| 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 |
| 12.12.519708953453125.1 |
$x^{12} - x^{11} - 12 x^{10} + 11 x^{9} + 46 x^{8} - 33 x^{7} - 71 x^{6} + 33 x^{5} + 46 x^{4} - 11 x^{3} - 12 x^{2} + x + 1$ |
$12$ |
[12,0] |
$5^{6}\cdot 541\cdot 7841^{2}$ |
$3$ |
$16.8388857343$ |
$4605.421261947706$ |
|
|
? |
$S_4^2:D_4$ (as 12T260) |
trivial |
$2$ |
$11$ |
$1603.96732323$ |
| 12.12.551709470703125.1 |
$x^{12} - x^{11} - 12 x^{10} + 11 x^{9} + 54 x^{8} - 43 x^{7} - 113 x^{6} + 71 x^{5} + 110 x^{4} - 46 x^{3} - 40 x^{2} + 8 x + 1$ |
$12$ |
[12,0] |
$5^{9}\cdot 7^{10}$ |
$2$ |
$16.9229421535$ |
$16.9229421535458$ |
|
✓ |
✓ |
$C_{12}$ (as 12T1) |
trivial |
$2$ |
$11$ |
$1656.08671936$ |
| 12.12.600281227113989.1 |
$x^{12} - 2 x^{11} - 11 x^{10} + 23 x^{9} + 37 x^{8} - 80 x^{7} - 53 x^{6} + 114 x^{5} + 32 x^{4} - 64 x^{3} - 4 x^{2} + 9 x - 1$ |
$12$ |
[12,0] |
$1709\cdot 592661^{2}$ |
$2$ |
$17.0423532677$ |
$31825.424569045423$ |
|
|
✓ |
$C_2^6.S_6$ (as 12T293) |
trivial |
$2$ |
$11$ |
$1736.26184583$ |
| 12.12.637026957477253.1 |
$x^{12} - x^{11} - 12 x^{10} + 8 x^{9} + 51 x^{8} - 20 x^{7} - 89 x^{6} + 23 x^{5} + 64 x^{4} - 13 x^{3} - 17 x^{2} + 3 x + 1$ |
$12$ |
[12,0] |
$7^{8}\cdot 181^{2}\cdot 3373$ |
$3$ |
$17.1269416288$ |
$2859.2106404242827$ |
|
|
✓ |
$D_4\wr C_3$ (as 12T222) |
trivial |
$2$ |
$11$ |
$1807.66404671$ |
| 12.12.669346477420869.1 |
$x^{12} - x^{11} - 12 x^{10} + 10 x^{9} + 50 x^{8} - 34 x^{7} - 87 x^{6} + 51 x^{5} + 61 x^{4} - 33 x^{3} - 12 x^{2} + 8 x - 1$ |
$12$ |
[12,0] |
$3^{3}\cdot 103^{2}\cdot 1327^{3}$ |
$3$ |
$17.1977216377$ |
$1386.3968786420157$ |
|
|
✓ |
$C_3\wr S_4$ (as 12T231) |
trivial |
$2$ |
$11$ |
$1861.72842337$ |
| 12.12.696248958578125.1 |
$x^{12} - 12 x^{10} + 51 x^{8} - 2 x^{7} - 94 x^{6} + 12 x^{5} + 74 x^{4} - 20 x^{3} - 19 x^{2} + 9 x - 1$ |
$12$ |
[12,0] |
$5^{6}\cdot 241\cdot 3329\cdot 55541$ |
$4$ |
$17.2542881493$ |
$472016.5958364176$ |
|
|
? |
$S_6\wr C_2$ (as 12T299) |
trivial |
$2$ |
$11$ |
$1891.1990811$ |
| 12.12.756680642578125.1 |
$x^{12} - 12 x^{10} - x^{9} + 54 x^{8} + 9 x^{7} - 112 x^{6} - 27 x^{5} + 105 x^{4} + 31 x^{3} - 36 x^{2} - 12 x + 1$ |
$12$ |
[12,0] |
$3^{18}\cdot 5^{9}$ |
$2$ |
$17.3743827793$ |
$17.374382779324037$ |
|
✓ |
✓ |
$C_{12}$ (as 12T1) |
trivial |
$2$ |
$11$ |
$2075.03148059$ |
| 12.12.803483858453125.1 |
$x^{12} - 13 x^{10} + 55 x^{8} - 2 x^{7} - 99 x^{6} + 8 x^{5} + 76 x^{4} - 9 x^{3} - 20 x^{2} + 3 x + 1$ |
$12$ |
[12,0] |
$5^{6}\cdot 601\cdot 85562341$ |
$3$ |
$17.4614952321$ |
$507064.921587956$ |
|
|
? |
$S_6\wr C_2$ (as 12T299) |
trivial |
$2$ |
$11$ |
$2069.99588561$ |
| 12.12.843466573910016.1 |
$x^{12} - 11 x^{10} + 44 x^{8} - 78 x^{6} + 60 x^{4} - 16 x^{2} + 1$ |
$12$ |
[12,0] |
$2^{12}\cdot 3^{6}\cdot 7^{10}$ |
$3$ |
$17.5323038886$ |
$17.532303888591755$ |
|
✓ |
✓ |
$C_6\times C_2$ (as 12T2) |
trivial |
$2$ |
$11$ |
$2121.69295548$ |
| 12.12.870852093010133.1 |
$x^{12} - x^{11} - 13 x^{10} + 15 x^{9} + 55 x^{8} - 70 x^{7} - 85 x^{6} + 115 x^{5} + 40 x^{4} - 50 x^{3} - 13 x^{2} + 4 x + 1$ |
$12$ |
[12,0] |
$13^{10}\cdot 6317$ |
$2$ |
$17.5790485938$ |
$673.8163818683267$ |
|
|
? |
$C_2\wr C_6$ (as 12T134) |
trivial |
$2$ |
$11$ |
$2163.5383357$ |
| 12.12.887040302925757.1 |
$x^{12} - x^{11} - 11 x^{10} + 10 x^{9} + 43 x^{8} - 33 x^{7} - 75 x^{6} + 45 x^{5} + 58 x^{4} - 25 x^{3} - 17 x^{2} + 5 x + 1$ |
$12$ |
[12,0] |
$79^{2}\cdot 613\cdot 15227^{2}$ |
$3$ |
$17.6060506145$ |
$27155.071883535864$ |
|
|
✓ |
$C_2^6.S_6$ (as 12T293) |
trivial |
$2$ |
$11$ |
$2179.13569124$ |
| 12.12.913378856890625.1 |
$x^{12} - x^{11} - 18 x^{10} + 8 x^{9} + 95 x^{8} - 14 x^{7} - 165 x^{6} + 23 x^{5} + 110 x^{4} - 17 x^{3} - 24 x^{2} + 2 x + 1$ |
$12$ |
[12,0] |
$5^{6}\cdot 3881^{3}$ |
$2$ |
$17.6490329067$ |
$139.30183056945089$ |
|
|
? |
$\SOPlus(4,2)$ (as 12T35) |
trivial |
$2$ |
$11$ |
$2191.75630691$ |
| 12.12.1037754255015625.1 |
$x^{12} - 2 x^{11} - 12 x^{10} + 19 x^{9} + 49 x^{8} - 57 x^{7} - 82 x^{6} + 72 x^{5} + 53 x^{4} - 40 x^{3} - 9 x^{2} + 8 x - 1$ |
$12$ |
[12,0] |
$5^{6}\cdot 7^{8}\cdot 41\cdot 281$ |
$4$ |
$17.8377967136$ |
$878.2714873461533$ |
|
|
? |
$C_2\wr C_6$ (as 12T134) |
trivial |
$2$ |
$11$ |
$2388.20102939$ |
| 12.12.1178849444515625.1 |
$x^{12} - 3 x^{11} - 9 x^{10} + 30 x^{9} + 23 x^{8} - 99 x^{7} - 11 x^{6} + 126 x^{5} - 9 x^{4} - 63 x^{3} + 5 x^{2} + 9 x - 1$ |
$12$ |
[12,0] |
$5^{6}\cdot 3881^{2}\cdot 5009$ |
$3$ |
$18.0283035532$ |
$9858.988031233226$ |
|
|
? |
$S_4^2:D_4$ (as 12T260) |
trivial |
$2$ |
$11$ |
$2557.73968274$ |
| 12.12.1272443408263937.1 |
$x^{12} - 2 x^{11} - 11 x^{10} + 18 x^{9} + 37 x^{8} - 52 x^{7} - 51 x^{6} + 58 x^{5} + 32 x^{4} - 24 x^{3} - 9 x^{2} + 3 x + 1$ |
$12$ |
[12,0] |
$7^{8}\cdot 13^{2}\cdot 29^{2}\cdot 1553$ |
$4$ |
$18.1434500334$ |
$2799.98107721201$ |
|
|
✓ |
$D_4\wr C_3$ (as 12T222) |
trivial |
$2$ |
$11$ |
$2653.8931265$ |
| 12.12.1278540355140625.1 |
$x^{12} - 2 x^{11} - 11 x^{10} + 20 x^{9} + 43 x^{8} - 67 x^{7} - 71 x^{6} + 90 x^{5} + 40 x^{4} - 49 x^{3} - x^{2} + 7 x - 1$ |
$12$ |
[12,0] |
$5^{6}\cdot 29^{3}\cdot 61\cdot 55001$ |
$4$ |
$18.1506787411$ |
$22056.378782565374$ |
|
|
✓ |
$S_3\wr D_4$ (as 12T274) |
trivial |
$2$ |
$11$ |
$2706.31561469$ |
| 12.12.1306484927252973.1 |
$x^{12} - x^{11} - 12 x^{10} + 12 x^{9} + 53 x^{8} - 53 x^{7} - 103 x^{6} + 103 x^{5} + 79 x^{4} - 79 x^{3} - 12 x^{2} + 12 x + 1$ |
$12$ |
[12,0] |
$3^{6}\cdot 13^{11}$ |
$2$ |
$18.1834114927$ |
$18.18341149267149$ |
|
✓ |
✓ |
$C_{12}$ (as 12T1) |
trivial |
$2$ |
$11$ |
$2784.79884663$ |
| 12.12.1356520905953125.1 |
$x^{12} - x^{11} - 16 x^{10} + 20 x^{9} + 60 x^{8} - 69 x^{7} - 79 x^{6} + 88 x^{5} + 35 x^{4} - 45 x^{3} - x^{2} + 7 x - 1$ |
$12$ |
[12,0] |
$5^{6}\cdot 11^{4}\cdot 181^{3}$ |
$3$ |
$18.2404496882$ |
$148.79422637191786$ |
|
|
? |
$\SOPlus(4,2)$ (as 12T35) |
trivial |
$2$ |
$11$ |
$2887.78342518$ |
| 12.12.1377319619634049.1 |
$x^{12} - x^{11} - 16 x^{10} + 11 x^{9} + 83 x^{8} - 19 x^{7} - 175 x^{6} - 27 x^{5} + 135 x^{4} + 60 x^{3} - 13 x^{2} - 9 x - 1$ |
$12$ |
[12,0] |
$7^{8}\cdot 13^{2}\cdot 29^{2}\cdot 41^{2}$ |
$4$ |
$18.2635933109$ |
$454.9475146044758$ |
|
|
? |
$C_2^2\wr C_3$ (as 12T90) |
trivial |
$2$ |
$11$ |
$2801.42243472$ |
| 12.12.1558117876000000.1 |
$x^{12} - 3 x^{11} - 9 x^{10} + 25 x^{9} + 31 x^{8} - 70 x^{7} - 47 x^{6} + 84 x^{5} + 29 x^{4} - 43 x^{3} - 4 x^{2} + 8 x - 1$ |
$12$ |
[12,0] |
$2^{8}\cdot 5^{6}\cdot 7^{2}\cdot 19^{4}\cdot 61$ |
$5$ |
$18.4522795648$ |
$522.261490781773$ |
|
|
✓ |
$A_4^2:D_4$ (as 12T208) |
trivial |
$2$ |
$11$ |
$3038.40386267$ |
| 12.12.1644873805328125.1 |
$x^{12} - 5 x^{11} - 2 x^{10} + 43 x^{9} - 35 x^{8} - 122 x^{7} + 160 x^{6} + 120 x^{5} - 225 x^{4} - 6 x^{3} + 90 x^{2} - 21 x + 1$ |
$12$ |
[12,0] |
$5^{6}\cdot 29^{3}\cdot 311\cdot 13879$ |
$4$ |
$18.5357877896$ |
$25017.464000173957$ |
|
|
✓ |
$S_3\wr D_4$ (as 12T274) |
trivial |
$2$ |
$11$ |
$3169.83410033$ |
| 12.12.1816178885163041.1 |
$x^{12} - 3 x^{11} - 8 x^{10} + 25 x^{9} + 22 x^{8} - 67 x^{7} - 30 x^{6} + 73 x^{5} + 22 x^{4} - 31 x^{3} - 8 x^{2} + 4 x + 1$ |
$12$ |
[12,0] |
$7^{8}\cdot 71\cdot 281\cdot 15791$ |
$4$ |
$18.6894513283$ |
$64951.00036926973$ |
|
|
✓ |
$S_4\wr C_3$ (as 12T292) |
trivial |
$2$ |
$11$ |
$3332.42513875$ |
| 12.12.1871944227828125.1 |
$x^{12} - 3 x^{11} - 9 x^{10} + 30 x^{9} + 15 x^{8} - 77 x^{7} - x^{6} + 76 x^{5} - 10 x^{4} - 30 x^{3} + 6 x^{2} + 4 x - 1$ |
$12$ |
[12,0] |
$5^{6}\cdot 11^{2}\cdot 31^{2}\cdot 101^{3}$ |
$4$ |
$18.7366125171$ |
$414.975902914856$ |
|
|
✓ |
$D_6\wr C_2$ (as 12T125) |
trivial |
$2$ |
$11$ |
$3295.71507174$ |
| 12.12.1952518144000000.1 |
$x^{12} - 4 x^{11} - 6 x^{10} + 32 x^{9} + 12 x^{8} - 86 x^{7} - 14 x^{6} + 92 x^{5} + 10 x^{4} - 40 x^{3} - 5 x^{2} + 6 x + 1$ |
$12$ |
[12,0] |
$2^{18}\cdot 5^{6}\cdot 271\cdot 1759$ |
$4$ |
$18.8025285386$ |
$4366.641730208697$ |
|
|
? |
$S_3\wr C_2^2$ (as 12T261) |
trivial |
$2$ |
$11$ |
$3404.04609138$ |
| 12.12.2093934172250000.1 |
$x^{12} - 13 x^{10} - x^{9} + 56 x^{8} + 9 x^{7} - 102 x^{6} - 25 x^{5} + 79 x^{4} + 28 x^{3} - 20 x^{2} - 10 x - 1$ |
$12$ |
[12,0] |
$2^{4}\cdot 5^{6}\cdot 89^{3}\cdot 109^{2}$ |
$4$ |
$18.9124119328$ |
$764.10141024132$ |
|
|
✓ |
$C_3\wr D_4$ (as 12T167) |
trivial |
$2$ |
$11$ |
$4234.21169932$ |
| 12.12.2154038935140625.1 |
$x^{12} - x^{11} - 16 x^{10} + 11 x^{9} + 79 x^{8} - 29 x^{7} - 145 x^{6} + 25 x^{5} + 107 x^{4} - 2 x^{3} - 27 x^{2} - 3 x + 1$ |
$12$ |
[12,0] |
$5^{6}\cdot 13^{10}$ |
$2$ |
$18.9570663049$ |
$18.957066304919827$ |
|
✓ |
? |
$C_6\times C_2$ (as 12T2) |
trivial |
$2$ |
$11$ |
$3586.95404679$ |
| 12.12.2196839556078125.1 |
$x^{12} - x^{11} - 17 x^{10} + 8 x^{9} + 79 x^{8} - 32 x^{7} - 126 x^{6} + 37 x^{5} + 81 x^{4} - 15 x^{3} - 19 x^{2} + 2 x + 1$ |
$12$ |
[12,0] |
$5^{6}\cdot 7^{8}\cdot 29^{3}$ |
$3$ |
$18.9881736599$ |
$44.06387579995631$ |
|
|
? |
$D_4 \times C_3$ (as 12T14) |
trivial |
$2$ |
$11$ |
$3668.73449811$ |
| 12.12.2436167488251136.1 |
$x^{12} - 5 x^{11} - 3 x^{10} + 49 x^{9} - 43 x^{8} - 140 x^{7} + 211 x^{6} + 114 x^{5} - 299 x^{4} + 37 x^{3} + 116 x^{2} - 36 x - 1$ |
$12$ |
[12,0] |
$2^{8}\cdot 37^{6}\cdot 3709$ |
$3$ |
$19.1525054791$ |
$588.0522858389772$ |
|
|
? |
$C_2\wr S_3$ (as 12T135) |
trivial |
$2$ |
$11$ |
$3912.32151276$ |
| 12.12.2474477972015625.1 |
$x^{12} - 17 x^{10} - 11 x^{9} + 73 x^{8} + 62 x^{7} - 102 x^{6} - 87 x^{5} + 52 x^{4} + 43 x^{3} - 5 x^{2} - 7 x - 1$ |
$12$ |
[12,0] |
$3^{8}\cdot 5^{6}\cdot 17^{6}$ |
$3$ |
$19.1774252815$ |
$39.890652095882146$ |
|
|
? |
$C_6\times S_3$ (as 12T18) |
trivial |
$2$ |
$11$ |
$4029.90861439$ |
| 12.12.2535525376000000.1 |
$x^{12} - 2 x^{11} - 14 x^{10} + 22 x^{9} + 67 x^{8} - 64 x^{7} - 138 x^{6} + 48 x^{5} + 109 x^{4} + 6 x^{3} - 28 x^{2} - 10 x - 1$ |
$12$ |
[12,0] |
$2^{16}\cdot 5^{6}\cdot 19^{5}$ |
$3$ |
$19.2164132691$ |
$82.57140271324806$ |
|
|
? |
$C_6\wr C_2$ (as 12T42) |
trivial |
$2$ |
$11$ |
$4759.10509283$ |
| 12.12.2755304652953125.1 |
$x^{12} - 3 x^{11} - 11 x^{10} + 35 x^{9} + 37 x^{8} - 140 x^{7} - 19 x^{6} + 217 x^{5} - 79 x^{4} - 88 x^{3} + 58 x^{2} - 6 x - 1$ |
$12$ |
[12,0] |
$5^{6}\cdot 7^{8}\cdot 13^{2}\cdot 181$ |
$4$ |
$19.349992549487943$ |
$396.91239279873855$ |
|
|
? |
$C_2\wr C_6$ (as 12T134) |
trivial |
$2$ |
$11$ |
$4164.646983587647$ |
| 12.12.2811266206890625.1 |
$x^{12} - 3 x^{11} - 9 x^{10} + 28 x^{9} + 24 x^{8} - 87 x^{7} - 19 x^{6} + 107 x^{5} + 2 x^{4} - 52 x^{3} + 8 x + 1$ |
$12$ |
[12,0] |
$5^{6}\cdot 11^{2}\cdot 38561^{2}$ |
$3$ |
$19.3824422061$ |
$1456.3155564643262$ |
|
|
? |
$S_4\wr C_2$ (as 12T203) |
trivial |
$2$ |
$11$ |
$4466.4963181$ |
| 12.12.2950947586890625.1 |
$x^{12} - 2 x^{11} - 16 x^{10} + 12 x^{9} + 74 x^{8} - 10 x^{7} - 119 x^{6} - 10 x^{5} + 74 x^{4} + 12 x^{3} - 16 x^{2} - 2 x + 1$ |
$12$ |
[12,0] |
$5^{6}\cdot 7^{8}\cdot 181^{2}$ |
$3$ |
$19.4609240614$ |
$110.08369108484274$ |
|
|
? |
$C_2^2 \times A_4$ (as 12T25) |
trivial |
$2$ |
$11$ |
$4267.13554712$ |
| 12.12.2992691444000000.1 |
$x^{12} - x^{11} - 15 x^{10} + 7 x^{9} + 83 x^{8} + 4 x^{7} - 197 x^{6} - 104 x^{5} + 151 x^{4} + 167 x^{3} + 52 x^{2} + 2 x - 1$ |
$12$ |
[12,0] |
$2^{8}\cdot 5^{6}\cdot 19^{4}\cdot 5741$ |
$4$ |
$19.4837177026$ |
$1914.9958626540792$ |
|
|
✓ |
$A_4^2:D_4$ (as 12T208) |
trivial |
$2$ |
$11$ |
$4298.56458855$ |
| 12.12.3111223068921856.1 |
$x^{12} - 2 x^{11} - 13 x^{10} + 32 x^{9} + 31 x^{8} - 102 x^{7} - 22 x^{6} + 114 x^{5} + 13 x^{4} - 46 x^{3} - 10 x^{2} + 4 x + 1$ |
$12$ |
[12,0] |
$2^{12}\cdot 7^{10}\cdot 2689$ |
$3$ |
$19.54688670899614$ |
$524.8966045985147$ |
|
|
? |
$C_2\wr C_6$ (as 12T134) |
trivial |
$2$ |
$11$ |
$4431.635320173742$ |
| 12.12.3185030335661329.1 |
$x^{12} - 4 x^{11} - 6 x^{10} + 38 x^{9} + 2 x^{8} - 134 x^{7} + 49 x^{6} + 213 x^{5} - 104 x^{4} - 146 x^{3} + 60 x^{2} + 33 x - 1$ |
$12$ |
[12,0] |
$17^{2}\cdot 101^{2}\cdot 32869^{2}$ |
$3$ |
$19.5851152303$ |
$7512.394624884931$ |
|
|
✓ |
$C_2^5:S_6$ (as 12T285) |
trivial |
$2$ |
$11$ |
$5379.62836167$ |
| 12.12.3217569633140625.1 |
$x^{12} - x^{11} - 19 x^{10} + 18 x^{9} + 110 x^{8} - 92 x^{7} - 218 x^{6} + 155 x^{5} + 166 x^{4} - 88 x^{3} - 40 x^{2} + 8 x + 1$ |
$12$ |
[12,0] |
$3^{6}\cdot 5^{6}\cdot 7^{10}$ |
$3$ |
$19.6017116485$ |
$19.601711648537535$ |
|
✓ |
? |
$C_6\times C_2$ (as 12T2) |
trivial |
$2$ |
$11$ |
$4500.30498389$ |
| 12.12.3356038763843584.1 |
$x^{12} - 11 x^{10} + 43 x^{8} - 73 x^{6} + 53 x^{4} - 15 x^{2} + 1$ |
$12$ |
[12,0] |
$2^{12}\cdot 7^{8}\cdot 13^{2}\cdot 29^{2}$ |
$4$ |
$19.6706591941$ |
$200.9621932869232$ |
|
|
✓ |
$C_2^2\wr C_3$ (as 12T90) |
trivial |
$2$ |
$11$ |
$5196.71997359$ |
| 12.12.3408269910093056.1 |
$x^{12} - 2 x^{11} - 14 x^{10} + 23 x^{9} + 65 x^{8} - 66 x^{7} - 137 x^{6} + 40 x^{5} + 117 x^{4} + 27 x^{3} - 19 x^{2} - 9 x - 1$ |
$12$ |
[12,0] |
$2^{8}\cdot 37^{6}\cdot 5189$ |
$3$ |
$19.6959907534$ |
$695.5516115033685$ |
|
|
? |
$C_2\wr S_3$ (as 12T135) |
trivial |
$2$ |
$11$ |
$4783.02205062$ |
| 12.12.3441144995703125.1 |
$x^{12} - 3 x^{11} - 11 x^{10} + 40 x^{9} + 23 x^{8} - 161 x^{7} + 56 x^{6} + 208 x^{5} - 168 x^{4} - 16 x^{3} + 34 x^{2} - 3 x - 1$ |
$12$ |
[12,0] |
$5^{8}\cdot 29^{3}\cdot 601^{2}$ |
$3$ |
$19.7117529614$ |
$441.4319244223498$ |
|
|
? |
$D_6\wr C_2$ (as 12T125) |
trivial |
$2$ |
$11$ |
$5038.29617221$ |
| 12.12.3545107547544689.1 |
$x^{12} - 3 x^{11} - 8 x^{10} + 25 x^{9} + 25 x^{8} - 73 x^{7} - 42 x^{6} + 89 x^{5} + 40 x^{4} - 39 x^{3} - 17 x^{2} + 2 x + 1$ |
$12$ |
[12,0] |
$7^{8}\cdot 1021\cdot 602309$ |
$3$ |
$19.7607057483$ |
$90744.69404605737$ |
|
|
✓ |
$S_4\wr C_3$ (as 12T292) |
trivial |
$2$ |
$11$ |
$5055.26910688$ |
| 12.12.3783372458265625.1 |
$x^{12} - 3 x^{11} - 13 x^{10} + 47 x^{9} + 42 x^{8} - 249 x^{7} + 46 x^{6} + 514 x^{5} - 361 x^{4} - 319 x^{3} + 379 x^{2} - 80 x - 5$ |
$12$ |
[12,0] |
$5^{6}\cdot 263^{2}\cdot 1871^{2}$ |
$3$ |
$19.8681116329$ |
$1568.5550675701506$ |
|
|
? |
$S_6\times C_2$ (as 12T219) |
trivial |
$2$ |
$11$ |
$5647.73665833$ |
| 12.12.3823196224000000.1 |
$x^{12} - 11 x^{10} + 42 x^{8} - 67 x^{6} + 45 x^{4} - 12 x^{2} + 1$ |
$12$ |
[12,0] |
$2^{12}\cdot 5^{6}\cdot 59^{2}\cdot 131^{2}$ |
$4$ |
$19.8854557555$ |
$721.0707811856453$ |
|
|
✓ |
$S_4\wr C_2$ (as 12T203) |
trivial |
$2$ |
$11$ |
$4925.67376296$ |
| 12.12.3958882310427733.1 |
$x^{12} - 4 x^{11} - 10 x^{10} + 53 x^{9} + 9 x^{8} - 205 x^{7} + 105 x^{6} + 204 x^{5} - 101 x^{4} - 90 x^{3} + 22 x^{2} + 16 x + 1$ |
$12$ |
[12,0] |
$13^{11}\cdot 47^{2}$ |
$2$ |
$19.9433318554$ |
$71.97201612445268$ |
|
|
? |
$C_4\times A_4$ (as 12T29) |
trivial |
$2$ |
$11$ |
$5234.40251791$ |
| 12.12.3989681137476125.1 |
$x^{12} - x^{11} - 17 x^{10} + 13 x^{9} + 96 x^{8} - 53 x^{7} - 212 x^{6} + 62 x^{5} + 175 x^{4} - 15 x^{3} - 44 x^{2} - 5 x + 1$ |
$12$ |
[12,0] |
$5^{3}\cdot 7^{8}\cdot 13^{2}\cdot 181^{2}$ |
$4$ |
$19.9562153717$ |
$396.91239279873855$ |
|
|
? |
$C_2\wr C_6$ (as 12T142) |
trivial |
$2$ |
$11$ |
$5321.42595657$ |
| 12.12.4238977831849489.1 |
$x^{12} - 3 x^{11} - 11 x^{10} + 30 x^{9} + 39 x^{8} - 87 x^{7} - 59 x^{6} + 87 x^{5} + 39 x^{4} - 30 x^{3} - 11 x^{2} + 3 x + 1$ |
$12$ |
[12,0] |
$17^{2}\cdot 19^{4}\cdot 103^{4}$ |
$3$ |
$20.0572672908$ |
$182.39791665476884$ |
|
|
? |
$C_4^2:D_6$ (as 12T95) |
trivial |
$2$ |
$11$ |
$5464.79790174$ |
| 12.12.4239150758955121.1 |
$x^{12} - 5 x^{11} - 3 x^{10} + 42 x^{9} - 25 x^{8} - 102 x^{7} + 97 x^{6} + 68 x^{5} - 70 x^{4} - 21 x^{3} + 17 x^{2} + 3 x - 1$ |
$12$ |
[12,0] |
$8069^{4}$ |
$1$ |
$20.0573354751$ |
$89.8276126811795$ |
|
|
? |
$C_4^2:S_3$ (as 12T62) |
trivial |
$2$ |
$11$ |
$5381.67911396$ |
| 12.12.4539981040386048.1 |
$x^{12} - 4 x^{11} - 9 x^{10} + 48 x^{9} + 10 x^{8} - 186 x^{7} + 91 x^{6} + 232 x^{5} - 210 x^{4} - 8 x^{3} + 43 x^{2} - 6 x - 1$ |
$12$ |
[12,0] |
$2^{16}\cdot 3^{3}\cdot 37^{6}$ |
$3$ |
$20.1722574977$ |
$33.448615700902295$ |
|
|
? |
$(C_6\times C_2):C_2$ (as 12T15) |
trivial |
$2$ |
$11$ |
$6578.32577119$ |
| 12.12.4555439265953125.1 |
$x^{12} - 6 x^{11} + 4 x^{10} + 35 x^{9} - 53 x^{8} - 64 x^{7} + 137 x^{6} + 26 x^{5} - 124 x^{4} + 27 x^{3} + 29 x^{2} - 12 x + 1$ |
$12$ |
[12,0] |
$5^{6}\cdot 11\cdot 71\cdot 139^{4}$ |
$4$ |
$20.177972310981808$ |
$1676.8223447898963$ |
|
|
✓ |
$A_4^2:D_4$ (as 12T208) |
trivial |
$2$ |
$11$ |
$6073.867680354858$ |
| 12.12.4638867626953125.1 |
$x^{12} - 6 x^{11} + 4 x^{10} + 35 x^{9} - 55 x^{8} - 56 x^{7} + 136 x^{6} + x^{5} - 105 x^{4} + 40 x^{3} + 14 x^{2} - 9 x + 1$ |
$12$ |
[12,0] |
$3^{6}\cdot 5^{11}\cdot 19^{4}$ |
$3$ |
$20.208511771$ |
$33.01109510676244$ |
|
|
? |
$S_3 \times C_4$ (as 12T11) |
trivial |
$2$ |
$11$ |
$6666.76699087$ |
