| 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 |
| 16.0.4919707275390625.1 |
$x^{16} - 5 x^{15} + 14 x^{14} - 29 x^{13} + 50 x^{12} - 77 x^{11} + 112 x^{10} - 149 x^{9} + 176 x^{8} - 182 x^{7} + 159 x^{6} - 118 x^{5} + 73 x^{4} - 36 x^{3} + 15 x^{2} - 4 x + 1$ |
$16$ |
[0,8] |
$5^{12}\cdot 67^{4}$ |
$2$ |
$9.56634862885$ |
$27.369376545007917$ |
|
|
? |
$C_4\times S_4$ (as 16T181) |
trivial |
$10$ |
$7$ |
$48.4508350282$ |
| 16.0.38416000000000000.1 |
$x^{16} - 8 x^{15} + 32 x^{14} - 84 x^{13} + 164 x^{12} - 256 x^{11} + 344 x^{10} - 422 x^{9} + 478 x^{8} - 480 x^{7} + 400 x^{6} - 260 x^{5} + 127 x^{4} - 46 x^{3} + 14 x^{2} - 4 x + 1$ |
$16$ |
[0,8] |
$2^{16}\cdot 5^{12}\cdot 7^{4}$ |
$3$ |
$10.8775730594$ |
$19.85995155932405$ |
|
|
? |
$C_4\times S_4$ (as 16T181) |
trivial |
$10$ |
$7$ |
$175.447877376$ |
| 16.0.117135062500000000.1 |
$x^{16} - 2 x^{15} + 3 x^{14} - 2 x^{13} + x^{12} + 2 x^{10} - 5 x^{9} + 7 x^{8} - 5 x^{7} - 3 x^{6} + 10 x^{5} - 9 x^{4} + 2 x^{3} + 3 x^{2} - 3 x + 1$ |
$16$ |
[0,8] |
$2^{8}\cdot 5^{12}\cdot 37^{4}$ |
$3$ |
$11.6625342481$ |
$32.28605847922135$ |
|
|
? |
$C_4\times S_4$ (as 16T181) |
trivial |
$10$ |
$7$ |
$333.853446138$ |
| 16.0.148333301025390625.1 |
$x^{16} - 4 x^{15} + 14 x^{14} - 36 x^{13} + 76 x^{12} - 137 x^{11} + 211 x^{10} - 281 x^{9} + 331 x^{8} - 336 x^{7} + 305 x^{6} - 244 x^{5} + 172 x^{4} - 108 x^{3} + 60 x^{2} - 24 x + 11$ |
$16$ |
[0,8] |
$5^{12}\cdot 157^{4}$ |
$2$ |
$11.8359307729$ |
$41.89646002154997$ |
|
|
? |
$C_4\times S_4$ (as 16T181) |
trivial |
$10$ |
$7$ |
$374.86019186$ |
| 16.8.934...456.1 |
$x^{16} - 4 x^{15} - 2 x^{14} + 20 x^{13} - 5 x^{12} - 36 x^{11} + 28 x^{10} + 20 x^{9} - 62 x^{8} + 12 x^{7} + 78 x^{6} - 8 x^{5} - 54 x^{4} - 12 x^{3} + 16 x^{2} + 8 x + 1$ |
$16$ |
[8,4] |
$2^{44}\cdot 3^{12}$ |
$2$ |
$15.3346345019$ |
$24.23672593327708$ |
|
|
? |
$C_4\times S_4$ (as 16T181) |
trivial |
$2$ |
$11$ |
$2452.93509651$ |
| 16.8.983...000.1 |
$x^{16} - 4 x^{15} + 14 x^{13} - 2 x^{12} - 18 x^{11} - 26 x^{10} + 18 x^{9} + 81 x^{8} - 14 x^{7} - 98 x^{6} - 2 x^{5} + 60 x^{4} + 6 x^{3} - 16 x^{2} + 1$ |
$16$ |
[8,4] |
$2^{24}\cdot 5^{12}\cdot 7^{4}$ |
$3$ |
$15.3832113463$ |
$26.50985484327206$ |
|
|
? |
$C_4\times S_4$ (as 16T181) |
trivial |
$2$ |
$11$ |
$2954.91741119$ |
| 16.0.780...000.1 |
$x^{16} + 4 x^{14} + 4 x^{12} - 2 x^{10} + 4 x^{8} + 16 x^{6} + 21 x^{4} + 12 x^{2} + 16$ |
$16$ |
[0,8] |
$2^{16}\cdot 5^{12}\cdot 47^{4}$ |
$3$ |
$17.5098313623$ |
$45.84652548285205$ |
|
|
|
$C_4\times S_4$ (as 16T181) |
$[2]$ |
$2$ |
$7$ |
$1300.69001393$ |
| 16.0.479...000.1 |
$x^{16} + 10 x^{12} + 100 x^{10} + 375 x^{8} + 500 x^{6} + 250 x^{4} + 625$ |
$16$ |
[0,8] |
$2^{20}\cdot 5^{12}\cdot 37^{4}$ |
$3$ |
$19.6139664839$ |
$51.250923193822786$ |
|
|
|
$C_4\times S_4$ (as 16T181) |
$[2]$ |
$2$ |
$7$ |
$2615.56096385$ |
| 16.0.358...625.1 |
$x^{16} + 4 x^{14} - x^{13} + 15 x^{12} + 12 x^{11} + 57 x^{10} + 34 x^{9} + 201 x^{8} + 67 x^{7} + 74 x^{6} + 33 x^{5} + 28 x^{4} - 9 x^{3} + 5 x^{2} - x + 1$ |
$16$ |
[0,8] |
$5^{12}\cdot 19^{4}\cdot 103^{4}$ |
$3$ |
$22.2395097645$ |
$147.91864371956444$ |
✓ |
|
|
$C_4\times S_4$ (as 16T181) |
$[5]$ |
$10$ |
$7$ |
$10491.0986114$ |
| 16.0.615...625.1 |
$x^{16} - 2 x^{15} + 7 x^{14} - 21 x^{13} + 48 x^{12} - 25 x^{11} + 66 x^{10} - 183 x^{9} + 463 x^{8} - 626 x^{7} + 649 x^{6} - 393 x^{5} + 298 x^{4} - 137 x^{3} + 43 x^{2} - 8 x + 1$ |
$16$ |
[0,8] |
$3^{12}\cdot 5^{12}\cdot 83^{4}$ |
$3$ |
$23.0058332371$ |
$109.75088053305629$ |
✓ |
|
? |
$C_4\times S_4$ (as 16T181) |
$[2, 2]$ |
$10$ |
$7$ |
$14789.2708979$ |
| 16.16.175...176.1 |
$x^{16} - 20 x^{14} + 158 x^{12} - 624 x^{10} + 1287 x^{8} - 1336 x^{6} + 650 x^{4} - 116 x^{2} + 1$ |
$16$ |
[16,0] |
$2^{52}\cdot 79^{4}$ |
$2$ |
$28.3631367405$ |
$92.21249671842511$ |
|
|
? |
$C_4\times S_4$ (as 16T181) |
trivial |
$2$ |
$15$ |
$2484052.66943$ |
| 16.16.248...000.1 |
$x^{16} - 6 x^{15} - 7 x^{14} + 88 x^{13} - 6 x^{12} - 542 x^{11} + 166 x^{10} + 1764 x^{9} - 522 x^{8} - 3120 x^{7} + 745 x^{6} + 2830 x^{5} - 598 x^{4} - 1092 x^{3} + 256 x^{2} + 78 x - 19$ |
$16$ |
[16,0] |
$2^{16}\cdot 5^{12}\cdot 353^{4}$ |
$3$ |
$28.9868601526$ |
$125.64489612056876$ |
|
|
? |
$C_4\times S_4$ (as 16T181) |
trivial |
$2$ |
$15$ |
$2794821.00742$ |
| 16.16.111...000.1 |
$x^{16} - 48 x^{14} + 890 x^{12} - 8236 x^{10} + 41097 x^{8} - 111928 x^{6} + 161520 x^{4} - 114256 x^{2} + 30976$ |
$16$ |
[16,0] |
$2^{8}\cdot 5^{4}\cdot 97^{12}$ |
$3$ |
$65.36365056999017$ |
$109.71107402649531$ |
|
|
|
$C_4\times S_4$ (as 16T181) |
trivial |
$2$ |
$15$ |
$5190457249.388809$ |
