| 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 |
| 18.0.295...643.3 |
$x^{18} - 6 x^{15} + 24 x^{12} - 74 x^{9} + 150 x^{6} + 12 x^{3} + 1$ |
$18$ |
[0,9] |
$-\,3^{45}$ |
$1$ |
$15.5884572681$ |
$17.6123217011059$ |
|
|
|
$C_3^2:C_6$ (as 18T21) |
trivial |
$6$ |
$8$ |
$12334.7656984$ |
| 18.0.117...043.1 |
$x^{18} - 3 x^{16} - 6 x^{15} + 6 x^{14} + 15 x^{13} - 6 x^{12} - 24 x^{11} - 3 x^{10} + 43 x^{9} + 54 x^{8} - 24 x^{7} - 12 x^{6} - 42 x^{5} + 12 x^{4} + 15 x^{3} + 6 x^{2} + 3 x + 1$ |
$18$ |
[0,9] |
$-\,3^{25}\cdot 7^{12}$ |
$2$ |
$16.8293407049$ |
$16.82934070487988$ |
|
|
|
$C_3^2:C_6$ (as 18T21) |
$[3]$ |
$6$ |
$8$ |
$9705.33840375$ |
| 18.0.121...728.2 |
$x^{18} - 6 x^{15} - 18 x^{14} - 3 x^{12} + 126 x^{11} + 288 x^{10} + 34 x^{9} + 378 x^{8} - 540 x^{7} - 363 x^{6} + 18 x^{5} + 540 x^{4} - 852 x^{3} + 1224 x^{2} - 828 x + 193$ |
$18$ |
[0,9] |
$-\,2^{12}\cdot 3^{45}$ |
$2$ |
$24.745133466$ |
$27.957817995937848$ |
|
|
|
$C_3^2:C_6$ (as 18T21) |
trivial |
$6$ |
$8$ |
$973205.89905439$ |
| 18.18.707...048.1 |
$x^{18} - 6 x^{17} - 24 x^{16} + 208 x^{15} + 12 x^{14} - 2394 x^{13} + 3125 x^{12} + 10464 x^{11} - 24564 x^{10} - 9916 x^{9} + 63708 x^{8} - 28836 x^{7} - 53993 x^{6} + 47538 x^{5} + 8760 x^{4} - 17236 x^{3} + 1836 x^{2} + 1794 x - 377$ |
$18$ |
[18,0] |
$2^{12}\cdot 3^{24}\cdot 7^{8}\cdot 13^{9}$ |
$4$ |
$58.8056617851$ |
$90.61888333825345$ |
|
|
|
$C_3^2:C_6$ (as 18T21) |
$[3]$ |
$2$ |
$17$ |
$11723192956.5$ |
| 18.18.178...136.1 |
$x^{18} - 9 x^{17} - 9 x^{16} + 264 x^{15} - 288 x^{14} - 2916 x^{13} + 5598 x^{12} + 14526 x^{11} - 39159 x^{10} - 27383 x^{9} + 128403 x^{8} - 17730 x^{7} - 188268 x^{6} + 110070 x^{5} + 90900 x^{4} - 76710 x^{3} - 9855 x^{2} + 13041 x - 623$ |
$18$ |
[18,0] |
$2^{12}\cdot 3^{37}\cdot 7^{13}$ |
$3$ |
$61.913377178$ |
$94.19764909571116$ |
|
|
|
$C_3^2:C_6$ (as 18T21) |
trivial |
$2$ |
$17$ |
$102184067250$ |
| 18.0.295...000.1 |
$x^{18} - 60 x^{15} + 360 x^{14} + 1401 x^{12} - 14400 x^{11} + 39600 x^{10} - 22700 x^{9} + 193320 x^{8} - 864000 x^{7} + 1154967 x^{6} - 1699200 x^{5} + 5724000 x^{4} - 1375800 x^{3} - 17377920 x^{2} - 1368000 x + 154736383$ |
$18$ |
[0,9] |
$-\,2^{12}\cdot 3^{45}\cdot 5^{12}$ |
$3$ |
$72.355209189$ |
$81.74915574184915$ |
|
|
|
$C_3^2:C_6$ (as 18T21) |
$[3, 3, 3]$ |
$6$ |
$8$ |
$597898480.2407053$ |
| 18.0.132...288.4 |
$x^{18} - 48 x^{15} + 1944 x^{12} - 28944 x^{9} + 409536 x^{6} + 2099520 x^{3} + 34012224$ |
$18$ |
[0,9] |
$-\,2^{12}\cdot 3^{33}\cdot 17^{12}$ |
$3$ |
$78.6517237226$ |
$113.43541474288524$ |
|
|
|
$C_3^2:C_6$ (as 18T21) |
$[3, 3, 9]$ |
$6$ |
$8$ |
$898516250.6729627$ |
| 18.0.503...488.12 |
$x^{18} - 60 x^{15} + 1752 x^{12} - 33120 x^{9} + 265824 x^{6} + 1073088 x^{3} + 1259712$ |
$18$ |
[0,9] |
$-\,2^{12}\cdot 3^{33}\cdot 19^{12}$ |
$3$ |
$84.7054520929$ |
$122.1664018837223$ |
|
|
|
$C_3^2:C_6$ (as 18T21) |
$[3, 3, 9]$ |
$6$ |
$8$ |
$1228939086.8309562$ |
| 18.0.149...448.5 |
$x^{18} - 258 x^{15} + 67464 x^{12} + 235656 x^{9} + 364176 x^{6} + 1555200 x^{3} + 2985984$ |
$18$ |
[0,9] |
$-\,2^{12}\cdot 3^{33}\cdot 37^{12}$ |
$3$ |
$132.09208038$ |
$190.5097461690282$ |
|
|
|
$C_3^2:C_6$ (as 18T21) |
$[3, 3, 9]$ |
$6$ |
$8$ |
$184287206649.34076$ |
