| 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 |
| 12.12.102...125.1 |
$x^{12} - 30 x^{10} - 15 x^{9} + 315 x^{8} + 315 x^{7} - 1310 x^{6} - 2025 x^{5} + 1350 x^{4} + 4050 x^{3} + 2250 x^{2} + 225 x - 25$ |
$12$ |
[12,0] |
$3^{16}\cdot 5^{10}\cdot 29^{3}$ |
$3$ |
$38.3915968168$ |
$170.83395556024902$ |
|
|
? |
$S_3^2:C_6$ (as 12T121) |
trivial |
$2$ |
$11$ |
$360939.969786$ |
| 16.0.124...000.1 |
$x^{16} - 18 x^{14} - 32 x^{13} + 129 x^{12} + 432 x^{11} + 456 x^{10} - 3672 x^{9} - 2178 x^{8} + 256 x^{7} + 42678 x^{6} - 50976 x^{5} + 46612 x^{4} - 260592 x^{3} + 660564 x^{2} - 685152 x + 301401$ |
$16$ |
[0,8] |
$2^{24}\cdot 3^{16}\cdot 5^{12}\cdot 29^{4}$ |
$4$ |
$65.8405198063$ |
|
|
|
? |
$(C_2^2:S_4)^2.C_6$ (as 16T1853) |
trivial |
$2$ |
$7$ |
$60822942.9569$ |
| 16.0.124...000.2 |
$x^{16} - 8 x^{15} + 48 x^{14} - 166 x^{13} + 623 x^{12} - 1734 x^{11} + 4902 x^{10} - 8388 x^{9} + 19071 x^{8} - 29948 x^{7} + 59884 x^{6} - 29112 x^{5} + 106183 x^{4} - 316766 x^{3} + 842118 x^{2} + 300362 x + 508619$ |
$16$ |
[0,8] |
$2^{24}\cdot 3^{16}\cdot 5^{12}\cdot 29^{4}$ |
$4$ |
$65.8405198063$ |
|
|
|
? |
$(C_2^2:S_4)^2.C_6$ (as 16T1853) |
trivial |
$2$ |
$7$ |
$67429157.9895$ |
| 16.8.464...000.1 |
$x^{16} - 36 x^{14} - 104 x^{13} + 834 x^{12} + 3888 x^{11} - 17216 x^{10} - 44736 x^{9} + 169971 x^{8} + 372864 x^{7} - 1075824 x^{6} - 3086976 x^{5} + 10316266 x^{4} - 1592976 x^{3} - 21122964 x^{2} + 22527288 x - 6191559$ |
$16$ |
[8,4] |
$2^{24}\cdot 3^{16}\cdot 5^{12}\cdot 29^{4}\cdot 61^{2}$ |
$5$ |
$110.067595802$ |
|
|
|
? |
$(C_2^2:S_4)^2.C_6$ (as 16T1853) |
trivial |
$2$ |
$11$ |
$23197110657.7$ |
| 16.0.258...000.1 |
$x^{16} - 36 x^{14} - 344 x^{13} + 1554 x^{12} + 11088 x^{11} - 4256 x^{10} - 338496 x^{9} - 135309 x^{8} + 5222784 x^{7} + 6354576 x^{6} - 67403136 x^{5} - 38670614 x^{4} + 482064144 x^{3} + 105535116 x^{2} - 2453189112 x + 2539806921$ |
$16$ |
[0,8] |
$2^{24}\cdot 3^{16}\cdot 5^{12}\cdot 11^{2}\cdot 29^{4}\cdot 131^{2}$ |
$6$ |
$163.427918197$ |
|
|
|
? |
$(C_2^2:S_4)^2.C_6$ (as 16T1853) |
$[2, 4]$ |
$2$ |
$7$ |
$13194217181.7$ |
| 16.12.133...000.1 |
$x^{16} - 156 x^{14} - 264 x^{13} + 9414 x^{12} + 29088 x^{11} - 264416 x^{10} - 1195416 x^{9} + 3314871 x^{8} + 24922944 x^{7} + 3431376 x^{6} - 255181896 x^{5} - 689990794 x^{4} - 637627536 x^{3} + 40279356 x^{2} + 339912288 x + 93960081$ |
$16$ |
[12,2] |
$2^{24}\cdot 3^{16}\cdot 5^{12}\cdot 7^{4}\cdot 29^{4}\cdot 211^{2}$ |
$6$ |
$209.075463313$ |
|
|
|
? |
$(C_2^2:S_4)^2.C_6$ (as 16T1853) |
trivial |
$2$ |
$13$ |
$10851375469300$ |
| 16.16.194...000.1 |
$x^{16} - 324 x^{14} - 968 x^{13} + 40074 x^{12} + 231984 x^{11} - 1997504 x^{10} - 19312512 x^{9} + 9637971 x^{8} + 588047232 x^{7} + 1761656544 x^{6} - 2571952512 x^{5} - 20639956214 x^{4} - 25700194128 x^{3} + 20254924044 x^{2} + 50504575896 x + 20808556641$ |
$16$ |
[16,0] |
$2^{24}\cdot 3^{16}\cdot 5^{12}\cdot 7^{4}\cdot 29^{4}\cdot 8059^{2}$ |
$6$ |
$329.649867423$ |
|
|
|
? |
$(C_2^2:S_4)^2.C_6$ (as 16T1853) |
trivial |
$2$ |
$15$ |
$904597057772000$ |
| 16.16.305...000.1 |
$x^{16} - 324 x^{14} - 1208 x^{13} + 38634 x^{12} + 291024 x^{11} - 1435904 x^{10} - 22872192 x^{9} - 52823469 x^{8} + 457836672 x^{7} + 3556633824 x^{6} + 10251984768 x^{5} + 10991206666 x^{4} - 10633046448 x^{3} - 41850562356 x^{2} - 41586585624 x - 13976251839$ |
$16$ |
[16,0] |
$2^{24}\cdot 3^{16}\cdot 5^{12}\cdot 29^{4}\cdot 31^{2}\cdot 50461^{2}$ |
$6$ |
$391.546137634$ |
|
|
|
? |
$(C_2^2:S_4)^2.C_6$ (as 16T1853) |
trivial |
$2$ |
$15$ |
$5717295893090000$ |
| 18.6.126...333.1 |
$x^{18} - 6 x^{16} - 9 x^{15} + 9 x^{14} + 45 x^{13} - 22 x^{12} - 54 x^{11} + 12 x^{10} + 186 x^{9} + 117 x^{8} - 216 x^{7} + 375 x^{6} - 108 x^{5} - 87 x^{4} + 225 x^{3} + 54 x^{2} + 90 x - 1$ |
$18$ |
[6,6] |
$3^{24}\cdot 31^{6}\cdot 37^{3}$ |
$3$ |
$24.8112812411$ |
|
|
|
? |
$C_3\times S_3\wr S_3$ (as 18T438) |
trivial |
$2$ |
$11$ |
$474748.682468$ |
