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 |
18.0.227...424.1 |
$x^{18} - 3 x^{17} + 6 x^{16} - 20 x^{15} + 57 x^{14} - 102 x^{13} + 159 x^{12} - 312 x^{11} + 567 x^{10} - 735 x^{9} + 855 x^{8} - 1155 x^{7} + 1382 x^{6} - 1122 x^{5} + 567 x^{4} - 172 x^{3} + 33 x^{2} - 6 x + 1$ |
$18$ |
[0,9] |
$-\,2^{6}\cdot 3^{21}\cdot 23^{7}$ |
$3$ |
$15.365461927$ |
|
|
|
? |
$C_2^3\wr C_3.S_3^2$ (as 18T734) |
$[2]$ |
$[2]$ |
$2$ |
$8$ |
$1034.74957973$ |
18.2.634...832.1 |
$x^{18} + 9 x^{16} + 30 x^{14} + 36 x^{12} - 9 x^{10} - 45 x^{8} + 162 x^{6} + 27 x^{4} + 27 x^{2} - 27$ |
$18$ |
[2,8] |
$2^{12}\cdot 3^{21}\cdot 23^{6}$ |
$3$ |
$16.2643760194$ |
|
|
|
? |
$C_2^3:A_4^2:D_6$ (as 18T587) |
trivial |
$[2]$ |
$2$ |
$9$ |
$4220.71080217$ |
18.2.634...832.2 |
$x^{18} - 6 x^{17} + 12 x^{16} - 8 x^{15} + 21 x^{14} - 153 x^{13} + 471 x^{12} - 780 x^{11} + 648 x^{10} + 45 x^{9} - 741 x^{8} + 756 x^{7} - 151 x^{6} - 258 x^{5} + 126 x^{4} + 14 x^{3} + 36 x^{2} - 27 x - 11$ |
$18$ |
[2,8] |
$2^{12}\cdot 3^{21}\cdot 23^{6}$ |
$3$ |
$16.2643760194$ |
|
|
|
? |
$C_2^3:A_4^2:D_6$ (as 18T587) |
trivial |
$[2]$ |
$2$ |
$9$ |
$4725.85533954$ |
18.2.201...617.1 |
$x^{18} - 3 x^{17} + 6 x^{16} - 14 x^{15} + 36 x^{14} - 96 x^{13} + 191 x^{12} - 297 x^{11} + 435 x^{10} - 690 x^{9} + 945 x^{8} - 813 x^{7} + 297 x^{6} + 105 x^{5} - 147 x^{4} + 44 x^{3} + 6 x^{2} - 6 x + 1$ |
$18$ |
[2,8] |
$3^{21}\cdot 7^{12}\cdot 139$ |
$3$ |
$17.3418943053$ |
|
|
|
? |
$C_2^4:A_4^2.D_6$ (as 18T657) |
trivial |
$[2]$ |
$2$ |
$9$ |
$6948.8935794$ |
18.6.496...429.1 |
$x^{18} - 19 x^{15} + 95 x^{12} - 6 x^{9} - 369 x^{6} - 164 x^{3} + 1$ |
$18$ |
[6,6] |
$3^{21}\cdot 7^{15}$ |
$2$ |
$18.2343308497$ |
$23.27645167546343$ |
|
|
? |
$C_3^2:D_6$ (as 18T42) |
trivial |
$[2]$ |
$2$ |
$11$ |
$20392.5627447$ |
18.6.593...088.1 |
$x^{18} - 3 x^{14} - 15 x^{12} - 18 x^{10} + 9 x^{8} + 81 x^{6} + 27 x^{4} - 54 x^{2} - 27$ |
$18$ |
[6,6] |
$2^{12}\cdot 3^{21}\cdot 7^{12}$ |
$3$ |
$20.9279563564$ |
|
|
|
? |
$C_2^3:A_4^2:C_6$ (as 18T513) |
trivial |
$[2]$ |
$2$ |
$11$ |
$102490.339302$ |
18.2.593...088.1 |
$x^{18} + 6 x^{16} + 6 x^{14} - 69 x^{12} - 441 x^{10} - 1341 x^{8} - 2241 x^{6} - 1998 x^{4} - 783 x^{2} - 27$ |
$18$ |
[2,8] |
$2^{12}\cdot 3^{21}\cdot 7^{12}$ |
$3$ |
$20.9279563564$ |
|
|
|
? |
$C_2^4:A_4^2.D_6$ (as 18T657) |
trivial |
$[2]$ |
$2$ |
$9$ |
$33272.9745321$ |