| 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 |
| 12.4.2535525376000000.1 |
$x^{12} + 9 x^{10} + 12 x^{8} - 35 x^{6} - 76 x^{4} - 19 x^{2} + 19$ |
$12$ |
[4,4] |
$2^{16}\cdot 5^{6}\cdot 19^{5}$ |
$3$ |
$19.21641326909542$ |
$92.01647650119014$ |
|
|
? |
$A_4^2:D_4$ (as 12T208) |
trivial |
$2$ |
$7$ |
$1034.9193313912845$ |
| 16.0.954...000.1 |
$x^{16} + 38 x^{14} + 524 x^{12} + 3268 x^{10} + 9161 x^{8} + 9768 x^{6} + 4128 x^{4} + 558 x^{2} + 9$ |
$16$ |
[0,8] |
$2^{20}\cdot 3^{6}\cdot 5^{8}\cdot 7^{4}\cdot 191^{4}$ |
$5$ |
$48.55409001$ |
|
✓ |
|
|
$C_2^7.\PGOPlus(4,3)$ (as 16T1867) |
$[2, 42]$ |
$2$ |
$7$ |
$179538.402106$ |
| 16.16.620...000.1 |
$x^{16} - 7 x^{15} - 26 x^{14} + 244 x^{13} + 154 x^{12} - 3075 x^{11} + 698 x^{10} + 17667 x^{9} - 8049 x^{8} - 51225 x^{7} + 22288 x^{6} + 73455 x^{5} - 22238 x^{4} - 43888 x^{3} + 6408 x^{2} + 7999 x + 1039$ |
$16$ |
[16,0] |
$2^{16}\cdot 3^{4}\cdot 5^{8}\cdot 7^{6}\cdot 191^{5}$ |
$5$ |
$63.0274887823$ |
$4693.349490473681$ |
|
|
? |
$C_2^8.\PGOPlus(4,3)$ (as 16T1887) |
trivial |
$2$ |
$15$ |
$4183971505.09$ |
| 16.16.772...000.1 |
$x^{16} - 51 x^{14} + 948 x^{12} - 8091 x^{10} + 32202 x^{8} - 54621 x^{6} + 36936 x^{4} - 9477 x^{2} + 729$ |
$16$ |
[16,0] |
$2^{20}\cdot 3^{10}\cdot 5^{8}\cdot 7^{4}\cdot 191^{4}$ |
$5$ |
$63.9007760847$ |
|
|
|
|
$C_2^7.\PGOPlus(4,3)$ (as 16T1867) |
trivial |
$2$ |
$15$ |
$3331376027.09$ |
| 18.2.351...696.1 |
$x^{18} + 7 x^{16} + 23 x^{14} + 45 x^{12} + 71 x^{10} + 80 x^{8} + 66 x^{6} + 37 x^{4} + 8 x^{2} - 1$ |
$18$ |
[2,8] |
$2^{22}\cdot 307^{6}$ |
$2$ |
$15.7388021302$ |
|
|
|
? |
$C_2^2:A_4^2.S_4$ (as 18T595) |
trivial |
$2$ |
$9$ |
$3198.65544505$ |
| 18.4.101...328.1 |
$x^{18} - 6 x^{16} - 8 x^{15} - 40 x^{14} + 312 x^{13} - 790 x^{12} - 568 x^{11} + 12172 x^{10} + 17028 x^{9} + 117012 x^{8} + 57240 x^{7} + 359980 x^{6} + 1191824 x^{5} - 773816 x^{4} + 1434912 x^{3} + 909808 x^{2} - 7490240 x + 1310048$ |
$18$ |
[4,7] |
$-\,2^{22}\cdot 307^{9}$ |
$2$ |
$40.8784799156492$ |
|
|
|
? |
$C_2^2:A_4^2.S_4$ (as 18T594) |
trivial |
$2$ |
$10$ |
$24652481.48203967$ |
| 18.2.283...992.1 |
$x^{18} + 42 x^{16} + 432 x^{14} - 873 x^{12} - 29574 x^{10} - 153036 x^{8} - 348975 x^{6} - 368982 x^{4} - 145962 x^{2} - 4563$ |
$18$ |
[2,8] |
$2^{26}\cdot 3^{25}\cdot 163^{8}$ |
$3$ |
$120.415946872$ |
|
|
|
? |
$C_2^9:C_3^2.\SL(2,3)$ (as 18T799) |
$[2]$ |
$2$ |
$9$ |
$1228235382920$ |
