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 |
12.0.41223887921.1 |
$x^{12} - 2 x^{11} + 2 x^{10} - x^{9} + 2 x^{8} - 5 x^{7} + 8 x^{6} - 7 x^{5} + 4 x^{4} - 3 x^{3} + 4 x^{2} - 3 x + 1$ |
$12$ |
[0,6] |
$37^{2}\cdot 41\cdot 857^{2}$ |
$3$ |
$7.66647538703$ |
$1140.2056831993077$ |
|
|
✓ |
$C_2^6.S_6$ (as 12T293) |
trivial |
$2$ |
$5$ |
$1.16313281573$ |
12.0.41479432225.1 |
$x^{12} - 4 x^{11} + 8 x^{10} - 11 x^{9} + 12 x^{8} - 9 x^{7} + 3 x^{6} + 2 x^{5} - 3 x^{4} + 2 x^{3} - x + 1$ |
$12$ |
[0,6] |
$5^{2}\cdot 7^{2}\cdot 11^{2}\cdot 23^{4}$ |
$4$ |
$7.67042451285$ |
$94.10100955887773$ |
|
|
✓ |
$C_2^2\wr S_3$ (as 12T139) |
trivial |
$2$ |
$5$ |
$1.16804069437$ |
12.0.42058512657.1 |
$x^{12} + 2 x^{10} - x^{9} + x^{8} - 5 x^{7} + 6 x^{6} - 10 x^{5} + 13 x^{4} - 10 x^{3} + 7 x^{2} - 4 x + 1$ |
$12$ |
[0,6] |
$3^{6}\cdot 7^{2}\cdot 73\cdot 127^{2}$ |
$4$ |
$7.67929160277$ |
$441.2380309991422$ |
|
|
✓ |
$S_4^2:D_4$ (as 12T260) |
trivial |
$6$ |
$5$ |
$3.53470566706$ |
12.0.42194001221.1 |
$x^{12} - 3 x^{11} + 7 x^{10} - 12 x^{9} + 17 x^{8} - 21 x^{7} + 24 x^{6} - 24 x^{5} + 22 x^{4} - 17 x^{3} + 10 x^{2} - 4 x + 1$ |
$12$ |
[0,6] |
$41\cdot 1029121981$ |
$2$ |
$7.68135009037$ |
$205411.7845231865$ |
|
|
✓ |
$S_{12}$ (as 12T301) |
trivial |
$2$ |
$5$ |
$1.18014639216$ |
12.0.42553255797.1 |
$x^{12} - x^{9} + 5 x^{8} - 2 x^{7} - x^{6} - 7 x^{5} + 8 x^{4} - 4 x^{3} + 5 x^{2} - 4 x + 1$ |
$12$ |
[0,6] |
$3^{6}\cdot 13^{3}\cdot 163^{2}$ |
$3$ |
$7.68677907982$ |
$186.34770126469456$ |
|
|
✓ |
$C_3\wr D_4$ (as 12T167) |
trivial |
$6$ |
$5$ |
$3.5586949501$ |
12.0.42925852301.1 |
$x^{12} - x^{11} - 2 x^{10} + 3 x^{9} + x^{8} - x^{7} - x^{6} - 2 x^{5} + 3 x^{4} + 2 x^{3} - 2 x^{2} - x + 1$ |
$12$ |
[0,6] |
$79\cdot 543365219$ |
$2$ |
$7.69236548534$ |
$207185.55041556348$ |
|
|
✓ |
$S_{12}$ (as 12T301) |
trivial |
$2$ |
$5$ |
$1.19267939797$ |
12.0.44223092609.1 |
$x^{12} - x^{11} + x^{9} - 2 x^{8} + x^{7} + 3 x^{4} - x^{3} - 2 x^{2} + 1$ |
$12$ |
[0,6] |
$89\cdot 22291^{2}$ |
$2$ |
$7.7114744831$ |
$1408.509495885633$ |
|
|
? |
$C_2^6.S_6$ (as 12T293) |
trivial |
$2$ |
$5$ |
$1.21605234252$ |
12.0.44533203125.1 |
$x^{12} - 2 x^{11} + 7 x^{10} - 7 x^{9} + 14 x^{8} - 6 x^{7} + 13 x^{6} - 2 x^{5} + 10 x^{4} - 2 x^{3} + 5 x^{2} - x + 1$ |
$12$ |
[0,6] |
$5^{9}\cdot 151^{2}$ |
$2$ |
$7.71596640012$ |
$94.81538251069664$ |
|
|
✓ |
$C_3\wr C_4$ (as 12T131) |
trivial |
$10$ |
$5$ |
$6.10223070288$ |
12.0.45425463296.1 |
$x^{12} - 2 x^{11} + 2 x^{9} - 2 x^{8} + 3 x^{6} - 2 x^{4} - 2 x^{3} + 2 x + 1$ |
$12$ |
[0,6] |
$2^{12}\cdot 89\cdot 353^{2}$ |
$3$ |
$7.7287325766$ |
$354.4968265020154$ |
|
|
✓ |
$S_4^2:D_4$ (as 12T260) |
trivial |
$4$ |
$5$ |
$2.47334952808$ |
12.0.45539379833.1 |
$x^{12} - x^{11} - x^{9} + 3 x^{8} - 2 x^{7} + x^{6} - 2 x^{5} + 3 x^{4} - x^{3} - x + 1$ |
$12$ |
[0,6] |
$17\cdot 73^{2}\cdot 709^{2}$ |
$3$ |
$7.730345879$ |
$938.0133261313508$ |
|
|
✓ |
$C_2^6.S_6$ (as 12T293) |
trivial |
$2$ |
$5$ |
$1.24111898861$ |
12.0.46060985097.1 |
$x^{12} - 5 x^{11} + 12 x^{10} - 19 x^{9} + 24 x^{8} - 27 x^{7} + 28 x^{6} - 24 x^{5} + 15 x^{4} - 5 x^{3} + x^{2} - x + 1$ |
$12$ |
[0,6] |
$3^{6}\cdot 337\cdot 433^{2}$ |
$3$ |
$7.73768600028$ |
$661.636607209728$ |
|
|
? |
$S_4^2:D_4$ (as 12T260) |
trivial |
$6$ |
$5$ |
$3.73838590524$ |
12.0.46110822453.1 |
$x^{12} - 2 x^{11} + x^{10} + x^{9} + x^{8} - 5 x^{7} + 6 x^{6} - 4 x^{5} + 4 x^{4} - 5 x^{3} + 5 x^{2} - 3 x + 1$ |
$12$ |
[0,6] |
$3^{6}\cdot 63252157$ |
$2$ |
$7.73838332708$ |
$13775.212194372905$ |
|
|
✓ |
$S_6\wr C_2$ (as 12T299) |
trivial |
$6$ |
$5$ |
$3.74818062756$ |
12.0.46574387721.1 |
$x^{12} - x^{11} - x^{10} + x^{9} + 2 x^{8} - 3 x^{6} + 2 x^{4} + x^{3} - x^{2} - x + 1$ |
$12$ |
[0,6] |
$3^{6}\cdot 7993^{2}$ |
$2$ |
$7.74483666021$ |
$154.85154180698365$ |
|
|
✓ |
$S_6\times C_2$ (as 12T219) |
trivial |
$6$ |
$5$ |
$3.77072282107$ |
12.0.46580196393.1 |
$x^{12} - 3 x^{10} - x^{9} + 5 x^{8} + x^{7} - 7 x^{6} - x^{5} + 8 x^{4} + 2 x^{3} - 4 x^{2} - x + 1$ |
$12$ |
[0,6] |
$3^{6}\cdot 157\cdot 406981$ |
$3$ |
$7.74491714909$ |
$13845.145394686182$ |
|
|
✓ |
$S_6\wr C_2$ (as 12T299) |
trivial |
$6$ |
$5$ |
$3.77092097525$ |
12.0.46716936381.1 |
$x^{12} - 4 x^{11} + 9 x^{10} - 15 x^{9} + 23 x^{8} - 33 x^{7} + 44 x^{6} - 50 x^{5} + 45 x^{4} - 29 x^{3} + 13 x^{2} - 4 x + 1$ |
$12$ |
[0,6] |
$3^{6}\cdot 23^{4}\cdot 229$ |
$3$ |
$7.74680925796$ |
$125.70202862324857$ |
|
|
? |
$C_2\wr D_6$ (as 12T193) |
trivial |
$6$ |
$5$ |
$3.77207610108$ |
12.0.46779109213.1 |
$x^{12} - 4 x^{11} + 8 x^{10} - 10 x^{9} + 8 x^{8} - 3 x^{7} - 2 x^{6} + 4 x^{5} - 2 x^{4} - x^{3} + 2 x^{2} - x + 1$ |
$12$ |
[0,6] |
$31^{4}\cdot 37^{3}$ |
$2$ |
$7.74766788221$ |
$83.52801100380672$ |
|
|
? |
$C_4\wr S_3$ (as 12T150) |
trivial |
$2$ |
$5$ |
$1.25722954293$ |
12.0.46911328256.1 |
$x^{12} - 2 x^{9} + 4 x^{8} - 4 x^{7} + x^{6} + 4 x^{4} - 8 x^{3} + 8 x^{2} - 4 x + 1$ |
$12$ |
[0,6] |
$2^{12}\cdot 13^{4}\cdot 401$ |
$3$ |
$7.74949039193$ |
$221.4272587292568$ |
|
|
? |
$A_4^2:D_4$ (as 12T208) |
trivial |
$4$ |
$5$ |
$2.52000020832$ |
12.0.47724987301.1 |
$x^{12} - 3 x^{11} + 7 x^{10} - 11 x^{9} + 16 x^{8} - 19 x^{7} + 20 x^{6} - 18 x^{5} + 15 x^{4} - 11 x^{3} + 6 x^{2} - 3 x + 1$ |
$12$ |
[0,6] |
$61\cdot 83^{2}\cdot 337^{2}$ |
$3$ |
$7.76060331827$ |
$1306.227774930544$ |
|
|
✓ |
$C_2^6.S_6$ (as 12T293) |
trivial |
$2$ |
$5$ |
$1.27712868376$ |
12.0.47738317081.1 |
$x^{12} - 3 x^{11} + x^{10} + 7 x^{9} - 8 x^{8} - 4 x^{7} + 13 x^{6} - 4 x^{5} - 8 x^{4} + 7 x^{3} + x^{2} - 3 x + 1$ |
$12$ |
[0,6] |
$7^{10}\cdot 13^{2}$ |
$2$ |
$7.76078392578$ |
$18.248200448594663$ |
|
|
✓ |
$C_2^2 \times A_4$ (as 12T25) |
trivial |
$14$ |
$5$ |
$8.9159604909$ |
12.0.48737056617.1 |
$x^{12} - 2 x^{11} + 5 x^{10} - 10 x^{9} + 16 x^{8} - 22 x^{7} + 30 x^{6} - 31 x^{5} + 28 x^{4} - 27 x^{3} + 19 x^{2} - 7 x + 1$ |
$12$ |
[0,6] |
$3^{9}\cdot 19^{5}$ |
$2$ |
$7.77418625735$ |
$26.51361476577414$ |
|
|
✓ |
$C_6\wr C_2$ (as 12T42) |
trivial |
$6$ |
$5$ |
$3.8758756969$ |
12.0.50551744653.1 |
$x^{12} - 4 x^{11} + 11 x^{10} - 21 x^{9} + 32 x^{8} - 40 x^{7} + 45 x^{6} - 46 x^{5} + 40 x^{4} - 26 x^{3} + 12 x^{2} - 4 x + 1$ |
$12$ |
[0,6] |
$3^{6}\cdot 37^{5}$ |
$2$ |
$7.79790630012$ |
$35.10713565663159$ |
|
|
? |
$C_6\wr C_2$ (as 12T42) |
trivial |
$6$ |
$5$ |
$3.95685086216$ |
12.0.51067940737.1 |
$x^{12} - 3 x^{11} + 6 x^{10} - 10 x^{9} + 15 x^{8} - 18 x^{7} + 20 x^{6} - 19 x^{5} + 16 x^{4} - 12 x^{3} + 7 x^{2} - 3 x + 1$ |
$12$ |
[0,6] |
$11^{2}\cdot 31^{4}\cdot 457$ |
$3$ |
$7.80451097147$ |
$394.76195358722197$ |
|
|
✓ |
$C_2\wr (C_2\times S_4)$ (as 12T250) |
trivial |
$2$ |
$5$ |
$1.32924669226$ |
12.0.51514924901.1 |
$x^{12} - 2 x^{11} - x^{10} + 2 x^{9} + 4 x^{8} - x^{7} - 7 x^{6} + x^{5} + 4 x^{4} - 2 x^{3} - x^{2} + 2 x + 1$ |
$12$ |
[0,6] |
$11^{2}\cdot 31^{4}\cdot 461$ |
$3$ |
$7.81018082983$ |
$396.4858131131554$ |
|
|
✓ |
$C_2\wr (C_2\times S_4)$ (as 12T250) |
trivial |
$2$ |
$5$ |
$1.33838343414$ |
12.0.53440955929.1 |
$x^{12} - x^{11} + x^{10} - 3 x^{9} + 4 x^{8} - 2 x^{7} + x^{6} - 2 x^{5} + 4 x^{4} - 3 x^{3} + x^{2} - x + 1$ |
$12$ |
[0,6] |
$19^{2}\cdot 23^{6}$ |
$2$ |
$7.83410734676$ |
$20.904544960366874$ |
|
|
? |
$C_2\times S_4$ (as 12T21) |
trivial |
$2$ |
$5$ |
$1.36801263468$ |
12.0.54507773961.1 |
$x^{12} - x^{11} - 2 x^{10} + 5 x^{9} - x^{8} - 4 x^{7} + 5 x^{6} - 4 x^{5} - x^{4} + 5 x^{3} - 2 x^{2} - x + 1$ |
$12$ |
[0,6] |
$3^{6}\cdot 8647^{2}$ |
$2$ |
$7.84702200576$ |
$161.06209982488122$ |
|
|
? |
$S_6\times C_2$ (as 12T219) |
trivial |
$6$ |
$5$ |
$4.14786100391$ |
12.0.55358453125.1 |
$x^{12} - 4 x^{11} + 11 x^{10} - 22 x^{9} + 35 x^{8} - 45 x^{7} + 49 x^{6} - 44 x^{5} + 33 x^{4} - 21 x^{3} + 11 x^{2} - 4 x + 1$ |
$12$ |
[0,6] |
$5^{6}\cdot 61\cdot 241^{2}$ |
$3$ |
$7.8571551481$ |
$271.1180554666177$ |
|
|
✓ |
$S_4^2:D_4$ (as 12T260) |
trivial |
$2$ |
$5$ |
$1.40064596697$ |
12.0.56689952000.1 |
$x^{12} - 5 x^{11} + 13 x^{10} - 25 x^{9} + 39 x^{8} - 50 x^{7} + 53 x^{6} - 48 x^{5} + 37 x^{4} - 23 x^{3} + 12 x^{2} - 4 x + 1$ |
$12$ |
[0,6] |
$2^{8}\cdot 5^{3}\cdot 11^{6}$ |
$3$ |
$7.87273272153$ |
$11.772481280020624$ |
|
|
✓ |
$(C_6\times C_2):C_2$ (as 12T15) |
trivial |
$2$ |
$5$ |
$1.4199505274$ |
12.0.58300115053.1 |
$x^{12} - x^{11} + 4 x^{10} - 4 x^{9} + 9 x^{8} - 6 x^{7} + 11 x^{6} - 6 x^{5} + 8 x^{4} - 3 x^{3} + 4 x^{2} - x + 1$ |
$12$ |
[0,6] |
$23^{4}\cdot 208333$ |
$2$ |
$7.8911285384$ |
$2188.985838236511$ |
|
|
✓ |
$A_4^3.(C_2\times S_4)$ (as 12T294) |
trivial |
$2$ |
$5$ |
$1.44906493339$ |
12.0.59081901957.1 |
$x^{12} - 3 x^{11} + 5 x^{10} - 6 x^{9} + 5 x^{8} - 2 x^{7} - x^{6} + 4 x^{5} - 4 x^{4} + 2 x^{3} - x + 1$ |
$12$ |
[0,6] |
$3^{6}\cdot 13^{3}\cdot 37\cdot 997$ |
$4$ |
$7.89989293816$ |
$1199.446122174731$ |
|
|
✓ |
$S_3\wr D_4$ (as 12T274) |
trivial |
$6$ |
$5$ |
$4.38856707636$ |
12.0.59182215273.1 |
$x^{12} - 5 x^{11} + 14 x^{10} - 31 x^{9} + 53 x^{8} - 72 x^{7} + 81 x^{6} - 72 x^{5} + 53 x^{4} - 31 x^{3} + 14 x^{2} - 5 x + 1$ |
$12$ |
[0,6] |
$3^{6}\cdot 433^{3}$ |
$2$ |
$7.90100981774$ |
$36.0416425818802$ |
|
|
✓ |
$\SOPlus(4,2)$ (as 12T35) |
trivial |
$6$ |
$5$ |
$4.35580546019$ |
12.0.59767578125.1 |
$x^{12} - 5 x^{11} + 13 x^{10} - 21 x^{9} + 24 x^{8} - 21 x^{7} + 18 x^{6} - 17 x^{5} + 15 x^{4} - 9 x^{3} + 4 x^{2} - 2 x + 1$ |
$12$ |
[0,6] |
$5^{9}\cdot 71\cdot 431$ |
$3$ |
$7.90749279408$ |
$584.9184395258499$ |
|
|
✓ |
$S_3\wr C_4$ (as 12T264) |
trivial |
$10$ |
$5$ |
$7.40729189233$ |
12.0.60454515625.1 |
$x^{12} - x^{11} - 2 x^{10} + 2 x^{9} + 4 x^{8} - 3 x^{7} - 5 x^{6} + 3 x^{5} + 5 x^{4} - x^{3} - 3 x^{2} + 1$ |
$12$ |
[0,6] |
$5^{6}\cdot 7^{2}\cdot 281^{2}$ |
$3$ |
$7.91502690536$ |
$99.17156850630124$ |
|
|
✓ |
$S_4^2:C_2^2$ (as 12T236) |
trivial |
$2$ |
$5$ |
$1.47630310859$ |
12.0.63518590021.1 |
$x^{12} - 2 x^{11} + 3 x^{10} - 2 x^{9} + 2 x^{8} - 4 x^{7} + 4 x^{6} - 2 x^{5} - x^{4} + 2 x^{2} - x + 1$ |
$12$ |
[0,6] |
$23^{4}\cdot 61^{3}$ |
$2$ |
$7.94770497569$ |
$104.6794167699507$ |
|
|
? |
$C_4\wr S_3$ (as 12T150) |
trivial |
$2$ |
$5$ |
$1.51948050623$ |
12.0.63568613376.1 |
$x^{12} - 4 x^{11} + 9 x^{10} - 14 x^{9} + 16 x^{8} - 14 x^{7} + 10 x^{6} - 6 x^{5} + 6 x^{4} - 6 x^{3} + 6 x^{2} - 4 x + 1$ |
$12$ |
[0,6] |
$2^{12}\cdot 3^{6}\cdot 61\cdot 349$ |
$4$ |
$7.94822638136$ |
$505.4384235492984$ |
|
|
? |
$S_3\wr C_2^2$ (as 12T261) |
trivial |
$12$ |
$5$ |
$9.18542221354$ |
12.0.63853279857.1 |
$x^{12} - 4 x^{11} + 9 x^{10} - 13 x^{9} + 17 x^{8} - 21 x^{7} + 25 x^{6} - 27 x^{5} + 26 x^{4} - 20 x^{3} + 12 x^{2} - 5 x + 1$ |
$12$ |
[0,6] |
$3^{6}\cdot 23^{4}\cdot 313$ |
$3$ |
$7.95118638902$ |
$146.9591780053223$ |
|
|
? |
$C_2\wr D_6$ (as 12T193) |
trivial |
$6$ |
$5$ |
$4.5780204292$ |
12.0.63995902381.1 |
$x^{12} - x^{11} + 2 x^{9} - x^{8} - 4 x^{7} + 5 x^{6} - x^{5} - x^{4} - x^{3} + 4 x^{2} - 3 x + 1$ |
$12$ |
[0,6] |
$73^{2}\cdot 229^{3}$ |
$2$ |
$7.95266485522$ |
$264.32179884736155$ |
|
|
? |
$C_3\wr S_4$ (as 12T231) |
trivial |
$2$ |
$5$ |
$1.54183330651$ |
12.0.66468114161.1 |
$x^{12} - x^{11} - 2 x^{10} + 4 x^{9} + x^{8} - 5 x^{7} + x^{6} + 5 x^{5} + x^{4} - 4 x^{3} - 2 x^{2} + x + 1$ |
$12$ |
[0,6] |
$23^{6}\cdot 449$ |
$2$ |
$7.9778239152$ |
$101.62184804460112$ |
|
|
? |
$C_2\wr S_3$ (as 12T135) |
trivial |
$2$ |
$5$ |
$1.56137956029$ |
12.0.66699927001.1 |
$x^{12} - x^{9} + x^{7} - x^{4} - x^{3} + x + 1$ |
$12$ |
[0,6] |
$47\cdot 1117\cdot 1270499$ |
$3$ |
$7.9801388252$ |
$258263.29007623208$ |
|
|
? |
$S_{12}$ (as 12T301) |
trivial |
$2$ |
$5$ |
$1.58972306672$ |
12.0.67030763409.1 |
$x^{12} - x^{11} - 2 x^{10} + 6 x^{8} - x^{7} - 5 x^{6} - x^{5} + 6 x^{4} - 2 x^{2} - x + 1$ |
$12$ |
[0,6] |
$3^{6}\cdot 43^{2}\cdot 223^{2}$ |
$3$ |
$7.98342985511$ |
$169.60837243485358$ |
|
|
? |
$S_6\times C_2$ (as 12T219) |
trivial |
$6$ |
$5$ |
$4.81968495903$ |
12.0.69637938597.1 |
$x^{12} - 2 x^{11} + 3 x^{10} - 2 x^{9} + 4 x^{6} - 11 x^{5} + 17 x^{4} - 16 x^{3} + 11 x^{2} - 5 x + 1$ |
$12$ |
[0,6] |
$3^{6}\cdot 19^{4}\cdot 733$ |
$3$ |
$8.00885613193$ |
$333.8989207608368$ |
|
|
? |
$A_4^2:D_4$ (as 12T208) |
trivial |
$6$ |
$5$ |
$4.89240598709$ |
12.0.70127513856.1 |
$x^{12} + x^{10} - 3 x^{8} - 3 x^{6} + 2 x^{4} + 2 x^{2} + 1$ |
$12$ |
[0,6] |
$2^{8}\cdot 3^{6}\cdot 613^{2}$ |
$3$ |
$8.01353313251$ |
$144.24253855791977$ |
|
|
? |
$S_4^2:C_2^2$ (as 12T236) |
trivial |
$6$ |
$5$ |
$4.86613553287$ |
12.0.70516271401.1 |
$x^{12} - 3 x^{11} + 4 x^{10} - x^{9} - 3 x^{8} + 4 x^{7} - 3 x^{6} + 4 x^{5} - 3 x^{4} - x^{3} + 4 x^{2} - 3 x + 1$ |
$12$ |
[0,6] |
$37^{2}\cdot 7177^{2}$ |
$2$ |
$8.01722573211$ |
$515.314467097519$ |
|
|
✓ |
$C_2^5:S_6$ (as 12T285) |
trivial |
$2$ |
$5$ |
$1.65463443861$ |
12.0.71939651121.1 |
$x^{12} - x^{11} - 3 x^{10} + x^{9} + 5 x^{8} + 3 x^{7} - 3 x^{6} - 7 x^{5} - 2 x^{4} + 3 x^{3} + 2 x^{2} + x + 1$ |
$12$ |
[0,6] |
$3^{6}\cdot 13^{3}\cdot 44917$ |
$3$ |
$8.03058827935$ |
$1323.5418391573423$ |
|
|
? |
$S_3\wr D_4$ (as 12T274) |
trivial |
$6$ |
$5$ |
$4.93206182745$ |
12.0.72509192309.1 |
$x^{12} - x^{10} - x^{9} + x^{7} + x^{6} + x^{5} - 2 x^{3} - x^{2} + x + 1$ |
$12$ |
[0,6] |
$72509192309$ |
$1$ |
$8.03586728509$ |
$269275.30950497487$ |
|
|
✓ |
$S_{12}$ (as 12T301) |
trivial |
$2$ |
$5$ |
$1.66307418431$ |
12.0.73358639104.1 |
$x^{12} - 2 x^{11} + 2 x^{10} - 2 x^{9} + 6 x^{8} - 10 x^{7} + 10 x^{6} - 12 x^{5} + 17 x^{4} - 14 x^{3} + 8 x^{2} - 4 x + 1$ |
$12$ |
[0,6] |
$2^{18}\cdot 23^{4}$ |
$2$ |
$8.04367050498$ |
$16.131190144457708$ |
|
|
? |
$C_2 \times S_4$ (as 12T23) |
trivial |
$4$ |
$5$ |
$3.42242551816$ |
12.0.73645476129.1 |
$x^{12} - x^{11} - x^{10} + 2 x^{9} - 2 x^{7} + 3 x^{5} - 2 x^{4} + 2 x^{2} - 2 x + 1$ |
$12$ |
[0,6] |
$3^{6}\cdot 19^{2}\cdot 23^{4}$ |
$3$ |
$8.046286759$ |
$36.207733980463345$ |
|
|
? |
$C_2^2\times S_4$ (as 12T48) |
trivial |
$6$ |
$5$ |
$4.99030501888$ |
12.0.74733890625.1 |
$x^{12} - 6 x^{11} + 21 x^{10} - 50 x^{9} + 93 x^{8} - 138 x^{7} + 164 x^{6} - 153 x^{5} + 111 x^{4} - 61 x^{3} + 24 x^{2} - 6 x + 1$ |
$12$ |
[0,6] |
$3^{14}\cdot 5^{6}$ |
$2$ |
$8.0561300054$ |
$8.05613000539548$ |
|
✓ |
? |
$D_6$ (as 12T3) |
trivial |
$6$ |
$5$ |
$5.15894342496$ |
12.0.74880094208.1 |
$x^{12} - 2 x^{11} + 2 x^{10} - 2 x^{9} + 5 x^{8} - 10 x^{7} + 14 x^{6} - 16 x^{5} + 17 x^{4} - 14 x^{3} + 9 x^{2} - 4 x + 1$ |
$12$ |
[0,6] |
$2^{12}\cdot 17^{3}\cdot 61^{2}$ |
$3$ |
$8.05744219486$ |
$127.78337260969369$ |
|
|
? |
$C_3\wr D_4$ (as 12T167) |
trivial |
$4$ |
$5$ |
$3.38131432466$ |
12.0.74948100349.1 |
$x^{12} - x^{11} - x^{10} + 2 x^{9} + 2 x^{8} - 5 x^{7} + 3 x^{6} + 2 x^{4} - 6 x^{3} + 7 x^{2} - 4 x + 1$ |
$12$ |
[0,6] |
$79^{2}\cdot 229^{3}$ |
$2$ |
$8.0580517556$ |
$278.61370060593055$ |
|
|
✓ |
$C_3\wr S_4$ (as 12T231) |
trivial |
$2$ |
$5$ |
$1.67713762237$ |
12.0.75794375168.1 |
$x^{12} - 4 x^{11} + 9 x^{10} - 12 x^{9} + 14 x^{8} - 19 x^{7} + 30 x^{6} - 39 x^{5} + 37 x^{4} - 26 x^{3} + 14 x^{2} - 5 x + 1$ |
$12$ |
[0,6] |
$2^{9}\cdot 23^{6}$ |
$2$ |
$8.06559507223$ |
$13.564659966250536$ |
|
|
? |
$(C_6\times C_2):C_2$ (as 12T15) |
trivial |
$2$ |
$5$ |
$1.74341488875$ |