31$ |
| 18.6.109...408.1 |
$x^{18} - 6 x^{17} + 18 x^{16} - 44 x^{15} + 87 x^{14} - 150 x^{13} + 203 x^{12} - 168 x^{11} - 153 x^{10} + 738 x^{9} - 1548 x^{8} + 2748 x^{7} - 4144 x^{6} + 5268 x^{5} - 5283 x^{4} + 2332 x^{3} - 225 x^{2} - 18 x + 1$ |
$18$ |
(6, 6) |
$2^{12}\cdot 3^{24}\cdot 37^{7}$ |
$3$ |
$27.9707790583$ |
$41.77814941501269$ |
|
|
? |
$S_3\times A_4$ (as 18T32) |
trivial |
trivial |
$2$ |
$11$ |
$1206805.78255$ |
$6$ |
$37$ |
| 18.0.615...944.1 |
$x^{18} + 28 x^{16} + 337 x^{14} + 2245 x^{12} + 8710 x^{10} + 18160 x^{8} + 14152 x^{6} - 5952 x^{4} - 5952 x^{2} + 1984$ |
$18$ |
(0, 9) |
$-\,2^{18}\cdot 31^{15}$ |
$2$ |
$34.9809344929$ |
$49.470511984396374$ |
|
|
? |
$S_3\times A_4$ (as 18T32) |
$[2, 4]$ |
$[2, 4]$ |
$2$ |
$8$ |
$390018.833589$ |
$0$ |
$31$ |
| 18.6.607...000.1 |
$x^{18} - 18 x^{16} - 30 x^{15} + 81 x^{14} + 342 x^{13} + 351 x^{12} - 738 x^{11} - 2331 x^{10} - 1444 x^{9} + 3294 x^{8} + 7542 x^{7} + 5634 x^{6} - 2952 x^{5} - 8595 x^{4} - 7212 x^{3} - 2529 x^{2} + 3204 x + 2699$ |
$18$ |
(6, 6) |
$2^{24}\cdot 3^{32}\cdot 5^{9}$ |
$3$ |
$39.7259135953$ |
$50.05151476499125$ |
|
|
? |
$S_3\times A_4$ (as 18T32) |
$[2]$ |
$[2]$ |
$2$ |
$11$ |
$17244009.6923$ |
$6$ |
$5$ |
| 18.18.619...497.1 |
$x^{18} - x^{17} - 52 x^{16} + 34 x^{15} + 965 x^{14} - 493 x^{13} - 7829 x^{12} + 5632 x^{11} + 29599 x^{10} - 32926 x^{9} - 39622 x^{8} + 72195 x^{7} - 19306 x^{6} - 14542 x^{5} + 6730 x^{4} - 229 x^{3} - 151 x^{2} + 5 x + 1$ |
$18$ |
(18, 0) |
$11^{7}\cdot 43^{15}$ |
$2$ |
$58.3726966885$ |
$76.19387402923972$ |
|
|
? |
$S_3\times A_4$ (as 18T32) |
trivial |
$[2]$ |
$2$ |
$17$ |
$19367773986.5$ |
$17$ |
$43$ |
| 18.18.241...008.1 |
$x^{18} - 2 x^{17} - 40 x^{16} + 12 x^{15} + 554 x^{14} + 321 x^{13} - 3409 x^{12} - 3886 x^{11} + 9240 x^{10} + 15122 x^{9} - 7993 x^{8} - 21840 x^{7} - 3261 x^{6} + 7458 x^{5} + 1322 x^{4} - 765 x^{3} - 115 x^{2} + 17 x + 1$ |
$18$ |
(18, 0) |
$2^{12}\cdot 11^{6}\cdot 37^{15}$ |
$3$ |
$71.5570336516$ |
$106.71310986078944$ |
|
|
? |
$S_3\times A_4$ (as 18T32) |
$[2]$ |
$[2, 2, 2, 4]$ |
$2$ |
$17$ |
$53195334384.7$ |
$14$ |
$37$ |
