| 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 |
| 12.0.46716936381.1 |
$x^{12} - 4 x^{11} + 9 x^{10} - 15 x^{9} + 23 x^{8} - 33 x^{7} + 44 x^{6} - 50 x^{5} + 45 x^{4} - 29 x^{3} + 13 x^{2} - 4 x + 1$ |
$12$ |
[0,6] |
$3^{6}\cdot 23^{4}\cdot 229$ |
$3$ |
$7.74680925796$ |
$125.70202862324857$ |
|
|
? |
$C_2\wr D_6$ (as 12T193) |
trivial |
$6$ |
$5$ |
$3.77207610108$ |
| 12.0.63853279857.1 |
$x^{12} - 4 x^{11} + 9 x^{10} - 13 x^{9} + 17 x^{8} - 21 x^{7} + 25 x^{6} - 27 x^{5} + 26 x^{4} - 20 x^{3} + 12 x^{2} - 5 x + 1$ |
$12$ |
[0,6] |
$3^{6}\cdot 23^{4}\cdot 313$ |
$3$ |
$7.95118638902$ |
$146.9591780053223$ |
|
|
? |
$C_2\wr D_6$ (as 12T193) |
trivial |
$6$ |
$5$ |
$4.5780204292$ |
| 12.2.257978421875.1 |
$x^{12} - 2 x^{11} + 2 x^{9} - 5 x^{7} + 10 x^{6} - 16 x^{5} + 20 x^{4} - 19 x^{3} + 12 x^{2} - 5 x + 1$ |
$12$ |
[2,5] |
$-\,5^{6}\cdot 23^{4}\cdot 59$ |
$3$ |
$8.93234074331$ |
$82.37111144084436$ |
|
|
? |
$C_2\wr D_6$ (as 12T193) |
trivial |
$2$ |
$6$ |
$4.57996864178$ |
| 12.2.566636000000.1 |
$x^{12} - 4 x^{10} - x^{9} + 7 x^{8} + 4 x^{7} - 5 x^{6} - 8 x^{5} + x^{4} + 7 x^{3} - x^{2} - 3 x + 1$ |
$12$ |
[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 |
$2$ |
$6$ |
$7.30104222822$ |
| 12.0.651504828125.1 |
$x^{12} - 4 x^{11} + 4 x^{10} + 3 x^{9} - 3 x^{8} - 9 x^{7} + 9 x^{6} + 3 x^{5} - x^{4} - 4 x^{3} - x^{2} + 2 x + 1$ |
$12$ |
[0,6] |
$5^{6}\cdot 23^{4}\cdot 149$ |
$3$ |
$9.64924062317$ |
$130.90072574283155$ |
|
|
✓ |
$C_2\wr D_6$ (as 12T193) |
trivial |
$2$ |
$5$ |
$6.01189861301$ |
| 12.0.1430996000000.1 |
$x^{12} - x^{11} - x^{10} - x^{9} + 3 x^{8} + x^{6} - 6 x^{5} + 5 x^{4} - x^{3} + 1$ |
$12$ |
[0,6] |
$2^{8}\cdot 5^{6}\cdot 7^{4}\cdot 149$ |
$4$ |
$10.3031463394$ |
$114.63409855014139$ |
|
|
? |
$C_2\wr D_6$ (as 12T193) |
trivial |
$2$ |
$5$ |
$11.4560019213$ |
| 12.0.1483275763712.1 |
$x^{12} - 4 x^{10} + 5 x^{8} - 4 x^{6} + 7 x^{4} - 6 x^{2} + 2$ |
$12$ |
[0,6] |
$2^{21}\cdot 29^{4}$ |
$2$ |
$10.334000821$ |
$41.254811891316024$ |
|
|
? |
$C_2\wr D_6$ (as 12T193) |
trivial |
$4$ |
$5$ |
$37.7646927116$ |
| 12.4.2278080640625.1 |
$x^{12} - x^{11} - x^{10} + 3 x^{9} - 4 x^{8} - 6 x^{7} + 7 x^{6} + 6 x^{5} - 4 x^{4} - 3 x^{3} - x^{2} + x + 1$ |
$12$ |
[4,4] |
$5^{6}\cdot 23^{4}\cdot 521$ |
$3$ |
$10.7101961434$ |
$244.7754072614322$ |
|
|
? |
$C_2\wr D_6$ (as 12T193) |
trivial |
$2$ |
$7$ |
$22.506602548$ |
| 12.0.2688437321728.1 |
$x^{12} - 2 x^{11} + 3 x^{10} - 4 x^{9} + 3 x^{8} - 4 x^{7} + 15 x^{6} - 34 x^{5} + 47 x^{4} - 38 x^{3} + 20 x^{2} - 6 x + 1$ |
$12$ |
[0,6] |
$2^{17}\cdot 29^{5}$ |
$2$ |
$10.85904567$ |
$84.06805244706045$ |
|
|
? |
$C_2\wr D_6$ (as 12T193) |
trivial |
$4$ |
$5$ |
$42.6739442574$ |
| 12.4.3304473578125.1 |
$x^{12} - x^{11} - 3 x^{10} + 2 x^{9} + 5 x^{8} - 8 x^{7} - 9 x^{6} + 4 x^{5} + 7 x^{4} - 3 x^{3} + 5 x^{2} + 2 x - 1$ |
$12$ |
[4,4] |
$5^{6}\cdot 31^{4}\cdot 229$ |
$3$ |
$11.047360434$ |
$188.40116772461894$ |
|
|
? |
$C_2\wr D_6$ (as 12T193) |
trivial |
$2$ |
$7$ |
$28.8293373209$ |
| 12.2.5061276073984.2 |
$x^{12} - 3 x^{10} + x^{8} + 3 x^{4} + 3 x^{2} - 1$ |
$12$ |
[2,5] |
$-\,2^{20}\cdot 13^{6}$ |
$2$ |
$11.4469117752$ |
$32.84768651624708$ |
|
|
? |
$C_2\wr D_6$ (as 12T193) |
trivial |
$2$ |
$6$ |
$30.8513151146$ |
| 12.0.7860327022592.1 |
$x^{12} - 4 x^{10} + 10 x^{8} - 14 x^{6} + 14 x^{4} - 8 x^{2} + 2$ |
$12$ |
[0,6] |
$2^{29}\cdot 11^{4}$ |
$2$ |
$11.8746290391$ |
$33.42948310377551$ |
|
|
✓ |
$C_2\wr D_6$ (as 12T193) |
trivial |
$4$ |
$5$ |
$74.8567676344$ |
| 12.0.7860327022592.4 |
$x^{12} - 2 x^{8} - 2 x^{6} + 6 x^{4} - 4 x^{2} + 2$ |
$12$ |
[0,6] |
$2^{29}\cdot 11^{4}$ |
$2$ |
$11.8746290391$ |
$33.42948310377551$ |
|
|
? |
$C_2\wr D_6$ (as 12T193) |
trivial |
$4$ |
$5$ |
$87.3288821645$ |
| 12.2.8745694265344.2 |
$x^{12} - 6 x^{6} + 6 x^{4} + 4 x^{2} - 1$ |
$12$ |
[2,5] |
$-\,2^{26}\cdot 19^{4}$ |
$2$ |
$11.9807183213$ |
$39.71091661565655$ |
|
|
|
$C_2\wr D_6$ (as 12T193) |
trivial |
$2$ |
$6$ |
$47.3853632196$ |
| 12.0.8886803708997.1 |
$x^{12} - 2 x^{11} + 4 x^{10} - 2 x^{9} - 6 x^{8} + 17 x^{7} - 20 x^{6} + 8 x^{5} + 22 x^{4} - 45 x^{3} + 36 x^{2} - 15 x + 3$ |
$12$ |
[0,6] |
$3^{7}\cdot 31\cdot 107^{4}$ |
$3$ |
$11.9967092169$ |
$131.28456720467148$ |
|
|
? |
$C_2\wr D_6$ (as 12T193) |
trivial |
$6$ |
$5$ |
$119.854513264$ |
| 12.2.10240000000000.2 |
$x^{12} + 7 x^{10} + 20 x^{8} + 25 x^{6} + 10 x^{4} - 3 x^{2} - 1$ |
$12$ |
[2,5] |
$-\,2^{20}\cdot 5^{10}$ |
$2$ |
$12.1392446201$ |
$34.83438237794665$ |
|
|
? |
$C_2\wr D_6$ (as 12T193) |
trivial |
$2$ |
$6$ |
$42.5028748801$ |
| 12.0.15045919506432.3 |
$x^{12} - 3 x^{10} + 9 x^{8} - 12 x^{6} + 15 x^{4} - 9 x^{2} + 3$ |
$12$ |
[0,6] |
$2^{20}\cdot 3^{15}$ |
$2$ |
$12.5348236358$ |
$35.96952308277431$ |
|
|
? |
$C_2\wr D_6$ (as 12T193) |
trivial |
$6$ |
$5$ |
$169.403335685$ |
| 12.2.20245104295936.1 |
$x^{12} + x^{10} + x^{8} - 4 x^{6} - 12 x^{4} - 12 x^{2} - 4$ |
$12$ |
[2,5] |
$-\,2^{22}\cdot 13^{6}$ |
$2$ |
$12.848724038$ |
$39.06270251649997$ |
|
|
? |
$C_2\wr D_6$ (as 12T193) |
trivial |
$2$ |
$6$ |
$63.3856356973$ |
| 12.0.20421060067328.1 |
$x^{12} - 2 x^{11} - 3 x^{10} + 4 x^{9} + 9 x^{8} - 10 x^{7} - 6 x^{6} + 10 x^{5} + 9 x^{4} - 4 x^{3} - 3 x^{2} + 2 x + 1$ |
$12$ |
[0,6] |
$2^{19}\cdot 79^{4}$ |
$2$ |
$12.8579931551$ |
$65.20408173974066$ |
|
|
? |
$C_2\wr D_6$ (as 12T193) |
trivial |
$4$ |
$5$ |
$282.918274705$ |
| 12.0.23732412219392.1 |
$x^{12} - 2 x^{10} + 5 x^{8} - 10 x^{6} + 11 x^{4} - 6 x^{2} + 2$ |
$12$ |
[0,6] |
$2^{25}\cdot 29^{4}$ |
$2$ |
$13.020025164$ |
$41.254811891316024$ |
|
|
? |
$C_2\wr D_6$ (as 12T193) |
trivial |
$4$ |
$5$ |
$175.599749771$ |
| 12.0.24917051441152.3 |
$x^{12} - 6 x^{11} + 20 x^{10} - 44 x^{9} + 76 x^{8} - 108 x^{7} + 120 x^{6} - 104 x^{5} + 78 x^{4} - 52 x^{3} + 32 x^{2} - 16 x + 4$ |
$12$ |
[0,6] |
$2^{26}\cdot 13^{5}$ |
$2$ |
$13.0729837317$ |
$42.233906376277666$ |
|
|
? |
$C_2\wr D_6$ (as 12T193) |
trivial |
$4$ |
$5$ |
$290.810487165$ |
| 12.2.34982777061376.1 |
$x^{12} - 2 x^{10} - x^{8} + 2 x^{4} + 8 x^{2} - 4$ |
$12$ |
[2,5] |
$-\,2^{28}\cdot 19^{4}$ |
$2$ |
$13.4479016272$ |
$47.22450458261855$ |
|
|
? |
$C_2\wr D_6$ (as 12T193) |
trivial |
$2$ |
$6$ |
$262.413833484$ |
| 12.2.34982777061376.2 |
$x^{12} + 6 x^{6} + 6 x^{4} - 4 x^{2} - 1$ |
$12$ |
[2,5] |
$-\,2^{28}\cdot 19^{4}$ |
$2$ |
$13.4479016272$ |
$39.71091661565655$ |
|
|
? |
$C_2\wr D_6$ (as 12T193) |
trivial |
$2$ |
$6$ |
$145.953865945$ |
| 12.2.35664401793024.2 |
$x^{12} - 6 x^{8} + 2 x^{6} + 24 x^{4} + 12 x^{2} - 1$ |
$12$ |
[2,5] |
$-\,2^{26}\cdot 3^{12}$ |
$2$ |
$13.4695445797$ |
$32.82272053472972$ |
|
|
? |
$C_2\wr D_6$ (as 12T193) |
trivial |
$2$ |
$6$ |
$267.734598333$ |
| 12.0.37559623221248.4 |
$x^{12} - 8 x^{10} + 28 x^{8} - 44 x^{6} + 28 x^{4} - 8 x^{2} + 8$ |
$12$ |
[0,6] |
$2^{27}\cdot 23^{4}$ |
$2$ |
$13.5277873862$ |
$43.2208631217174$ |
|
|
? |
$C_2\wr D_6$ (as 12T193) |
trivial |
$4$ |
$5$ |
$194.210514072$ |
| 12.0.37559623221248.9 |
$x^{12} - 4 x^{10} + 12 x^{8} - 4 x^{6} + 12 x^{4} + 24 x^{2} + 8$ |
$12$ |
[0,6] |
$2^{27}\cdot 23^{4}$ |
$2$ |
$13.5277873862$ |
$43.2208631217174$ |
|
|
? |
$C_2\wr D_6$ (as 12T193) |
trivial |
$4$ |
$5$ |
$101.964016288$ |
| 12.2.40960000000000.2 |
$x^{12} + x^{10} - 5 x^{8} - 10 x^{6} - 10 x^{4} - 4 x^{2} - 4$ |
$12$ |
[2,5] |
$-\,2^{22}\cdot 5^{10}$ |
$2$ |
$13.6258413812$ |
$41.42529537057956$ |
|
|
? |
$C_2\wr D_6$ (as 12T193) |
trivial |
$2$ |
$6$ |
$121.89920604$ |
| 12.0.43014997147648.1 |
$x^{12} - 6 x^{10} - 4 x^{9} + 19 x^{8} + 28 x^{7} - 24 x^{6} - 68 x^{5} + 3 x^{4} + 92 x^{3} + 78 x^{2} + 16 x + 1$ |
$12$ |
[0,6] |
$2^{21}\cdot 29^{5}$ |
$2$ |
$13.6815402214$ |
$41.254811891316024$ |
|
|
? |
$C_2\wr D_6$ (as 12T193) |
trivial |
$4$ |
$5$ |
$251.67276909$ |
| 12.0.43014997147648.2 |
$x^{12} - 10 x^{10} + 44 x^{8} - 104 x^{6} + 137 x^{4} - 110 x^{2} + 58$ |
$12$ |
[0,6] |
$2^{21}\cdot 29^{5}$ |
$2$ |
$13.6815402214$ |
$41.254811891316024$ |
|
|
? |
$C_2\wr D_6$ (as 12T193) |
trivial |
$4$ |
$5$ |
$226.905972784$ |
| 12.0.43014997147648.3 |
$x^{12} - 6 x^{10} + 40 x^{6} - 19 x^{4} - 58 x^{2} + 58$ |
$12$ |
[0,6] |
$2^{21}\cdot 29^{5}$ |
$2$ |
$13.6815402214$ |
$91.67686126362786$ |
|
|
? |
$C_2\wr D_6$ (as 12T193) |
trivial |
$4$ |
$5$ |
$240.631954452$ |
| 12.2.51200000000000.1 |
$x^{12} + 5 x^{10} + 5 x^{8} - 5 x^{4} - 5 x^{2} - 5$ |
$12$ |
[2,5] |
$-\,2^{20}\cdot 5^{11}$ |
$2$ |
$13.8815884105$ |
$39.8341555707031$ |
|
|
|
$C_2\wr D_6$ (as 12T193) |
trivial |
$2$ |
$6$ |
$174.95746509$ |
| 12.0.60183678025728.4 |
$x^{12} + 9 x^{10} + 33 x^{8} + 60 x^{6} + 60 x^{4} + 36 x^{2} + 12$ |
$12$ |
[0,6] |
$2^{22}\cdot 3^{15}$ |
$2$ |
$14.0698638134$ |
$42.775212773289816$ |
|
|
? |
$C_2\wr D_6$ (as 12T193) |
trivial |
$6$ |
$5$ |
$315.376965071$ |
| 12.2.61334280470528.2 |
$x^{12} - 2 x^{10} + 3 x^{8} - 4 x^{6} - 8 x^{4} + 8 x^{2} - 2$ |
$12$ |
[2,5] |
$-\,2^{31}\cdot 13^{4}$ |
$2$ |
$14.0920856109$ |
$50.658057734962696$ |
|
|
? |
$C_2\wr D_6$ (as 12T193) |
trivial |
$2$ |
$6$ |
$200.969555355$ |
| 12.2.61334280470528.3 |
$x^{12} + 2 x^{10} + 11 x^{8} - 4 x^{6} + 8 x^{4} + 16 x^{2} - 2$ |
$12$ |
[2,5] |
$-\,2^{31}\cdot 13^{4}$ |
$2$ |
$14.0920856109$ |
$50.658057734962696$ |
|
|
|
$C_2\wr D_6$ (as 12T193) |
trivial |
$2$ |
$6$ |
$520.445712561$ |
| 12.0.61334280470528.2 |
$x^{12} + 2 x^{10} + x^{8} - 2 x^{6} - 3 x^{4} + 2$ |
$12$ |
[0,6] |
$2^{31}\cdot 13^{4}$ |
$2$ |
$14.0920856109$ |
$43.53095781435477$ |
|
|
✓ |
$C_2\wr D_6$ (as 12T193) |
trivial |
$2$ |
$5$ |
$169.112542598$ |
| 12.0.61334280470528.3 |
$x^{12} - 2 x^{10} + x^{8} + 2 x^{6} - 3 x^{4} + 2$ |
$12$ |
[0,6] |
$2^{31}\cdot 13^{4}$ |
$2$ |
$14.0920856109$ |
$43.53095781435477$ |
|
|
✓ |
$C_2\wr D_6$ (as 12T193) |
trivial |
$2$ |
$5$ |
$131.49319383$ |
| 12.0.61334280470528.4 |
$x^{12} - 2 x^{10} + 3 x^{8} + 4 x^{6} + 2$ |
$12$ |
[0,6] |
$2^{31}\cdot 13^{4}$ |
$2$ |
$14.0920856109$ |
$51.76732475571399$ |
|
|
? |
$C_2\wr D_6$ (as 12T193) |
trivial |
$4$ |
$5$ |
$417.205691166$ |
| 12.0.61334280470528.9 |
$x^{12} - 6 x^{10} + 17 x^{8} - 28 x^{6} + 28 x^{4} - 16 x^{2} + 8$ |
$12$ |
[0,6] |
$2^{31}\cdot 13^{4}$ |
$2$ |
$14.0920856109$ |
$51.76732475571399$ |
|
|
? |
$C_2\wr D_6$ (as 12T193) |
trivial |
$4$ |
$5$ |
$486.109843108$ |
| 12.2.65796588961792.1 |
$x^{12} + 7 x^{10} + 16 x^{8} + 5 x^{6} - 30 x^{4} - 39 x^{2} - 13$ |
$12$ |
[2,5] |
$-\,2^{20}\cdot 13^{7}$ |
$2$ |
$14.1748002734$ |
$62.372137181647794$ |
|
|
|
$C_2\wr D_6$ (as 12T193) |
trivial |
$2$ |
$6$ |
$176.728305899$ |
| 12.0.69965554122752.1 |
$x^{12} - 2 x^{10} + 4 x^{8} - 10 x^{6} + 14 x^{4} - 8 x^{2} + 2$ |
$12$ |
[0,6] |
$2^{29}\cdot 19^{4}$ |
$2$ |
$14.2475554706$ |
$43.934948266651354$ |
|
|
|
$C_2\wr D_6$ (as 12T193) |
trivial |
$4$ |
$5$ |
$321.054861893$ |
| 12.0.69965554122752.6 |
$x^{12} - 2 x^{10} - 2 x^{6} + 6 x^{4} + 4 x^{2} + 2$ |
$12$ |
[0,6] |
$2^{29}\cdot 19^{4}$ |
$2$ |
$14.2475554706$ |
$43.934948266651354$ |
|
|
|
$C_2\wr D_6$ (as 12T193) |
trivial |
$4$ |
$5$ |
$331.218212989$ |
| 12.0.77964682330112.1 |
$x^{12} - 2 x^{11} + 5 x^{10} + 6 x^{9} - 4 x^{8} + 16 x^{7} + 37 x^{6} + 8 x^{5} - 5 x^{4} + 28 x^{3} + 40 x^{2} + 16 x + 2$ |
$12$ |
[0,6] |
$2^{17}\cdot 29^{6}$ |
$2$ |
$14.3766652117$ |
$84.06805244706045$ |
|
|
|
$C_2\wr D_6$ (as 12T193) |
trivial |
$4$ |
$5$ |
$408.909538356$ |
| 12.0.77964682330112.2 |
$x^{12} - 4 x^{11} + 5 x^{10} + 8 x^{9} - 35 x^{8} + 48 x^{7} - 16 x^{6} - 80 x^{5} + 202 x^{4} - 264 x^{3} + 232 x^{2} - 128 x + 32$ |
$12$ |
[0,6] |
$2^{17}\cdot 29^{6}$ |
$2$ |
$14.3766652117$ |
$84.06805244706045$ |
|
|
|
$C_2\wr D_6$ (as 12T193) |
trivial |
$4$ |
$5$ |
$408.77217809$ |
| 12.2.80980417183744.2 |
$x^{12} + 3 x^{10} + x^{8} + 3 x^{4} - 3 x^{2} - 1$ |
$12$ |
[2,5] |
$-\,2^{24}\cdot 13^{6}$ |
$2$ |
$14.4222051019$ |
$32.84768651624708$ |
|
|
|
$C_2\wr D_6$ (as 12T193) |
trivial |
$2$ |
$6$ |
$176.405228195$ |
| 12.0.94929648877568.3 |
$x^{12} - 4 x^{8} - 12 x^{6} + 40 x^{4} - 32 x^{2} + 8$ |
$12$ |
[0,6] |
$2^{27}\cdot 29^{4}$ |
$2$ |
$14.6144841146$ |
$44.98869137713074$ |
|
|
? |
$C_2\wr D_6$ (as 12T193) |
trivial |
$4$ |
$5$ |
$359.163809196$ |
| 12.0.94929648877568.7 |
$x^{12} - 4 x^{10} + 12 x^{8} - 12 x^{6} + 24 x^{4} + 8$ |
$12$ |
[0,6] |
$2^{27}\cdot 29^{4}$ |
$2$ |
$14.6144841146$ |
$44.98869137713074$ |
|
|
? |
$C_2\wr D_6$ (as 12T193) |
trivial |
$4$ |
$5$ |
$339.19941302$ |
| 12.0.99668205764608.3 |
$x^{12} + 3 x^{8} - 16 x^{6} + 31 x^{4} + 13$ |
$12$ |
[0,6] |
$2^{28}\cdot 13^{5}$ |
$2$ |
$14.6739280969$ |
$42.233906376277666$ |
|
|
? |
$C_2\wr D_6$ (as 12T193) |
trivial |
$4$ |
$5$ |
$555.537512274$ |
| 12.0.99668205764608.5 |
$x^{12} - 6 x^{10} + 19 x^{8} - 4 x^{6} + 15 x^{4} + 26 x^{2} + 13$ |
$12$ |
[0,6] |
$2^{28}\cdot 13^{5}$ |
$2$ |
$14.6739280969$ |
$50.22486195702819$ |
|
|
? |
$C_2\wr D_6$ (as 12T193) |
trivial |
$4$ |
$5$ |
$557.084952459$ |
| 12.0.123952890380288.2 |
$x^{12} - 6 x^{10} + 18 x^{8} - 28 x^{6} + 40 x^{4} - 16 x^{2} + 8$ |
$12$ |
[0,6] |
$2^{27}\cdot 31^{4}$ |
$2$ |
$14.943008891$ |
$50.177655376356505$ |
|
|
|
$C_2\wr D_6$ (as 12T193) |
trivial |
$4$ |
$5$ |
$289.323120397$ |
| 12.0.123952890380288.8 |
$x^{12} - 6 x^{10} + 18 x^{8} - 20 x^{6} - 8 x^{4} + 16 x^{2} + 8$ |
$12$ |
[0,6] |
$2^{27}\cdot 31^{4}$ |
$2$ |
$14.943008891$ |
$50.177655376356505$ |
|
|
|
$C_2\wr D_6$ (as 12T193) |
trivial |
$4$ |
$5$ |
$252.876365574$ |
