| 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 |
| 16.0.589...936.2 |
$x^{16} + 14 x^{12} - 48 x^{10} + 55 x^{8} - 40 x^{6} + 26 x^{4} + 4 x^{2} + 9$ |
$16$ |
[0,8] |
$2^{24}\cdot 37^{8}$ |
$2$ |
$17.2046505341$ |
$21.059413447565383$ |
|
|
? |
$\GL(2,\mathbb{Z}/4)$ (as 16T193) |
trivial |
trivial |
$2$ |
$7$ |
$5088.52344445$ |
| 16.0.141...336.1 |
$x^{16} + 6 x^{14} - 10 x^{13} + 20 x^{12} - 48 x^{11} + 96 x^{10} - 188 x^{9} + 251 x^{8} + 140 x^{7} + 2132 x^{6} + 2368 x^{5} + 4286 x^{4} + 1780 x^{3} + 1120 x^{2} - 990 x + 243$ |
$16$ |
[0,8] |
$2^{24}\cdot 7^{4}\cdot 37^{8}$ |
$3$ |
$27.9846813109$ |
$55.71797073914738$ |
|
|
|
$\GL(2,\mathbb{Z}/4)$ (as 16T193) |
$[8]$ |
$[8]$ |
$2$ |
$7$ |
$80443.548319$ |
| 16.8.176...000.2 |
$x^{16} - 16 x^{14} + 20 x^{12} - 64 x^{10} + 124 x^{8} - 224 x^{6} + 320 x^{4} - 176 x^{2} + 16$ |
$16$ |
[8,4] |
$2^{24}\cdot 3^{16}\cdot 5^{12}$ |
$3$ |
$28.3722482701$ |
$50.088103145153255$ |
|
|
? |
$C_2\wr S_3$ (as 16T765) |
trivial |
$[2]$ |
$2$ |
$11$ |
$682261.38123$ |
| 16.8.907...000.1 |
$x^{16} - 6 x^{15} + 50 x^{13} - 50 x^{12} - 4 x^{11} - 396 x^{10} + 680 x^{9} + 700 x^{8} - 2800 x^{7} - 156 x^{6} + 2956 x^{5} + 15760 x^{4} + 12120 x^{3} - 22320 x^{2} - 19656 x - 324$ |
$16$ |
[8,4] |
$2^{24}\cdot 5^{12}\cdot 53^{6}$ |
$3$ |
$41.9156251525$ |
$96.3736588314662$ |
|
|
? |
$(C_2^2\times D_4):S_4$ (as 16T1054) |
trivial |
$[2, 2]$ |
$2$ |
$11$ |
$17632128.4078$ |
| 16.8.907...000.2 |
$x^{16} - 2 x^{15} - 32 x^{14} + 36 x^{13} + 412 x^{12} - 184 x^{11} - 2872 x^{10} - 74 x^{9} + 14487 x^{8} + 13864 x^{7} - 35744 x^{6} - 99102 x^{5} - 104826 x^{4} - 55822 x^{3} - 13854 x^{2} - 1018 x + 101$ |
$16$ |
[8,4] |
$2^{24}\cdot 5^{12}\cdot 53^{6}$ |
$3$ |
$41.9156251525$ |
$96.3736588314662$ |
|
|
? |
$(C_2^2\times D_4):S_4$ (as 16T1054) |
trivial |
$[2, 2]$ |
$2$ |
$11$ |
$19525572.1304$ |
| 20.2.129...000.1 |
$x^{20} - x^{18} + x^{16} + 6 x^{14} - 15 x^{12} + 21 x^{10} - 21 x^{8} + 14 x^{6} - x^{4} - 5 x^{2} - 1$ |
$20$ |
[2,9] |
$-\,2^{28}\cdot 5^{10}\cdot 149^{4}$ |
$3$ |
$16.0532973395$ |
|
|
|
|
$A_5^2:D_4$ (as 20T546) |
trivial |
trivial |
$2$ |
$10$ |
$11903.1740533$ |
| 20.2.129...000.2 |
$x^{20} + x^{18} + x^{16} - 6 x^{14} - 15 x^{12} - 21 x^{10} - 21 x^{8} - 14 x^{6} - x^{4} + 5 x^{2} - 1$ |
$20$ |
[2,9] |
$-\,2^{28}\cdot 5^{10}\cdot 149^{4}$ |
$3$ |
$16.0532973395$ |
|
|
|
|
$A_5^2:D_4$ (as 20T546) |
trivial |
trivial |
$2$ |
$10$ |
$11165.4876136$ |
| 20.6.125...000.1 |
$x^{20} - 11 x^{18} + 29 x^{16} + 94 x^{14} - 559 x^{12} + 307 x^{10} + 2271 x^{8} - 2834 x^{6} - 2397 x^{4} + 2549 x^{2} - 1$ |
$20$ |
[6,7] |
$-\,2^{28}\cdot 3^{4}\cdot 5^{10}\cdot 17^{4}\cdot 29^{4}$ |
$5$ |
$25.4050837477$ |
|
|
|
|
$A_5^2:(C_2\times D_4)$ (as 20T658) |
trivial |
trivial |
$2$ |
$12$ |
$3187004.5686$ |
| 20.6.125...000.2 |
$x^{20} + 11 x^{18} + 29 x^{16} - 94 x^{14} - 559 x^{12} - 307 x^{10} + 2271 x^{8} + 2834 x^{6} - 2397 x^{4} - 2549 x^{2} - 1$ |
$20$ |
[6,7] |
$-\,2^{28}\cdot 3^{4}\cdot 5^{10}\cdot 17^{4}\cdot 29^{4}$ |
$5$ |
$25.4050837477$ |
|
|
|
|
$A_5^2:(C_2\times D_4)$ (as 20T658) |
trivial |
trivial |
$2$ |
$12$ |
$2654351.34358$ |
