| 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 $p$ |
| 18.18.109...616.1 |
$x^{18} - 126 x^{16} - 105 x^{15} + 6048 x^{14} + 10080 x^{13} - 134862 x^{12} - 343980 x^{11} + 1320858 x^{10} + 5052327 x^{9} - 3016440 x^{8} - 31698702 x^{7} - 30425535 x^{6} + 53454492 x^{5} + 139796118 x^{4} + 120494934 x^{3} + 45611748 x^{2} + 6271020 x - 38388$ |
$18$ |
(18, 0) |
$2^{4}\cdot 3^{45}\cdot 7^{17}$ |
$3$ |
$114.247535466$ |
|
|
|
|
$C_3^5.C_6$ (as 18T325) |
$[3]$ |
$[6]$ |
$2$ |
$17$ |
$8163959857150$ |
$17$ |
$7$ |
| 18.18.109...616.2 |
$x^{18} - 126 x^{16} - 189 x^{15} + 6048 x^{14} + 17010 x^{13} - 126294 x^{12} - 523908 x^{11} + 933030 x^{10} + 6401171 x^{9} - 15876 x^{8} - 35452368 x^{7} - 26151111 x^{6} + 92218392 x^{5} + 100555938 x^{4} - 106331442 x^{3} - 129056004 x^{2} + 41847372 x + 39538324$ |
$18$ |
(18, 0) |
$2^{4}\cdot 3^{45}\cdot 7^{17}$ |
$3$ |
$114.247535466$ |
|
|
|
|
$C_3^5.C_6$ (as 18T325) |
$[3]$ |
$[6]$ |
$2$ |
$17$ |
$8564289735630$ |
$17$ |
$7$ |
| 18.18.175...856.1 |
$x^{18} - 126 x^{16} + 5859 x^{14} - 1638 x^{13} - 127218 x^{12} + 94122 x^{11} + 1325016 x^{10} - 1554980 x^{9} - 5803812 x^{8} + 7838712 x^{7} + 10350144 x^{6} - 13756176 x^{5} - 6336288 x^{4} + 5916288 x^{3} + 1342656 x^{2} + 88704 x + 1792$ |
$18$ |
(18, 0) |
$2^{8}\cdot 3^{45}\cdot 7^{17}$ |
$3$ |
$133.273067821$ |
$203.9133533639344$ |
|
|
|
$C_3^4.C_6$ (as 18T160) |
$[3]$ |
$[6]$ |
$2$ |
$17$ |
$37167481634600$ |
$17$ |
$7$ |
| 18.18.281...696.1 |
$x^{18} - 126 x^{16} + 6048 x^{14} - 142296 x^{12} + 1792224 x^{10} - 97216 x^{9} - 12446784 x^{8} + 2123856 x^{7} + 46428480 x^{6} - 15706656 x^{5} - 82978560 x^{4} + 46099200 x^{3} + 49787136 x^{2} - 47021184 x + 10295488$ |
$18$ |
(18, 0) |
$2^{12}\cdot 3^{45}\cdot 7^{17}$ |
$3$ |
$155.466903806$ |
$168.64763862118394$ |
|
|
|
$C_3^3.C_6$ (as 18T84) |
$[3]$ |
$[6]$ |
$2$ |
$17$ |
$91153181939300$ |
$17$ |
$7$ |
