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 |
12.6.3495224609375.1 |
$x^{12} - x^{11} - 4 x^{10} + 5 x^{9} - 5 x^{8} + 14 x^{7} - 19 x^{6} + 14 x^{5} - 5 x^{4} + 5 x^{3} - 4 x^{2} - x + 1$ |
$12$ |
[6,3] |
$-\,5^{10}\cdot 71^{3}$ |
$2$ |
$11.0991466793$ |
$32.21841549588632$ |
|
|
? |
$\SOPlus(4,2)$ (as 12T35) |
trivial |
$2$ |
$8$ |
$36.6945439221$ |
12.6.3647529984375.1 |
$x^{12} - x^{11} - 5 x^{10} + 3 x^{9} + 10 x^{8} - 4 x^{7} - 7 x^{6} + 6 x^{5} - 9 x^{3} - x^{2} + 5 x + 1$ |
$12$ |
[6,3] |
$-\,3^{4}\cdot 5^{6}\cdot 79\cdot 191^{2}$ |
$4$ |
$11.1386674793$ |
$475.74678138690547$ |
|
|
✓ |
$S_4^2:D_4$ (as 12T260) |
trivial |
$2$ |
$8$ |
$37.5915890729$ |
12.6.3722179279923.1 |
$x^{12} - 3 x^{11} - x^{10} + 11 x^{9} - 10 x^{8} - 14 x^{7} + 24 x^{6} + 10 x^{5} - 12 x^{4} - 2 x^{3} - 3 x^{2} - x + 1$ |
$12$ |
[6,3] |
$-\,3^{3}\cdot 13^{10}$ |
$2$ |
$11.1574883129$ |
$14.684080418380853$ |
|
|
? |
$D_4 \times C_3$ (as 12T14) |
trivial |
$2$ |
$8$ |
$38.0840901912$ |
12.6.3924967206547.1 |
$x^{12} - 2 x^{11} - 2 x^{10} + 10 x^{9} - 12 x^{8} + x^{7} + 12 x^{6} - 20 x^{5} + 6 x^{4} + 12 x^{3} - 6 x^{2} - 2 x + 1$ |
$12$ |
[6,3] |
$-\,43\cdot 302123^{2}$ |
$2$ |
$11.2069216589$ |
$3604.343074680877$ |
|
|
? |
$C_2^6.S_6$ (as 12T293) |
trivial |
$2$ |
$8$ |
$39.3020113964$ |
12.6.3959860197871.1 |
$x^{12} - x^{11} - 5 x^{10} + 7 x^{9} + 7 x^{8} - 20 x^{7} + 3 x^{6} + 25 x^{5} - 15 x^{4} - 10 x^{3} + 11 x^{2} - x - 1$ |
$12$ |
[6,3] |
$-\,67^{2}\cdot 151\cdot 2417^{2}$ |
$3$ |
$11.2151904896$ |
$4944.9761374550635$ |
|
|
✓ |
$C_2^6.S_6$ (as 12T293) |
trivial |
$2$ |
$8$ |
$39.4198384491$ |
12.6.4008072671875.1 |
$x^{12} - 4 x^{10} - 4 x^{9} + x^{8} + 8 x^{7} + 8 x^{6} + x^{5} - 5 x^{4} - 6 x^{3} - 2 x^{2} + 1$ |
$12$ |
[6,3] |
$-\,5^{6}\cdot 61\cdot 4205191$ |
$3$ |
$11.2265065033$ |
$35813.171529480605$ |
|
|
✓ |
$S_6\wr C_2$ (as 12T299) |
trivial |
$2$ |
$8$ |
$39.6887581471$ |
12.6.4008854234375.1 |
$x^{12} - x^{11} - 3 x^{10} + 2 x^{9} + 2 x^{8} - 5 x^{7} + 8 x^{6} + 8 x^{5} - 9 x^{4} - 8 x^{3} + 3 x + 1$ |
$12$ |
[6,3] |
$-\,5^{6}\cdot 19^{2}\cdot 61^{2}\cdot 191$ |
$4$ |
$11.226688915$ |
$1052.0670130747376$ |
|
|
? |
$S_4^2:D_4$ (as 12T260) |
trivial |
$2$ |
$8$ |
$39.6657239253$ |
12.6.4457810171875.1 |
$x^{12} - 3 x^{11} + 2 x^{10} + 3 x^{9} - 8 x^{8} + 3 x^{7} + 7 x^{6} + x^{5} - 4 x^{4} - 5 x^{3} + x + 1$ |
$12$ |
[6,3] |
$-\,5^{6}\cdot 31\cdot 101\cdot 91121$ |
$4$ |
$11.3264409262$ |
$37769.02507346463$ |
|
|
✓ |
$S_6\wr C_2$ (as 12T299) |
trivial |
$2$ |
$8$ |
$42.3975316008$ |
12.6.4466170043531.1 |
$x^{12} - 2 x^{11} - 4 x^{10} + 10 x^{9} + 3 x^{8} - 22 x^{7} + 7 x^{6} + 22 x^{5} - 17 x^{4} - 8 x^{3} + 11 x^{2} - x - 1$ |
$12$ |
[6,3] |
$-\,7^{8}\cdot 43^{2}\cdot 419$ |
$3$ |
$11.3282094759$ |
$491.1791606329313$ |
|
|
✓ |
$D_4\wr C_3$ (as 12T222) |
trivial |
$2$ |
$8$ |
$42.3028923905$ |
12.6.4471579046875.1 |
$x^{12} - x^{11} - 3 x^{10} - 3 x^{9} + x^{8} + 9 x^{7} + 11 x^{6} + 9 x^{5} + x^{4} - 3 x^{3} - 3 x^{2} - x + 1$ |
$12$ |
[6,3] |
$-\,5^{6}\cdot 19\cdot 3881^{2}$ |
$3$ |
$11.3293521465$ |
$607.2026021024614$ |
|
|
? |
$S_4^2:D_4$ (as 12T260) |
trivial |
$2$ |
$8$ |
$42.5473962095$ |
12.6.4608482796875.1 |
$x^{12} - 4 x^{10} - 3 x^{9} + 3 x^{8} + 13 x^{7} + 4 x^{6} - 15 x^{5} - 11 x^{4} + 5 x^{3} + 8 x^{2} + x - 1$ |
$12$ |
[6,3] |
$-\,5^{6}\cdot 419\cdot 839^{2}$ |
$3$ |
$11.3578596444$ |
$1325.784673316146$ |
|
|
? |
$S_4^2:D_4$ (as 12T260) |
trivial |
$2$ |
$8$ |
$43.200654948$ |
12.6.4617771109375.1 |
$x^{12} - 3 x^{11} + x^{10} + 5 x^{9} - 3 x^{8} - 10 x^{7} + 11 x^{6} + 3 x^{5} - 9 x^{4} + 8 x^{3} - x^{2} - 3 x + 1$ |
$12$ |
[6,3] |
$-\,5^{6}\cdot 151\cdot 1399^{2}$ |
$3$ |
$11.3597655143$ |
$1027.7378070305674$ |
|
|
? |
$S_4^2:D_4$ (as 12T260) |
trivial |
$2$ |
$8$ |
$43.1943606275$ |
12.6.4770738948267.1 |
$x^{12} - 3 x^{10} - 4 x^{9} + 12 x^{7} + x^{6} - 3 x^{5} + 3 x^{4} - 7 x^{3} - 3 x^{2} + 3 x + 1$ |
$12$ |
[6,3] |
$-\,3^{16}\cdot 19^{2}\cdot 307$ |
$3$ |
$11.3906577868$ |
$330.45144947292306$ |
|
|
? |
$D_4\wr C_3$ (as 12T222) |
trivial |
$2$ |
$8$ |
$43.9848803763$ |
12.6.5029275805211.1 |
$x^{12} - x^{11} - 4 x^{10} + 7 x^{9} + 2 x^{8} - 14 x^{7} + 7 x^{6} + 8 x^{5} - 10 x^{4} - x^{3} + 5 x^{2} - 1$ |
$12$ |
[6,3] |
$-\,7^{8}\cdot 872411$ |
$2$ |
$11.4408630692$ |
$3417.899273333768$ |
|
|
✓ |
$S_4\wr C_3$ (as 12T292) |
trivial |
$2$ |
$8$ |
$45.5165696715$ |
12.6.5099237430147.1 |
$x^{12} - x^{11} - 7 x^{10} + 8 x^{9} + 16 x^{8} - 16 x^{7} - 18 x^{6} + 13 x^{5} + 10 x^{4} - 8 x^{3} - 3 x^{2} + 3 x + 1$ |
$12$ |
[6,3] |
$-\,3^{3}\cdot 7^{8}\cdot 181^{2}$ |
$3$ |
$11.4540419535$ |
$85.27046045212757$ |
|
|
? |
$C_2\wr C_6$ (as 12T142) |
trivial |
$2$ |
$8$ |
$45.8680277949$ |
12.6.5124671732159.1 |
$x^{12} - x^{11} - x^{10} - x^{9} - 6 x^{8} + 11 x^{7} + 10 x^{6} - 10 x^{5} - 5 x^{4} - x^{3} + 3 x^{2} + 2 x - 1$ |
$12$ |
[6,3] |
$-\,7^{8}\cdot 888959$ |
$2$ |
$11.4587920376$ |
$3450.1625670601557$ |
|
|
? |
$S_4\wr C_3$ (as 12T292) |
trivial |
$2$ |
$8$ |
$45.9665196579$ |
12.6.5134519671875.1 |
$x^{12} - 3 x^{11} + 8 x^{9} - 4 x^{8} - 8 x^{7} - 3 x^{6} + 14 x^{5} + 5 x^{4} - 14 x^{3} + 3 x^{2} + 3 x - 1$ |
$12$ |
[6,3] |
$-\,5^{6}\cdot 11^{3}\cdot 246889$ |
$3$ |
$11.4606254269$ |
$3684.9552236085583$ |
|
|
? |
$S_3\wr D_4$ (as 12T274) |
trivial |
$2$ |
$8$ |
$46.0186796017$ |
12.6.5192327768191.1 |
$x^{12} - 5 x^{10} + 9 x^{8} - 2 x^{7} - 9 x^{6} + 6 x^{5} + 8 x^{4} - 4 x^{3} - 5 x^{2} + x + 1$ |
$12$ |
[6,3] |
$-\,5192327768191$ |
$1$ |
$11.4713229966$ |
$2278667.9811220854$ |
|
|
✓ |
$S_{12}$ (as 12T301) |
trivial |
$2$ |
$8$ |
$46.2686748261$ |
12.6.5528913603539.1 |
$x^{12} - 3 x^{11} + 2 x^{10} + 7 x^{9} - 13 x^{8} + 3 x^{7} + 13 x^{6} - 14 x^{5} + 7 x^{3} - 4 x^{2} - x + 1$ |
$12$ |
[6,3] |
$-\,197\cdot 2251\cdot 12468037$ |
$3$ |
$11.5315224888$ |
$2351364.200531045$ |
|
|
✓ |
$S_{12}$ (as 12T301) |
trivial |
$2$ |
$8$ |
$48.299736144$ |
12.6.5559960326067.1 |
$x^{12} - 5 x^{11} + 6 x^{10} + 9 x^{9} - 26 x^{8} + 15 x^{7} - x^{6} + 12 x^{5} - 6 x^{4} - 16 x^{3} + 5 x^{2} + 6 x + 1$ |
$12$ |
[6,3] |
$-\,3^{9}\cdot 7^{10}$ |
$2$ |
$11.5369047675$ |
$11.53690476748077$ |
|
|
? |
$D_4 \times C_3$ (as 12T14) |
trivial |
$2$ |
$8$ |
$48.1439095362$ |
12.6.6337710296875.1 |
$x^{12} - x^{11} - 4 x^{10} + 5 x^{9} + 5 x^{8} - 9 x^{7} - 5 x^{6} + 6 x^{5} + 6 x^{4} - 3 x^{3} - 4 x^{2} + x + 1$ |
$12$ |
[6,3] |
$-\,5^{6}\cdot 29^{3}\cdot 16631$ |
$3$ |
$11.6634679044$ |
$1552.898902053833$ |
|
|
✓ |
$S_3\wr D_4$ (as 12T274) |
trivial |
$2$ |
$8$ |
$53.3055263997$ |
12.6.6395326109375.1 |
$x^{12} - 4 x^{11} + 17 x^{9} - 14 x^{8} - 23 x^{7} + 32 x^{6} + 4 x^{5} - 21 x^{4} + 11 x^{3} - 5 x + 1$ |
$12$ |
[6,3] |
$-\,5^{6}\cdot 7^{8}\cdot 71$ |
$3$ |
$11.672267301$ |
$68.94660244848463$ |
|
|
? |
$C_2\wr C_6$ (as 12T134) |
trivial |
$2$ |
$8$ |
$52.4475924124$ |
12.6.6574568745051.1 |
$x^{12} - 3 x^{11} + 3 x^{10} - 3 x^{9} + 3 x^{8} + 3 x^{7} - 8 x^{6} + 6 x^{5} - 3 x^{4} - 3 x^{3} + 6 x^{2} - 1$ |
$12$ |
[6,3] |
$-\,3^{16}\cdot 163\cdot 937$ |
$3$ |
$11.699184928480138$ |
$1690.928603284853$ |
|
|
? |
$S_4\wr C_3$ (as 12T292) |
trivial |
$2$ |
$8$ |
$53.959540130132055$ |
12.6.6815156734375.1 |
$x^{12} - 2 x^{11} - 2 x^{10} + 11 x^{9} - 6 x^{8} - 21 x^{7} + 19 x^{6} + 12 x^{5} - 19 x^{4} + 2 x^{3} + 8 x^{2} - x - 1$ |
$12$ |
[6,3] |
$-\,5^{6}\cdot 11^{4}\cdot 31^{3}$ |
$3$ |
$11.7342765866$ |
$61.57829207131912$ |
|
|
? |
$\SOPlus(4,2)$ (as 12T35) |
trivial |
$2$ |
$8$ |
$54.8065567524$ |
12.6.6889511421875.1 |
$x^{12} - x^{11} - 5 x^{10} + 5 x^{9} + 6 x^{8} - 6 x^{7} + 2 x^{6} - 3 x^{5} - 3 x^{4} + 7 x^{3} - 3 x^{2} - 2 x + 1$ |
$12$ |
[6,3] |
$-\,5^{6}\cdot 29^{3}\cdot 101\cdot 179$ |
$4$ |
$11.7448922107$ |
$1619.09079424225$ |
|
|
? |
$S_3\wr D_4$ (as 12T274) |
trivial |
$2$ |
$8$ |
$55.3025292271$ |
12.6.7295734234375.1 |
$x^{12} - 4 x^{11} + 5 x^{10} - 2 x^{9} - 5 x^{8} + 14 x^{7} - 17 x^{6} + 14 x^{5} - 5 x^{4} - 2 x^{3} + 5 x^{2} - 4 x + 1$ |
$12$ |
[6,3] |
$-\,5^{6}\cdot 31\cdot 3881^{2}$ |
$3$ |
$11.8010980058$ |
$775.5997679215743$ |
|
|
? |
$S_4^2:D_4$ (as 12T260) |
trivial |
$2$ |
$8$ |
$56.9271303227$ |
12.6.7811642290603.1 |
$x^{12} - 3 x^{11} - x^{10} + 7 x^{9} + 4 x^{8} - 11 x^{7} - 3 x^{6} + 3 x^{5} - 3 x^{4} + 8 x^{3} + 3 x^{2} - 3 x - 1$ |
$12$ |
[6,3] |
$-\,491^{3}\cdot 65993$ |
$2$ |
$11.8684825518$ |
$5692.3249204521$ |
|
|
? |
$S_3\wr S_4$ (as 12T289) |
trivial |
$2$ |
$8$ |
$58.9525792483$ |
12.6.8099130339328.1 |
$x^{12} - 2 x^{11} - 4 x^{10} - 4 x^{9} - 2 x^{8} + 8 x^{7} + 7 x^{6} + 8 x^{5} - 2 x^{4} - 4 x^{3} - 4 x^{2} - 2 x + 1$ |
$12$ |
[6,3] |
$-\,2^{12}\cdot 7^{11}$ |
$2$ |
$11.9042818$ |
$11.90428180002048$ |
|
|
? |
$D_4 \times C_3$ (as 12T14) |
trivial |
$2$ |
$8$ |
$63.8207000652$ |
12.6.8121007759123.1 |
$x^{12} - 2 x^{11} - 2 x^{10} + 4 x^{9} - 2 x^{8} + 7 x^{7} - 14 x^{5} + 6 x^{4} + 3 x^{3} - 4 x^{2} + x + 1$ |
$12$ |
[6,3] |
$-\,7^{8}\cdot 43\cdot 181^{2}$ |
$3$ |
$11.906958148$ |
$322.8287530078796$ |
|
|
? |
$D_4\wr C_3$ (as 12T222) |
trivial |
$2$ |
$8$ |
$60.0607066436$ |
12.6.8192886833152.1 |
$x^{12} - 2 x^{10} - 2 x^{9} - 2 x^{8} + 4 x^{7} + 3 x^{6} + 4 x^{5} - 2 x^{4} - 2 x^{3} - 2 x^{2} + 1$ |
$12$ |
[6,3] |
$-\,2^{18}\cdot 7\cdot 2113^{2}$ |
$3$ |
$11.915705098690154$ |
$343.98837189649305$ |
|
|
✓ |
$S_4^2:D_4$ (as 12T260) |
trivial |
$2$ |
$8$ |
$64.12166932416741$ |
12.6.9120427796875.1 |
$x^{12} - x^{11} - x^{10} - x^{9} + 2 x^{8} - 2 x^{7} - 3 x^{6} + 19 x^{5} - 21 x^{4} + 6 x^{3} + 6 x^{2} - 5 x + 1$ |
$12$ |
[6,3] |
$-\,5^{6}\cdot 19\cdot 79\cdot 388879$ |
$4$ |
$12.0226794336$ |
$54023.48466176539$ |
|
|
? |
$S_6\wr C_2$ (as 12T299) |
trivial |
$2$ |
$8$ |
$66.162967534$ |
12.6.9842374000287.1 |
$x^{12} - 4 x^{11} + 3 x^{10} + 15 x^{9} - 40 x^{8} + 30 x^{7} + 18 x^{6} - 39 x^{5} + 12 x^{4} + 9 x^{3} - 7 x^{2} + 1$ |
$12$ |
[6,3] |
$-\,3^{6}\cdot 103\cdot 107^{4}$ |
$3$ |
$12.0992464222$ |
$239.30481785925204$ |
|
|
? |
$C_2\wr (C_2\times S_4)$ (as 12T250) |
trivial |
$2$ |
$8$ |
$70.0148733812$ |
12.6.9904396000000.1 |
$x^{12} - 3 x^{11} - x^{10} + 7 x^{9} - x^{8} - 2 x^{7} + 7 x^{6} - 16 x^{5} - 9 x^{4} + 19 x^{3} + 4 x^{2} - 4 x - 1$ |
$12$ |
[6,3] |
$-\,2^{8}\cdot 5^{6}\cdot 19^{5}$ |
$3$ |
$12.1055817906$ |
$41.28570135662403$ |
|
|
? |
$C_6\wr C_2$ (as 12T42) |
trivial |
$2$ |
$8$ |
$67.9024659123$ |
12.6.10218945315584.1 |
$x^{12} - 3 x^{11} - x^{10} + 9 x^{9} - x^{8} - 16 x^{7} + 3 x^{6} + 24 x^{5} - 9 x^{4} - 19 x^{3} + 8 x^{2} + 6 x - 1$ |
$12$ |
[6,3] |
$-\,2^{8}\cdot 19^{2}\cdot 37^{4}\cdot 59$ |
$4$ |
$12.1371626771$ |
$323.28855651411374$ |
|
|
? |
$C_2\wr (C_2\times S_4)$ (as 12T250) |
trivial |
$2$ |
$8$ |
$70.3410949906$ |
12.6.10513415548928.1 |
$x^{12} - 2 x^{11} - x^{10} + 4 x^{9} - 11 x^{8} + 20 x^{7} - 12 x^{6} + 8 x^{4} - 4 x^{3} - x^{2} - 2 x + 1$ |
$12$ |
[6,3] |
$-\,2^{12}\cdot 67^{2}\cdot 83^{3}$ |
$3$ |
$12.1659301654$ |
$300.5745763472249$ |
|
|
? |
$C_3\wr S_4$ (as 12T231) |
trivial |
$2$ |
$8$ |
$69.1711510134$ |
12.6.10578455953408.1 |
$x^{12} - 2 x^{11} - x^{10} - 2 x^{9} + 3 x^{8} + 14 x^{7} - 20 x^{6} + 34 x^{4} + 12 x^{3} - x^{2} + 2 x + 1$ |
$12$ |
[6,3] |
$-\,2^{18}\cdot 7^{9}$ |
$2$ |
$12.1721844145$ |
$14.315066180821045$ |
|
|
? |
$D_4 \times C_3$ (as 12T14) |
trivial |
$2$ |
$8$ |
$74.2304379605$ |
12.6.10721964631207.1 |
$x^{12} - 2 x^{11} - x^{10} + 8 x^{9} - 7 x^{8} - 3 x^{7} + 7 x^{6} - 9 x^{5} + 7 x^{4} - 6 x^{2} + 5 x - 1$ |
$12$ |
[6,3] |
$-\,61^{2}\cdot 1423^{3}$ |
$2$ |
$12.1858603703$ |
$584.5509088050569$ |
|
|
? |
$C_3\wr S_4$ (as 12T231) |
trivial |
$2$ |
$8$ |
$73.9804186368$ |
12.6.10888658888551.1 |
$x^{12} - 2 x^{11} - 2 x^{10} + 15 x^{9} - 21 x^{8} + x^{7} + 36 x^{6} - 50 x^{5} + 29 x^{4} - 11 x^{2} + 6 x - 1$ |
$12$ |
[6,3] |
$-\,31\cdot 592661^{2}$ |
$2$ |
$12.2015367617$ |
$4286.3143841766905$ |
|
|
? |
$C_2^6.S_6$ (as 12T293) |
trivial |
$2$ |
$8$ |
$70.8841951241$ |
12.6.10890820856071.1 |
$x^{12} - 4 x^{11} + 2 x^{10} + 13 x^{9} - 27 x^{8} + 15 x^{7} + 22 x^{6} - 42 x^{5} + 27 x^{4} - 11 x^{2} + 6 x - 1$ |
$12$ |
[6,3] |
$-\,13^{10}\cdot 79$ |
$2$ |
$12.2017386302$ |
$75.35284821191699$ |
|
|
? |
$C_2\wr C_6$ (as 12T134) |
trivial |
$2$ |
$8$ |
$71.0426080758$ |
12.6.11808520366783.1 |
$x^{12} - 6 x^{11} + 15 x^{10} - 20 x^{9} + 11 x^{8} + 10 x^{7} - 30 x^{6} + 37 x^{5} - 15 x^{4} - 13 x^{3} + 17 x^{2} - 7 x + 1$ |
$12$ |
[6,3] |
$-\,7^{8}\cdot 127^{3}$ |
$2$ |
$12.2842776429$ |
$41.23828102000196$ |
|
|
? |
$C_2^3.(C_2\times A_4)$ (as 12T104) |
trivial |
$2$ |
$8$ |
$77.2262907733$ |
12.6.11808520366783.2 |
$x^{12} - x^{11} - 5 x^{10} + 6 x^{9} + 16 x^{8} - 6 x^{7} - 26 x^{6} - 3 x^{5} + 18 x^{4} + 6 x^{3} - 6 x^{2} - 2 x + 1$ |
$12$ |
[6,3] |
$-\,7^{8}\cdot 127^{3}$ |
$2$ |
$12.2842776429$ |
$41.23828102000196$ |
|
|
✓ |
$C_2^3.(C_2\times A_4)$ (as 12T104) |
trivial |
$2$ |
$8$ |
$77.2262907733$ |
12.6.12110614233088.1 |
$x^{12} - 4 x^{11} + 4 x^{10} + 4 x^{9} - 15 x^{8} + 14 x^{7} + 12 x^{6} - 22 x^{5} - 7 x^{4} + 10 x^{3} + 5 x^{2} - 2 x - 1$ |
$12$ |
[6,3] |
$-\,2^{18}\cdot 7^{3}\cdot 367^{2}$ |
$3$ |
$12.3101642483$ |
$143.3596874996594$ |
|
|
? |
$D_6\wr C_2$ (as 12T125) |
trivial |
$2$ |
$8$ |
$76.0465779983$ |
12.6.12520427171875.1 |
$x^{12} - x^{11} - 3 x^{10} + x^{9} + 2 x^{8} + 10 x^{7} - 7 x^{6} - 12 x^{5} + 11 x^{4} - x^{3} - 5 x^{2} + 2 x + 1$ |
$12$ |
[6,3] |
$-\,5^{6}\cdot 7^{8}\cdot 139$ |
$3$ |
$12.3443510061$ |
$96.46973724535417$ |
|
|
? |
$C_2\wr C_6$ (as 12T134) |
trivial |
$2$ |
$8$ |
$76.6620065786$ |
12.6.12685282671875.1 |
$x^{12} - 3 x^{11} - x^{10} + 11 x^{9} - 6 x^{8} - 12 x^{7} - x^{6} + x^{5} + 12 x^{4} + 18 x^{3} + 14 x^{2} + 6 x + 1$ |
$12$ |
[6,3] |
$-\,5^{6}\cdot 11^{5}\cdot 71^{2}$ |
$3$ |
$12.3578147066$ |
$62.489999199871974$ |
|
|
? |
$D_6\wr C_2$ (as 12T125) |
trivial |
$2$ |
$8$ |
$79.9911716957$ |
12.6.12779495296875.1 |
$x^{12} - 3 x^{11} + 6 x^{10} - 10 x^{9} + 9 x^{8} - 6 x^{7} - 12 x^{6} + 18 x^{5} - 6 x^{4} + 10 x^{3} - 9 x^{2} + 1$ |
$12$ |
[6,3] |
$-\,3^{16}\cdot 5^{6}\cdot 19$ |
$3$ |
$12.365437173107072$ |
$42.17192986702622$ |
|
|
? |
$C_2\wr C_6$ (as 12T134) |
trivial |
$2$ |
$8$ |
$80.39469472298418$ |
12.6.12782924000000.1 |
$x^{12} - x^{11} - 2 x^{10} + 14 x^{9} - 15 x^{8} - 16 x^{7} + 37 x^{6} - 16 x^{5} - 15 x^{4} + 14 x^{3} - 2 x^{2} - x + 1$ |
$12$ |
[6,3] |
$-\,2^{8}\cdot 5^{6}\cdot 7^{4}\cdot 11^{3}$ |
$4$ |
$12.3657136068$ |
$39.242833740697165$ |
|
|
? |
$S_3^2:C_2^2$ (as 12T78) |
trivial |
$2$ |
$8$ |
$81.5937102666$ |
12.6.13409105834831.1 |
$x^{12} - 4 x^{11} + 5 x^{10} - 10 x^{8} + 18 x^{7} - 11 x^{6} - 16 x^{5} + 22 x^{4} - 8 x^{2} + x + 1$ |
$12$ |
[6,3] |
$-\,7^{8}\cdot 71\cdot 181^{2}$ |
$3$ |
$12.415093221$ |
$414.8271331635092$ |
|
|
? |
$D_4\wr C_3$ (as 12T222) |
trivial |
$2$ |
$8$ |
$82.8552918261$ |
12.6.13907109998592.1 |
$x^{12} - 3 x^{10} - 4 x^{9} + 14 x^{7} + 2 x^{6} - 18 x^{5} + 5 x^{4} + 10 x^{3} - 5 x^{2} - 2 x + 1$ |
$12$ |
[6,3] |
$-\,2^{12}\cdot 3^{6}\cdot 167^{3}$ |
$3$ |
$12.4528782135$ |
$160.92665210764017$ |
|
|
? |
$S_4^2:C_2^2$ (as 12T235) |
trivial |
$2$ |
$8$ |
$86.4729185957$ |
12.6.14501103264256.1 |
$x^{12} - x^{11} - 7 x^{10} + 6 x^{9} + 13 x^{8} - 16 x^{7} - x^{6} + 19 x^{5} - 17 x^{4} - 5 x^{3} + 13 x^{2} - 3 x - 1$ |
$12$ |
[6,3] |
$-\,2^{9}\cdot 7^{8}\cdot 17^{3}$ |
$3$ |
$12.4963569039$ |
$42.67447112735335$ |
|
|
? |
$C_3\times S_4$ (as 12T45) |
trivial |
$2$ |
$8$ |
$93.643207835$ |
12.6.14941367239327.1 |
$x^{12} - x^{11} - 6 x^{10} + 4 x^{9} + 16 x^{8} - 6 x^{7} - 25 x^{6} + x^{5} + 26 x^{4} + 9 x^{3} - 14 x^{2} - 7 x + 1$ |
$12$ |
[6,3] |
$-\,283^{3}\cdot 659221$ |
$2$ |
$12.5275418342$ |
$13658.68013389288$ |
|
|
? |
$S_3\wr S_4$ (as 12T289) |
trivial |
$2$ |
$8$ |
$86.8510076113$ |