| 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 |
| 16.0.218103593994140625.1 |
$x^{16} - 3 x^{15} + 6 x^{14} - 8 x^{13} + 26 x^{12} - 69 x^{11} + 129 x^{10} - 183 x^{9} + 276 x^{8} - 467 x^{7} + 780 x^{6} - 1077 x^{5} + 1152 x^{4} - 901 x^{3} + 495 x^{2} - 172 x + 31$ |
$16$ |
[0,8] |
$3^{12}\cdot 5^{12}\cdot 41^{2}$ |
$3$ |
$12.1245722659$ |
$48.80455673313263$ |
|
|
|
$(C_2^3\times C_4):C_4$ (as 16T292) |
trivial |
trivial |
$30$ |
$7$ |
$1278.94388647$ |
| 16.0.130...344.1 |
$x^{16} - 8 x^{15} + 28 x^{14} - 48 x^{13} + 12 x^{12} + 128 x^{11} - 300 x^{10} + 296 x^{9} + 2 x^{8} - 376 x^{7} + 540 x^{6} - 448 x^{5} + 260 x^{4} - 112 x^{3} + 36 x^{2} - 8 x + 1$ |
$16$ |
[0,8] |
$2^{52}\cdot 17^{2}$ |
$2$ |
$13.5566879991$ |
$39.22581236713814$ |
|
|
? |
$(C_2^3\times C_4):C_4$ (as 16T292) |
trivial |
trivial |
$16$ |
$7$ |
$3458.0422126$ |
| 16.0.344...000.1 |
$x^{16} - 8 x^{15} + 26 x^{14} - 42 x^{13} + 33 x^{12} - 16 x^{11} + 21 x^{10} - 6 x^{9} - 59 x^{8} + 96 x^{7} - 69 x^{6} + 40 x^{5} - 10 x^{4} - 22 x^{3} + 57 x^{2} - 42 x + 31$ |
$16$ |
[0,8] |
$2^{24}\cdot 5^{12}\cdot 29^{2}$ |
$3$ |
$14.4069565534$ |
$50.92974429446663$ |
|
|
? |
$(C_2^3\times C_4):C_4$ (as 16T292) |
trivial |
trivial |
$10$ |
$7$ |
$1674.03195575$ |
| 16.0.881...000.1 |
$x^{16} - 6 x^{14} - 8 x^{13} + 18 x^{12} + 16 x^{11} + 64 x^{10} - 116 x^{9} - 56 x^{8} - 104 x^{7} + 148 x^{6} + 240 x^{5} + 17 x^{4} - 72 x^{3} - 166 x^{2} - 16 x + 71$ |
$16$ |
[0,8] |
$2^{32}\cdot 5^{12}\cdot 29^{2}$ |
$3$ |
$20.3745133503$ |
$85.65327881401062$ |
|
|
? |
$(C_2^3\times C_4):C_4$ (as 16T292) |
$[2]$ |
$[2]$ |
$10$ |
$7$ |
$16683.0378758$ |
| 16.12.429...000.1 |
$x^{16} - 16 x^{14} + 74 x^{12} - 72 x^{10} - 81 x^{8} + 136 x^{6} - 34 x^{4} - 8 x^{2} + 1$ |
$16$ |
[12,2] |
$2^{44}\cdot 5^{12}$ |
$2$ |
$22.4936530076$ |
$30.46215435643493$ |
|
|
? |
$(C_2^3\times C_4):C_4$ (as 16T292) |
trivial |
$[2]$ |
$2$ |
$13$ |
$166632.64612$ |
| 16.4.429...000.2 |
$x^{16} + 16 x^{14} + 74 x^{12} + 72 x^{10} - 81 x^{8} - 136 x^{6} - 34 x^{4} + 8 x^{2} + 1$ |
$16$ |
[4,6] |
$2^{44}\cdot 5^{12}$ |
$2$ |
$22.4936530076$ |
$30.46215435643493$ |
|
|
? |
$(C_2^3\times C_4):C_4$ (as 16T292) |
trivial |
$[2]$ |
$2$ |
$9$ |
$25801.6680564$ |
| 16.12.687...000.2 |
$x^{16} - 10 x^{14} + 28 x^{12} - 86 x^{8} + 100 x^{6} - 33 x^{4} + 1$ |
$16$ |
[12,2] |
$2^{32}\cdot 3^{8}\cdot 5^{12}$ |
$3$ |
$23.1658437058$ |
$35.72661494273978$ |
|
|
✓ |
$(C_2^3\times C_4):C_4$ (as 16T292) |
trivial |
$[2]$ |
$2$ |
$13$ |
$163373.585869$ |
| 16.4.687...000.2 |
$x^{16} + 10 x^{14} + 28 x^{12} - 86 x^{8} - 100 x^{6} - 33 x^{4} + 1$ |
$16$ |
[4,6] |
$2^{32}\cdot 3^{8}\cdot 5^{12}$ |
$3$ |
$23.1658437058$ |
$35.72661494273978$ |
|
|
✓ |
$(C_2^3\times C_4):C_4$ (as 16T292) |
trivial |
$[2]$ |
$2$ |
$9$ |
$31559.3321698$ |
| 16.8.145...000.1 |
$x^{16} - 4 x^{15} - x^{14} + 4 x^{13} + 23 x^{12} + 66 x^{11} - 229 x^{10} - 112 x^{9} + 524 x^{8} + 224 x^{7} - 676 x^{6} - 426 x^{5} + 623 x^{4} + 280 x^{3} - 192 x^{2} - 32 x + 16$ |
$16$ |
[8,4] |
$2^{6}\cdot 5^{8}\cdot 17^{12}$ |
$3$ |
$24.2777224189$ |
$52.95008805866152$ |
|
|
? |
$(C_2^3\times C_4):C_4$ (as 16T292) |
trivial |
trivial |
$2$ |
$11$ |
$150305.070723$ |
| 16.12.302...144.3 |
$x^{16} - 8 x^{14} + 4 x^{12} + 72 x^{10} - 80 x^{8} - 64 x^{6} + 120 x^{4} - 48 x^{2} + 4$ |
$16$ |
[12,2] |
$2^{62}\cdot 3^{8}$ |
$2$ |
$25.412761497225222$ |
$33.677922740001875$ |
|
|
? |
$(C_2^3\times C_4):C_4$ (as 16T292) |
trivial |
$[2]$ |
$2$ |
$13$ |
$677922.2214308998$ |
| 16.4.302...144.35 |
$x^{16} + 8 x^{14} + 4 x^{12} - 72 x^{10} - 80 x^{8} + 64 x^{6} + 120 x^{4} + 48 x^{2} + 4$ |
$16$ |
[4,6] |
$2^{62}\cdot 3^{8}$ |
$2$ |
$25.412761497225222$ |
$33.677922740001875$ |
|
|
? |
$(C_2^3\times C_4):C_4$ (as 16T292) |
trivial |
$[2]$ |
$2$ |
$9$ |
$94159.34556737287$ |
| 16.8.233...000.1 |
$x^{16} - 6 x^{15} + 2 x^{14} + 56 x^{13} - 144 x^{12} + 98 x^{11} + 39 x^{10} + 113 x^{9} - 451 x^{8} + 364 x^{7} + 49 x^{6} - 213 x^{5} + 106 x^{4} - 2 x^{3} - 17 x^{2} + 5 x + 1$ |
$16$ |
[8,4] |
$2^{10}\cdot 5^{8}\cdot 17^{12}$ |
$3$ |
$28.8712402366$ |
$74.88273266140878$ |
|
|
|
$(C_2^3\times C_4):C_4$ (as 16T292) |
trivial |
$[2]$ |
$2$ |
$11$ |
$628294.842196$ |
| 16.12.245...664.4 |
$x^{16} - 72 x^{12} + 216 x^{10} + 198 x^{8} - 1296 x^{6} + 1512 x^{4} - 648 x^{2} + 81$ |
$16$ |
[12,2] |
$2^{62}\cdot 3^{12}$ |
$2$ |
$33.44507500385779$ |
$44.32263892833827$ |
|
|
? |
$(C_2^3\times C_4):C_4$ (as 16T292) |
trivial |
$[2]$ |
$2$ |
$13$ |
$6828348.410317181$ |
| 16.4.245...664.110 |
$x^{16} - 72 x^{12} - 216 x^{10} + 198 x^{8} + 1296 x^{6} + 1512 x^{4} + 648 x^{2} + 81$ |
$16$ |
[4,6] |
$2^{62}\cdot 3^{12}$ |
$2$ |
$33.44507500385779$ |
$44.32263892833827$ |
|
|
? |
$(C_2^3\times C_4):C_4$ (as 16T292) |
trivial |
$[2]$ |
$2$ |
$9$ |
$1005463.8913972725$ |
| 16.0.317...504.1 |
$x^{16} + 8 x^{14} - 24 x^{13} + 88 x^{12} - 120 x^{11} + 648 x^{10} - 880 x^{9} + 1766 x^{8} - 3760 x^{7} + 2888 x^{6} - 7824 x^{5} + 6372 x^{4} - 4512 x^{3} + 13480 x^{2} + 2720 x + 9406$ |
$16$ |
[0,8] |
$2^{58}\cdot 3^{8}\cdot 41^{2}$ |
$3$ |
$33.9932230334$ |
$155.82222959264388$ |
✓ |
|
? |
$(C_2^3\times C_4):C_4$ (as 16T292) |
$[34]$ |
$[34]$ |
$2$ |
$7$ |
$11964.3106427$ |
| 16.16.317...504.1 |
$x^{16} - 32 x^{14} - 16 x^{13} + 340 x^{12} + 328 x^{11} - 1520 x^{10} - 2096 x^{9} + 2842 x^{8} + 5744 x^{7} - 960 x^{6} - 6752 x^{5} - 2988 x^{4} + 2160 x^{3} + 2392 x^{2} + 800 x + 94$ |
$16$ |
[16,0] |
$2^{58}\cdot 3^{8}\cdot 41^{2}$ |
$3$ |
$33.9932230334$ |
$155.82222959264388$ |
|
|
? |
$(C_2^3\times C_4):C_4$ (as 16T292) |
trivial |
$[2]$ |
$2$ |
$15$ |
$17156663.2489$ |
| 16.0.361...000.1 |
$x^{16} + 32 x^{14} + 386 x^{12} + 2256 x^{10} + 7059 x^{8} + 12208 x^{6} + 11354 x^{4} + 5104 x^{2} + 841$ |
$16$ |
[0,8] |
$2^{44}\cdot 5^{12}\cdot 29^{2}$ |
$3$ |
$34.2657104776$ |
$132.0954138186518$ |
✓ |
|
? |
$(C_2^3\times C_4):C_4$ (as 16T292) |
$[5, 10]$ |
$[5, 10]$ |
$2$ |
$7$ |
$7114.13535725$ |
| 16.16.361...000.1 |
$x^{16} - 32 x^{14} + 386 x^{12} - 2256 x^{10} + 7059 x^{8} - 12208 x^{6} + 11354 x^{4} - 5104 x^{2} + 841$ |
$16$ |
[16,0] |
$2^{44}\cdot 5^{12}\cdot 29^{2}$ |
$3$ |
$34.2657104776$ |
$132.0954138186518$ |
|
|
? |
$(C_2^3\times C_4):C_4$ (as 16T292) |
trivial |
$[2]$ |
$2$ |
$15$ |
$12396037.6487$ |
| 16.8.361...000.1 |
$x^{16} - 16 x^{14} - 76 x^{12} + 528 x^{10} + 734 x^{8} - 3184 x^{6} - 2844 x^{4} + 1392 x^{2} + 841$ |
$16$ |
[8,4] |
$2^{44}\cdot 5^{12}\cdot 29^{2}$ |
$3$ |
$34.2657104776$ |
$132.0954138186518$ |
|
|
? |
$(C_2^3\times C_4):C_4$ (as 16T292) |
trivial |
$[2]$ |
$2$ |
$11$ |
$1828598.13777$ |
| 16.8.361...000.2 |
$x^{16} + 16 x^{14} - 76 x^{12} - 528 x^{10} + 734 x^{8} + 3184 x^{6} - 2844 x^{4} - 1392 x^{2} + 841$ |
$16$ |
[8,4] |
$2^{44}\cdot 5^{12}\cdot 29^{2}$ |
$3$ |
$34.2657104776$ |
$132.0954138186518$ |
|
|
? |
$(C_2^3\times C_4):C_4$ (as 16T292) |
trivial |
$[2]$ |
$2$ |
$11$ |
$1609532.75093$ |
| 16.12.980...656.8 |
$x^{16} - 84 x^{12} + 504 x^{10} - 1260 x^{8} + 1512 x^{6} - 756 x^{4} + 81$ |
$16$ |
[12,2] |
$2^{64}\cdot 3^{12}$ |
$2$ |
$36.47211291127644$ |
$48.33418048348305$ |
|
|
? |
$(C_2^3\times C_4):C_4$ (as 16T292) |
trivial |
$[2]$ |
$2$ |
$13$ |
$13055439.286257848$ |
| 16.12.980...656.9 |
$x^{16} - 24 x^{14} + 192 x^{12} - 576 x^{10} + 324 x^{8} + 1296 x^{6} - 1728 x^{4} + 324$ |
$16$ |
[12,2] |
$2^{64}\cdot 3^{12}$ |
$2$ |
$36.47211291127644$ |
$48.33418048348305$ |
|
|
? |
$(C_2^3\times C_4):C_4$ (as 16T292) |
trivial |
$[2]$ |
$2$ |
$13$ |
$11315909.271630786$ |
| 16.4.980...656.204 |
$x^{16} - 84 x^{12} - 504 x^{10} - 1260 x^{8} - 1512 x^{6} - 756 x^{4} + 81$ |
$16$ |
[4,6] |
$2^{64}\cdot 3^{12}$ |
$2$ |
$36.47211291127644$ |
$48.33418048348305$ |
|
|
? |
$(C_2^3\times C_4):C_4$ (as 16T292) |
trivial |
$[2]$ |
$2$ |
$9$ |
$1697518.2313426146$ |
| 16.4.980...656.268 |
$x^{16} + 24 x^{14} + 192 x^{12} + 576 x^{10} + 324 x^{8} - 1296 x^{6} - 1728 x^{4} + 324$ |
$16$ |
[4,6] |
$2^{64}\cdot 3^{12}$ |
$2$ |
$36.47211291127644$ |
$48.33418048348305$ |
|
|
? |
$(C_2^3\times C_4):C_4$ (as 16T292) |
trivial |
$[2]$ |
$2$ |
$9$ |
$2173080.72262807$ |
