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 |
12.2.167630295667.1 |
$x^{12} - 3 x^{11} + 4 x^{10} - x^{9} - 6 x^{8} + 15 x^{7} - 19 x^{6} + 15 x^{5} - 6 x^{4} - x^{3} + 4 x^{2} - 3 x + 1$ |
$12$ |
[2,5] |
$-\,29^{2}\cdot 43\cdot 2153^{2}$ |
$3$ |
$8.61713127762$ |
$1638.5331855046452$ |
|
|
✓ |
$C_2^6.S_6$ (as 12T293) |
trivial |
$2$ |
$6$ |
$3.5044254879$ |
12.2.168661105243.1 |
$x^{12} - 5 x^{11} + 12 x^{10} - 16 x^{9} + 12 x^{8} - 4 x^{7} + x^{6} - 3 x^{5} + 4 x^{4} - 3 x^{3} + x^{2} - 1$ |
$12$ |
[2,5] |
$-\,67\cdot 131^{2}\cdot 383^{2}$ |
$3$ |
$8.62153466041$ |
$1833.46420744993$ |
|
|
✓ |
$C_2^6.S_6$ (as 12T293) |
trivial |
$2$ |
$6$ |
$3.51670744388$ |
12.2.173809422763.1 |
$x^{12} - 2 x^{11} + 3 x^{10} - 2 x^{9} - 2 x^{8} + 4 x^{7} - 2 x^{5} + 4 x^{3} - 3 x^{2} - x + 1$ |
$12$ |
[2,5] |
$-\,31^{4}\cdot 53^{2}\cdot 67$ |
$3$ |
$8.64316445422$ |
$331.7845686586403$ |
|
|
? |
$C_2\wr (C_2\times S_4)$ (as 12T250) |
trivial |
$2$ |
$6$ |
$3.58278358615$ |
12.2.175113024319.1 |
$x^{12} - 4 x^{11} + 8 x^{10} - 9 x^{9} + 4 x^{8} + 5 x^{7} - 16 x^{6} + 23 x^{5} - 24 x^{4} + 19 x^{3} - 12 x^{2} + 5 x - 1$ |
$12$ |
[2,5] |
$-\,23^{4}\cdot 79\cdot 89^{2}$ |
$3$ |
$8.64854807832$ |
$402.1355492865559$ |
|
|
? |
$C_2\wr (C_2\times S_4)$ (as 12T250) |
trivial |
$2$ |
$6$ |
$3.59783369219$ |
12.2.175122415616.1 |
$x^{12} - 4 x^{11} + 10 x^{10} - 16 x^{9} + 17 x^{8} - 6 x^{7} - 12 x^{6} + 30 x^{5} - 37 x^{4} + 30 x^{3} - 17 x^{2} + 6 x - 1$ |
$12$ |
[2,5] |
$-\,2^{18}\cdot 71\cdot 97^{2}$ |
$3$ |
$8.64858672911$ |
$234.72537144501445$ |
|
|
? |
$S_4^2:D_4$ (as 12T260) |
trivial |
$2$ |
$6$ |
$3.6007962841$ |
12.2.177788874752.1 |
$x^{12} - 4 x^{9} + 3 x^{8} - 4 x^{7} + 11 x^{6} - 8 x^{5} + 8 x^{4} - 14 x^{3} + 13 x^{2} - 6 x + 1$ |
$12$ |
[2,5] |
$-\,2^{12}\cdot 31^{4}\cdot 47$ |
$3$ |
$8.65948468434$ |
$107.96295661012624$ |
|
|
? |
$C_2\wr S_4$ (as 12T227) |
trivial |
$2$ |
$6$ |
$3.63511170932$ |
12.2.204800642687.1 |
$x^{12} - 3 x^{11} + 5 x^{10} - 3 x^{9} - 4 x^{8} + 12 x^{7} - 15 x^{6} + 12 x^{5} - 4 x^{4} - 3 x^{3} + 5 x^{2} - 3 x + 1$ |
$12$ |
[2,5] |
$-\,23\cdot 197^{2}\cdot 479^{2}$ |
$3$ |
$8.76215523154$ |
$1473.2104398218198$ |
|
|
✓ |
$C_2^6.S_6$ (as 12T293) |
trivial |
$2$ |
$6$ |
$3.96195936431$ |
12.2.205567038859.1 |
$x^{12} - x^{11} + 2 x^{10} + x^{8} + 4 x^{7} - 5 x^{6} + 4 x^{5} - 8 x^{4} + 4 x^{3} - 4 x^{2} + 2 x - 1$ |
$12$ |
[2,5] |
$-\,7^{8}\cdot 13^{2}\cdot 211$ |
$3$ |
$8.7648830029$ |
$191.65122394707694$ |
|
|
? |
$D_4\wr C_3$ (as 12T222) |
trivial |
$2$ |
$6$ |
$3.97256263188$ |
12.2.206487484375.1 |
$x^{12} - x^{11} + 2 x^{10} + x^{9} - 3 x^{8} + 8 x^{7} - 13 x^{6} + 16 x^{5} - 17 x^{4} + 13 x^{3} - 8 x^{2} + 3 x - 1$ |
$12$ |
[2,5] |
$-\,5^{6}\cdot 79\cdot 409^{2}$ |
$3$ |
$8.76814677513$ |
$401.9390501058587$ |
|
|
? |
$S_4^2:D_4$ (as 12T260) |
trivial |
$2$ |
$6$ |
$3.98211224603$ |
12.2.208976546875.1 |
$x^{12} - 2 x^{11} + 4 x^{10} - 5 x^{9} + 4 x^{8} + x^{7} - 9 x^{6} + 18 x^{5} - 22 x^{4} + 19 x^{3} - 12 x^{2} + 5 x - 1$ |
$12$ |
[2,5] |
$-\,5^{6}\cdot 19\cdot 839^{2}$ |
$3$ |
$8.7769063085$ |
$282.32073958531635$ |
|
|
✓ |
$S_4^2:D_4$ (as 12T260) |
trivial |
$2$ |
$6$ |
$4.01927343849$ |
12.2.225117671875.1 |
$x^{12} - x^{10} - x^{9} - x^{8} + 3 x^{7} + 3 x^{6} - 2 x^{4} - 2 x^{3} - 1$ |
$12$ |
[2,5] |
$-\,5^{6}\cdot 179\cdot 80489$ |
$3$ |
$8.83149306815$ |
$8487.499926362298$ |
|
|
? |
$S_6\wr C_2$ (as 12T299) |
trivial |
$2$ |
$6$ |
$4.20942666663$ |
12.2.233544944483.1 |
$x^{12} - 3 x^{11} + 2 x^{10} + 5 x^{9} - 9 x^{8} + 3 x^{7} + 6 x^{6} - 7 x^{5} + 3 x^{4} + x^{3} - x^{2} + x - 1$ |
$12$ |
[2,5] |
$-\,23^{4}\cdot 101\cdot 8263$ |
$3$ |
$8.8585819242$ |
$4381.204058247002$ |
|
|
✓ |
$A_4^3.(C_2\times S_4)$ (as 12T294) |
trivial |
$2$ |
$6$ |
$4.29199444222$ |
12.2.238362687139.1 |
$x^{12} - 2 x^{11} + 4 x^{10} - 4 x^{9} + x^{8} + 3 x^{7} - 8 x^{6} + 7 x^{5} - 3 x^{4} - 2 x^{3} + 4 x^{2} - 3 x + 1$ |
$12$ |
[2,5] |
$-\,23^{4}\cdot 317\cdot 2687$ |
$3$ |
$8.87366827443$ |
$4426.162785076934$ |
|
|
✓ |
$A_4^3.(C_2\times S_4)$ (as 12T294) |
trivial |
$2$ |
$6$ |
$4.36197960563$ |
12.2.239557046875.1 |
$x^{12} - x^{10} - x^{9} + 2 x^{7} - 2 x^{6} + x^{4} + x^{3} - x + 1$ |
$12$ |
[2,5] |
$-\,5^{6}\cdot 19\cdot 806929$ |
$3$ |
$8.87736505338$ |
$8755.470004517176$ |
|
|
? |
$S_6\wr C_2$ (as 12T299) |
trivial |
$2$ |
$6$ |
$4.3666138828$ |
12.2.247087671875.1 |
$x^{12} - x^{11} - 3 x^{9} + x^{7} + 3 x^{6} + x^{5} - 3 x^{3} - x + 1$ |
$12$ |
[2,5] |
$-\,5^{6}\cdot 11^{3}\cdot 109^{2}$ |
$3$ |
$8.9002920261$ |
$77.42738533619743$ |
|
|
✓ |
$D_6\wr C_2$ (as 12T125) |
trivial |
$2$ |
$6$ |
$4.50528335209$ |
12.2.255609008128.1 |
$x^{12} - 2 x^{11} + 3 x^{10} - 4 x^{9} + 7 x^{8} - 8 x^{7} - 2 x^{6} + 18 x^{5} - 28 x^{4} + 22 x^{3} - 11 x^{2} + 4 x - 1$ |
$12$ |
[2,5] |
$-\,2^{12}\cdot 23^{4}\cdot 223$ |
$3$ |
$8.92547517214$ |
$202.56357026869367$ |
|
|
? |
$C_2\wr S_4$ (as 12T227) |
trivial |
$2$ |
$6$ |
$4.5370381911$ |
12.2.257978421875.1 |
$x^{12} - 2 x^{11} + 2 x^{9} - 5 x^{7} + 10 x^{6} - 16 x^{5} + 20 x^{4} - 19 x^{3} + 12 x^{2} - 5 x + 1$ |
$12$ |
[2,5] |
$-\,5^{6}\cdot 23^{4}\cdot 59$ |
$3$ |
$8.93234074331$ |
$82.37111144084436$ |
|
|
? |
$C_2\wr D_6$ (as 12T193) |
trivial |
$2$ |
$6$ |
$4.57996864178$ |
12.2.266846228071.1 |
$x^{12} - x^{11} + 2 x^{10} - 3 x^{9} + 3 x^{8} - 4 x^{7} + 3 x^{6} - 4 x^{5} + 3 x^{4} - 3 x^{3} + 2 x^{2} - x + 1$ |
$12$ |
[2,5] |
$-\,31\cdot 92779^{2}$ |
$2$ |
$8.95753311463$ |
$1695.9212835506253$ |
|
|
✓ |
$C_2^6.S_6$ (as 12T293) |
trivial |
$2$ |
$6$ |
$4.68688998752$ |
12.2.273636802651.1 |
$x^{12} - x^{11} + 5 x^{10} - 4 x^{9} + 12 x^{8} - 6 x^{7} + 15 x^{6} - 6 x^{5} + 9 x^{4} - 5 x^{3} + x^{2} - 3 x - 1$ |
$12$ |
[2,5] |
$-\,283^{3}\cdot 12073$ |
$2$ |
$8.97631068037$ |
$1848.420677226913$ |
|
|
? |
$S_3\wr S_4$ (as 12T289) |
trivial |
$2$ |
$6$ |
$4.7852559363$ |
12.2.279198105664.1 |
$x^{12} - 5 x^{10} + 9 x^{8} - 7 x^{6} + x^{4} + 3 x^{2} - 1$ |
$12$ |
[2,5] |
$-\,2^{6}\cdot 257^{4}$ |
$2$ |
$8.99137350807$ |
$53.92238017965345$ |
|
|
? |
$C_2\wr S_4$ (as 12T227) |
trivial |
$2$ |
$6$ |
$4.94368204571$ |
12.2.288323843827.1 |
$x^{12} - 3 x^{11} + 8 x^{9} - 6 x^{8} - 7 x^{7} + 10 x^{6} + x^{5} - 7 x^{4} + x^{3} + 4 x^{2} - 1$ |
$12$ |
[2,5] |
$-\,283^{3}\cdot 12721$ |
$2$ |
$9.01550475138$ |
$1897.3779275621396$ |
|
|
? |
$S_3\wr S_4$ (as 12T289) |
trivial |
$2$ |
$6$ |
$4.93877212902$ |
12.2.293890894259.1 |
$x^{12} - x^{9} - x^{4} + x + 1$ |
$12$ |
[2,5] |
$-\,103\cdot 2853309653$ |
$2$ |
$9.02988412951$ |
$542117.0484858413$ |
|
|
✓ |
$S_{12}$ (as 12T301) |
trivial |
$2$ |
$6$ |
$4.93923668618$ |
12.2.299095170283.1 |
$x^{12} - 2 x^{11} + 4 x^{10} - x^{9} - 2 x^{8} + 6 x^{7} - 4 x^{6} - 2 x^{5} + 2 x^{4} - 2 x^{3} - 2 x^{2} + 1$ |
$12$ |
[2,5] |
$-\,7^{8}\cdot 13^{2}\cdot 307$ |
$3$ |
$9.04310242902$ |
$231.1743031850907$ |
|
|
? |
$D_4\wr C_3$ (as 12T222) |
trivial |
$2$ |
$6$ |
$4.96264024524$ |
12.2.307980921875.1 |
$x^{12} - 2 x^{11} + 3 x^{10} - 7 x^{9} + 12 x^{8} - 12 x^{7} + 13 x^{6} - 12 x^{5} + 5 x^{4} + 2 x^{3} - 3 x^{2} + 2 x - 1$ |
$12$ |
[2,5] |
$-\,5^{6}\cdot 11^{3}\cdot 59\cdot 251$ |
$4$ |
$9.06519153456$ |
$902.4937672914976$ |
|
|
? |
$S_3\wr D_4$ (as 12T274) |
trivial |
$2$ |
$6$ |
$5.1470744096$ |
12.2.314972378176.1 |
$x^{12} - x^{10} - 3 x^{8} + x^{6} + 3 x^{4} - x^{2} - 1$ |
$12$ |
[2,5] |
$-\,2^{6}\cdot 31^{4}\cdot 73^{2}$ |
$3$ |
$9.08216468198$ |
$95.14199913813037$ |
|
|
? |
$C_2\wr D_6$ (as 12T186) |
trivial |
$2$ |
$6$ |
$5.32083463663$ |
12.2.327779546875.1 |
$x^{12} - 2 x^{11} + 2 x^{10} - 3 x^{9} + x^{8} + x^{7} + x^{4} - x^{3} + x^{2} + x - 1$ |
$12$ |
[2,5] |
$-\,5^{6}\cdot 11^{3}\cdot 15761$ |
$3$ |
$9.11237997258$ |
$931.0504819825829$ |
|
|
? |
$S_3\wr D_4$ (as 12T274) |
trivial |
$2$ |
$6$ |
$5.41339781061$ |
12.2.336393921875.1 |
$x^{12} - x^{11} - x^{10} - x^{9} + 3 x^{8} - x^{7} - x^{6} - x^{5} + 3 x^{4} - x^{3} - x^{2} - x + 1$ |
$12$ |
[2,5] |
$-\,5^{6}\cdot 11\cdot 1399^{2}$ |
$3$ |
$9.13210041657$ |
$277.3896176860266$ |
|
|
✓ |
$S_4^2:D_4$ (as 12T260) |
trivial |
$2$ |
$6$ |
$5.43541349035$ |
12.2.341962230519.1 |
$x^{12} - 4 x^{11} + 10 x^{10} - 20 x^{9} + 31 x^{8} - 43 x^{7} + 52 x^{6} - 56 x^{5} + 52 x^{4} - 39 x^{3} + 21 x^{2} - 7 x + 1$ |
$12$ |
[2,5] |
$-\,3^{3}\cdot 7^{8}\cdot 13^{3}$ |
$3$ |
$9.14460277171$ |
$43.39271609609281$ |
|
|
? |
$C_4^3:C_6$ (as 12T141) |
trivial |
$2$ |
$6$ |
$5.44076103214$ |
12.2.349257427087.1 |
$x^{12} - 4 x^{11} + 8 x^{10} - 10 x^{9} + 9 x^{8} - 12 x^{7} + 18 x^{6} - 18 x^{5} + 14 x^{4} - 9 x^{3} + 5 x^{2} - 2 x - 1$ |
$12$ |
[2,5] |
$-\,127\cdot 229^{4}$ |
$2$ |
$9.16070302373$ |
$170.53738593047566$ |
|
|
? |
$C_2\wr S_4$ (as 12T227) |
trivial |
$2$ |
$6$ |
$5.49728358002$ |
12.2.353996898304.1 |
$x^{12} - 2 x^{11} + x^{10} + 4 x^{7} - 4 x^{6} + 2 x^{5} - 2 x^{4} + 4 x^{2} - 4 x + 1$ |
$12$ |
[2,5] |
$-\,2^{18}\cdot 7^{3}\cdot 31\cdot 127$ |
$4$ |
$9.170998478582437$ |
$469.54446008871196$ |
|
|
? |
$S_3\wr D_4$ (as 12T274) |
trivial |
$2$ |
$6$ |
$5.5369431385384855$ |
12.2.362031460339.1 |
$x^{12} - x^{7} + x^{6} + 2 x^{5} - 2 x^{4} + x^{3} - x^{2} - x + 1$ |
$12$ |
[2,5] |
$-\,362031460339$ |
$1$ |
$9.18816656011$ |
$601690.5021179909$ |
|
|
? |
$S_{12}$ (as 12T301) |
trivial |
$2$ |
$6$ |
$5.64279808125$ |
12.2.373065296875.1 |
$x^{12} - 2 x^{11} - 2 x^{10} + 8 x^{9} - 12 x^{7} + 3 x^{6} + 11 x^{5} - 5 x^{4} - 6 x^{3} + 3 x^{2} + x - 1$ |
$12$ |
[2,5] |
$-\,5^{6}\cdot 19^{3}\cdot 59^{2}$ |
$3$ |
$9.21118286768$ |
$74.86654793697917$ |
|
|
? |
$D_6\wr C_2$ (as 12T125) |
trivial |
$2$ |
$6$ |
$5.72023263089$ |
12.2.396228830787.1 |
$x^{12} - 2 x^{11} - x^{10} + 4 x^{9} - 3 x^{7} - x^{6} + 3 x^{4} + x^{3} - 3 x^{2} - x + 1$ |
$12$ |
[2,5] |
$-\,3^{3}\cdot 23^{4}\cdot 229^{2}$ |
$3$ |
$9.25753805701$ |
$125.70202862324857$ |
|
|
✓ |
$C_2\wr D_6$ (as 12T186) |
trivial |
$2$ |
$6$ |
$6.09548763154$ |
12.2.398786546875.1 |
$x^{12} - 3 x^{11} + 4 x^{10} - 3 x^{9} + 4 x^{8} - 7 x^{7} + 7 x^{6} - x^{5} - 4 x^{4} + 4 x^{3} - x^{2} + x - 1$ |
$12$ |
[2,5] |
$-\,5^{6}\cdot 19^{3}\cdot 61^{2}$ |
$3$ |
$9.26250328277$ |
$76.12489737267302$ |
|
|
? |
$D_6\wr C_2$ (as 12T125) |
trivial |
$2$ |
$6$ |
$5.94217649784$ |
12.2.417344000000.1 |
$x^{12} - 2 x^{11} + 2 x^{10} - 2 x^{9} + x^{8} - 4 x^{7} + 4 x^{6} + 5 x^{4} - 6 x^{3} + x^{2} + 1$ |
$12$ |
[2,5] |
$-\,2^{12}\cdot 5^{6}\cdot 6521$ |
$3$ |
$9.297678278879234$ |
$510.7249749131131$ |
|
|
? |
$S_3\wr D_4$ (as 12T274) |
trivial |
$2$ |
$6$ |
$6.215565115061368$ |
12.2.419159399791.1 |
$x^{12} - 2 x^{11} + 3 x^{9} - 2 x^{8} - x^{7} + x^{6} - x^{5} + x^{4} + 2 x^{3} - 2 x^{2} + 1$ |
$12$ |
[2,5] |
$-\,11^{4}\cdot 31^{5}$ |
$2$ |
$9.30104189993$ |
$18.466185312619388$ |
|
|
? |
$C_2 \times S_4$ (as 12T22) |
trivial |
$2$ |
$6$ |
$6.24841548478$ |
12.2.438976000000.1 |
$x^{12} - x^{11} + 2 x^{10} - 3 x^{8} + 6 x^{7} - 9 x^{6} + 6 x^{5} - 3 x^{4} + 2 x^{2} - x + 1$ |
$12$ |
[2,5] |
$-\,2^{12}\cdot 5^{6}\cdot 19^{3}$ |
$3$ |
$9.33691484757$ |
$38.98717737923585$ |
|
|
? |
$D_6\wr C_2$ (as 12T125) |
trivial |
$2$ |
$6$ |
$6.34204903952$ |
12.2.447330484375.1 |
$x^{12} - 2 x^{11} + x^{10} - 3 x^{9} + 8 x^{8} - 3 x^{7} - 2 x^{6} - 4 x^{5} + 2 x^{4} + 9 x^{3} - 9 x^{2} + 4 x - 1$ |
$12$ |
[2,5] |
$-\,5^{6}\cdot 31^{5}$ |
$2$ |
$9.35159538434$ |
$12.449899597988733$ |
|
|
? |
$(C_6\times C_2):C_2$ (as 12T13) |
trivial |
$2$ |
$6$ |
$6.55949888698$ |
12.2.451992187175.1 |
$x^{12} - x^{11} + 4 x^{10} + x^{9} - x^{8} + 12 x^{7} - 9 x^{6} + 12 x^{5} - x^{4} + x^{3} + 4 x^{2} - x + 1$ |
$12$ |
[2,5] |
$-\,5^{2}\cdot 23^{5}\cdot 53^{2}$ |
$3$ |
$9.35967805722$ |
$170.96956786104076$ |
|
|
? |
$C_2\wr S_4$ (as 12T223) |
trivial |
$2$ |
$6$ |
$6.4136566416$ |
12.2.458342033107.1 |
$x^{12} - 3 x^{11} + 2 x^{10} + 3 x^{9} - 6 x^{8} + 3 x^{7} + 4 x^{6} - 10 x^{5} + 8 x^{4} - x^{3} - 2 x^{2} + x - 1$ |
$12$ |
[2,5] |
$-\,7^{8}\cdot 43^{3}$ |
$2$ |
$9.37056564065$ |
$23.99567223510292$ |
|
|
? |
$C_2^3.(C_2\times A_4)$ (as 12T104) |
trivial |
$2$ |
$6$ |
$6.54549766683$ |
12.2.458342033107.2 |
$x^{12} - 4 x^{11} + 6 x^{10} - 4 x^{9} + x^{8} - 3 x^{7} + 5 x^{6} - 3 x^{5} + x^{4} - 4 x^{3} + 6 x^{2} - 4 x + 1$ |
$12$ |
[2,5] |
$-\,7^{8}\cdot 43^{3}$ |
$2$ |
$9.37056564065$ |
$23.99567223510292$ |
|
|
✓ |
$C_2^3.(C_2\times A_4)$ (as 12T104) |
trivial |
$2$ |
$6$ |
$6.54549766683$ |
12.2.530569362483.1 |
$x^{12} - x^{11} + x^{10} - 3 x^{9} + 6 x^{8} - 7 x^{7} + 4 x^{6} - 6 x^{5} + 10 x^{4} - 11 x^{3} + 5 x^{2} + x - 1$ |
$12$ |
[2,5] |
$-\,3^{4}\cdot 17^{2}\cdot 283^{3}$ |
$3$ |
$9.48553536042$ |
$192.64295262991146$ |
|
|
? |
$C_3^3:(S_3\times S_4)$ (as 12T258) |
trivial |
$2$ |
$6$ |
$7.20273603042$ |
12.2.533806460928.1 |
$x^{12} - 5 x^{11} + 13 x^{10} - 23 x^{9} + 31 x^{8} - 32 x^{7} + 27 x^{6} - 17 x^{5} + 8 x^{4} - 2 x^{3} + x - 1$ |
$12$ |
[2,5] |
$-\,2^{12}\cdot 3^{3}\cdot 13^{6}$ |
$3$ |
$9.49034467201$ |
$17.663521732655695$ |
|
|
? |
$S_3\times D_4$ (as 12T28) |
trivial |
$2$ |
$6$ |
$7.11195238102$ |
12.2.562523516779.1 |
$x^{12} - 2 x^{11} - x^{10} + 7 x^{9} - 5 x^{8} - 6 x^{7} + 11 x^{6} - 3 x^{5} - 5 x^{4} + 6 x^{3} - 2 x^{2} - x + 1$ |
$12$ |
[2,5] |
$-\,7^{8}\cdot 97579$ |
$2$ |
$9.53187613796$ |
$1143.0806547161178$ |
|
|
✓ |
$S_4\wr C_3$ (as 12T292) |
trivial |
$2$ |
$6$ |
$7.7037339724$ |
12.2.566636000000.1 |
$x^{12} - 4 x^{10} - x^{9} + 7 x^{8} + 4 x^{7} - 5 x^{6} - 8 x^{5} + x^{4} + 7 x^{3} - x^{2} - 3 x + 1$ |
$12$ |
[2,5] |
$-\,2^{8}\cdot 5^{6}\cdot 7^{4}\cdot 59$ |
$4$ |
$9.53766388736$ |
$72.13510890035327$ |
|
|
? |
$C_2\wr D_6$ (as 12T193) |
trivial |
$2$ |
$6$ |
$7.30104222822$ |
12.2.620200350784.1 |
$x^{12} + 3 x^{10} + 5 x^{8} + 5 x^{6} + x^{4} - x^{2} - 1$ |
$12$ |
[2,5] |
$-\,2^{6}\cdot 7^{8}\cdot 41^{2}$ |
$3$ |
$9.609725905426268$ |
$78.8121389064205$ |
|
|
? |
$D_4\wr C_3$ (as 12T222) |
trivial |
$2$ |
$6$ |
$8.168059297232562$ |
12.2.644204000000.1 |
$x^{12} - 3 x^{11} + 3 x^{10} - x^{9} - 3 x^{8} + 4 x^{7} - x^{6} + 8 x^{5} - 7 x^{4} - 3 x^{3} - 2 x^{2} + 4 x - 1$ |
$12$ |
[2,5] |
$-\,2^{8}\cdot 5^{6}\cdot 11^{5}$ |
$3$ |
$9.64018314536$ |
$11.772481280020624$ |
|
|
? |
$(C_6\times C_2):C_2$ (as 12T13) |
trivial |
$2$ |
$6$ |
$8.09867909721$ |
12.2.644204000000.2 |
$x^{12} - 3 x^{11} + 2 x^{10} + 4 x^{9} - 7 x^{8} + 2 x^{7} + 3 x^{6} + 2 x^{5} - 7 x^{4} + 4 x^{3} + 2 x^{2} - 3 x + 1$ |
$12$ |
[2,5] |
$-\,2^{8}\cdot 5^{6}\cdot 11^{5}$ |
$3$ |
$9.64018314536$ |
$32.98695556602207$ |
|
|
? |
$D_6:D_6$ (as 12T81) |
trivial |
$2$ |
$6$ |
$8.15346214121$ |
12.2.659081523200.1 |
$x^{12} - 2 x^{11} + 5 x^{10} - 2 x^{9} + 6 x^{8} - 2 x^{7} + 11 x^{6} + 2 x^{5} - x^{4} + 2 x^{3} + 4 x - 1$ |
$12$ |
[2,5] |
$-\,2^{12}\cdot 5^{2}\cdot 23^{5}$ |
$3$ |
$9.65854249046$ |
$30.331501776206203$ |
|
|
? |
$C_2^3:S_4$ (as 12T100) |
trivial |
$2$ |
$6$ |
$7.95702343355$ |
12.2.713607421387.1 |
$x^{12} - 4 x^{10} - 2 x^{9} + 6 x^{8} + 10 x^{7} - x^{6} - 13 x^{5} - 9 x^{4} + 4 x^{3} + 9 x^{2} + 5 x + 1$ |
$12$ |
[2,5] |
$-\,7^{8}\cdot 123787$ |
$2$ |
$9.72273121475$ |
$1287.4673146347911$ |
|
|
✓ |
$S_4\wr C_3$ (as 12T292) |
trivial |
$2$ |
$6$ |
$8.88769174833$ |