| 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 |
| 12.0.117236328125.1 |
$x^{12} - 4 x^{11} + 9 x^{10} - 20 x^{9} + 40 x^{8} - 64 x^{7} + 81 x^{6} - 81 x^{5} + 65 x^{4} - 40 x^{3} + 19 x^{2} - 6 x + 1$ |
$12$ |
[0,6] |
$5^{11}\cdot 7^{4}$ |
$2$ |
$8.36415073054$ |
$11.568352777429151$ |
|
|
? |
$S_3 \times C_4$ (as 12T11) |
trivial |
$10$ |
$5$ |
$11.9978872283$ |
| 12.0.200000000000.1 |
$x^{12} - 4 x^{11} + 9 x^{10} - 15 x^{9} + 15 x^{8} + x^{7} - 19 x^{6} + 14 x^{5} + 5 x^{4} - 10 x^{3} + 4 x^{2} - x + 1$ |
$12$ |
[0,6] |
$2^{12}\cdot 5^{11}$ |
$2$ |
$8.74485272221$ |
$12.367089320707036$ |
|
|
? |
$S_3 \times C_4$ (as 12T11) |
trivial |
$10$ |
$5$ |
$16.6769530035$ |
| 12.0.546564453125.1 |
$x^{12} - x^{11} + x^{10} - x^{8} - 2 x^{7} + 2 x^{6} - 3 x^{5} + x^{4} + x^{3} + x^{2} + 1$ |
$12$ |
[0,6] |
$5^{9}\cdot 23^{4}$ |
$2$ |
$9.50904235709$ |
$16.03582917757843$ |
|
|
✓ |
$S_3 \times C_4$ (as 12T11) |
trivial |
$10$ |
$5$ |
$32.3656237465$ |
| 12.0.1012500000000.1 |
$x^{12} - 3 x^{11} + 11 x^{10} - 25 x^{9} + 55 x^{8} - 88 x^{7} + 119 x^{6} - 118 x^{5} + 95 x^{4} - 55 x^{3} + 26 x^{2} - 8 x + 1$ |
$12$ |
[0,6] |
$2^{8}\cdot 3^{4}\cdot 5^{11}$ |
$3$ |
$10.0103574601$ |
$12.021808208412303$ |
|
|
? |
$S_3 \times C_4$ (as 12T11) |
trivial |
$10$ |
$5$ |
$46.6043886559$ |
| 12.0.1037970703125.1 |
$x^{12} - 2 x^{9} + 4 x^{6} - 3 x^{3} + 1$ |
$12$ |
[0,6] |
$3^{12}\cdot 5^{9}$ |
$2$ |
$10.0311045746$ |
$12.046724184927836$ |
|
|
✓ |
$S_3 \times C_4$ (as 12T11) |
trivial |
$10$ |
$5$ |
$46.5914285344$ |
| 12.0.1200500000000.1 |
$x^{12} - 2 x^{11} + 2 x^{10} - x^{9} + 5 x^{8} + 2 x^{7} - 3 x^{6} + 2 x^{5} + 5 x^{4} + 9 x^{3} + 7 x^{2} + 3 x + 1$ |
$12$ |
[0,6] |
$2^{8}\cdot 5^{9}\cdot 7^{4}$ |
$3$ |
$10.1534471757$ |
$14.043106421634382$ |
|
|
? |
$S_3 \times C_4$ (as 12T11) |
trivial |
$10$ |
$5$ |
$44.4179208274$ |
| 12.0.1803751953125.3 |
$x^{12} - x^{10} - x^{9} + x^{8} - 3 x^{7} + 2 x^{5} + 3 x^{4} - 2 x^{3} + x^{2} - x + 1$ |
$12$ |
[0,6] |
$5^{9}\cdot 31^{4}$ |
$2$ |
$10.5038392776$ |
$18.616942190179014$ |
|
|
✓ |
$S_3 \times C_4$ (as 12T11) |
trivial |
$10$ |
$5$ |
$55.7455420814$ |
| 12.4.5744580078125.1 |
$x^{12} - 2 x^{11} + x^{10} + 5 x^{9} - 12 x^{7} - x^{6} + 18 x^{5} - 20 x^{4} - 5 x^{3} + 16 x^{2} - 7 x + 1$ |
$12$ |
[4,4] |
$5^{11}\cdot 7^{6}$ |
$2$ |
$11.5683527774$ |
$11.568352777429151$ |
|
|
? |
$S_3 \times C_4$ (as 12T11) |
trivial |
$2$ |
$7$ |
$41.9630859692$ |
| 12.0.7320500000000.2 |
$x^{12} - x^{11} + 2 x^{9} - 3 x^{8} + 2 x^{7} + 3 x^{6} - 8 x^{5} + 7 x^{4} + 4 x^{3} + 2 x^{2} + x + 1$ |
$12$ |
[0,6] |
$2^{8}\cdot 5^{9}\cdot 11^{4}$ |
$3$ |
$11.8044311122$ |
$17.603965534028475$ |
|
|
? |
$S_3 \times C_4$ (as 12T11) |
trivial |
$10$ |
$5$ |
$141.9815003$ |
| 12.4.9112500000000.1 |
$x^{12} - 6 x^{11} + 14 x^{10} - 15 x^{9} + 5 x^{8} + 4 x^{7} - 9 x^{6} + 16 x^{5} - 15 x^{4} + 5 x^{3} - x^{2} + x + 1$ |
$12$ |
[4,4] |
$2^{8}\cdot 3^{6}\cdot 5^{11}$ |
$3$ |
$12.0218082084$ |
$12.021808208412303$ |
|
|
? |
$S_3 \times C_4$ (as 12T11) |
trivial |
$2$ |
$7$ |
$56.4359851616$ |
| 12.4.9341736328125.1 |
$x^{12} - 6 x^{11} + 15 x^{10} - 11 x^{9} - 27 x^{8} + 69 x^{7} - 40 x^{6} - 45 x^{5} + 57 x^{4} + 8 x^{3} - 24 x^{2} - 3 x + 1$ |
$12$ |
[4,4] |
$3^{14}\cdot 5^{9}$ |
$2$ |
$12.0467241849$ |
$12.046724184927836$ |
|
|
? |
$S_3 \times C_4$ (as 12T11) |
trivial |
$2$ |
$7$ |
$56.4202909911$ |
| 12.4.12800000000000.1 |
$x^{12} - 2 x^{11} + x^{10} - 10 x^{8} + 18 x^{7} - 26 x^{6} + 8 x^{5} + 15 x^{4} - 20 x^{3} + 6 x^{2} + 8 x - 4$ |
$12$ |
[4,4] |
$2^{18}\cdot 5^{11}$ |
$2$ |
$12.3670893207$ |
$12.367089320707036$ |
|
|
? |
$S_3 \times C_4$ (as 12T11) |
trivial |
$2$ |
$7$ |
$78.0328195859$ |
| 12.0.13213283203125.1 |
$x^{12} - 4 x^{11} + 5 x^{10} - 9 x^{8} + 30 x^{7} - 41 x^{6} - 20 x^{5} + 106 x^{4} - 95 x^{3} + 30 x^{2} + x + 1$ |
$12$ |
[0,6] |
$3^{4}\cdot 5^{9}\cdot 17^{4}$ |
$3$ |
$12.399882274413569$ |
$23.87880512635518$ |
|
|
? |
$S_3 \times C_4$ (as 12T11) |
trivial |
$10$ |
$5$ |
$205.6035190856011$ |
| 12.0.25949267578125.1 |
$x^{12} - 5 x^{9} + 15 x^{6} - 15 x^{3} + 5$ |
$12$ |
[0,6] |
$3^{12}\cdot 5^{11}$ |
$2$ |
$13.1172790833$ |
$15.753025202513207$ |
|
|
? |
$S_3 \times C_4$ (as 12T11) |
trivial |
$10$ |
$5$ |
$277.288481269$ |
| 12.0.39357658203125.1 |
$x^{12} - 4 x^{11} + 7 x^{10} - 10 x^{9} + 9 x^{8} - 8 x^{7} + 21 x^{6} - 14 x^{5} + 6 x^{4} - 31 x^{3} + 16 x^{2} + 7 x + 1$ |
$12$ |
[0,6] |
$5^{9}\cdot 67^{4}$ |
$2$ |
$13.580604576842257$ |
$27.369376545007917$ |
|
|
? |
$S_3 \times C_4$ (as 12T11) |
$[2]$ |
$10$ |
$5$ |
$172.1554240836862$ |
| 12.0.43436029431808.1 |
$x^{12} - 6 x^{11} + 19 x^{10} - 39 x^{9} + 63 x^{8} - 77 x^{7} + 71 x^{6} - 44 x^{5} + 39 x^{4} - 10 x^{3} + 8 x^{2} + x + 1$ |
$12$ |
[0,6] |
$2^{12}\cdot 13^{9}$ |
$2$ |
$13.692650084$ |
$19.364331453687083$ |
|
|
? |
$S_3 \times C_4$ (as 12T11) |
trivial |
$2$ |
$5$ |
$54.6840897429$ |
| 12.4.51200000000000.2 |
$x^{12} + 10 x^{6} - 20 x^{2} + 5$ |
$12$ |
[4,4] |
$2^{20}\cdot 5^{11}$ |
$2$ |
$13.8815884105$ |
$17.489705444423358$ |
|
|
|
$S_3 \times C_4$ (as 12T11) |
trivial |
$2$ |
$7$ |
$197.800498269$ |
| 12.4.58824500000000.1 |
$x^{12} - x^{11} - 2 x^{10} + 8 x^{9} - 5 x^{8} - 14 x^{7} + 33 x^{6} + 24 x^{5} - 25 x^{4} + 12 x^{3} + 18 x^{2} - 29 x - 19$ |
$12$ |
[4,4] |
$2^{8}\cdot 5^{9}\cdot 7^{6}$ |
$3$ |
$14.0431064216$ |
$14.043106421634382$ |
|
|
? |
$S_3 \times C_4$ (as 12T11) |
trivial |
$2$ |
$7$ |
$155.35343805$ |
| 12.4.85465283203125.1 |
$x^{12} - 4 x^{11} + 9 x^{10} - 10 x^{9} + 16 x^{7} - 24 x^{6} - 41 x^{5} + 45 x^{4} - 10 x^{3} - 6 x^{2} + 14 x + 1$ |
$12$ |
[4,4] |
$3^{6}\cdot 5^{11}\cdot 7^{4}$ |
$3$ |
$14.4871340275$ |
$20.036974770387825$ |
|
|
? |
$S_3 \times C_4$ (as 12T11) |
trivial |
$2$ |
$7$ |
$210.207248027$ |
| 12.0.117128000000000.2 |
$x^{12} - 2 x^{11} + 7 x^{10} - 11 x^{9} + 30 x^{8} - 13 x^{7} + 32 x^{6} + 67 x^{5} + 20 x^{4} - 11 x^{3} - 3 x^{2} + 3 x + 1$ |
$12$ |
[0,6] |
$2^{12}\cdot 5^{9}\cdot 11^{4}$ |
$3$ |
$14.872651240288148$ |
$31.366700656905365$ |
|
|
? |
$S_3 \times C_4$ (as 12T11) |
trivial |
$10$ |
$5$ |
$769.2278076585833$ |
| 12.4.118919548828125.1 |
$x^{12} - 6 x^{11} + 17 x^{10} - 22 x^{9} - 12 x^{8} + 83 x^{7} - 127 x^{6} + 83 x^{5} - 12 x^{4} - 22 x^{3} + 17 x^{2} - 6 x + 1$ |
$12$ |
[4,4] |
$3^{6}\cdot 5^{9}\cdot 17^{4}$ |
$3$ |
$14.89147686317512$ |
$23.87880512635518$ |
|
|
? |
$S_3 \times C_4$ (as 12T11) |
trivial |
$2$ |
$7$ |
$301.86432812746887$ |
| 12.0.139920500000000.1 |
$x^{12} - x^{11} - x^{10} + x^{9} + 13 x^{8} - 62 x^{7} + 89 x^{6} - 16 x^{5} - 53 x^{4} - 33 x^{3} + 198 x^{2} - 216 x + 81$ |
$12$ |
[0,6] |
$2^{8}\cdot 5^{9}\cdot 23^{4}$ |
$3$ |
$15.09466384085731$ |
$25.455292105670352$ |
|
|
? |
$S_3 \times C_4$ (as 12T11) |
$[2]$ |
$10$ |
$5$ |
$291.9505434072523$ |
| 12.4.145800000000000.1 |
$x^{12} - 4 x^{11} + 9 x^{10} - 5 x^{9} - 10 x^{8} + 21 x^{7} - 24 x^{6} - 31 x^{5} + 10 x^{4} + 15 x^{3} - 31 x^{2} - 11 x + 1$ |
$12$ |
[4,4] |
$2^{12}\cdot 3^{6}\cdot 5^{11}$ |
$3$ |
$15.1465292196$ |
$21.42042704520706$ |
|
|
? |
$S_3 \times C_4$ (as 12T11) |
trivial |
$2$ |
$7$ |
$256.4625112$ |
| 12.0.204800000000000.2 |
$x^{12} + 10 x^{10} + 35 x^{8} + 70 x^{6} + 85 x^{4} + 60 x^{2} + 20$ |
$12$ |
[0,6] |
$2^{22}\cdot 5^{11}$ |
$2$ |
$15.5815561611$ |
$17.489705444423358$ |
|
|
|
$S_3 \times C_4$ (as 12T11) |
$[2]$ |
$2$ |
$5$ |
$102.745462078$ |
| 12.0.219825939453125.1 |
$x^{12} + 2 x^{10} - 5 x^{9} + 4 x^{8} - 10 x^{7} + 23 x^{6} - 40 x^{5} + 56 x^{4} - 65 x^{3} + 60 x^{2} - 50 x + 25$ |
$12$ |
[0,6] |
$5^{9}\cdot 103^{4}$ |
$2$ |
$15.673761889267645$ |
$33.93486420206204$ |
|
|
? |
$S_3 \times C_4$ (as 12T11) |
$[2]$ |
$10$ |
$5$ |
$438.3305767013016$ |
| 12.4.233543408203125.2 |
$x^{12} - 6 x^{11} + 9 x^{10} - 6 x^{7} - 4 x^{6} + 6 x^{5} + 9 x^{2} + 6 x + 1$ |
$12$ |
[4,4] |
$3^{14}\cdot 5^{11}$ |
$2$ |
$15.7530252025$ |
$15.753025202513207$ |
|
|
? |
$S_3 \times C_4$ (as 12T11) |
trivial |
$2$ |
$7$ |
$335.784870604$ |
| 12.4.259200000000000.1 |
$x^{12} - 10 x^{10} + 35 x^{8} - 60 x^{6} + 55 x^{4} - 10 x^{2} + 5$ |
$12$ |
[4,4] |
$2^{16}\cdot 3^{4}\cdot 5^{11}$ |
$3$ |
$15.8904519628$ |
$19.083430996593624$ |
|
|
? |
$S_3 \times C_4$ (as 12T11) |
trivial |
$2$ |
$7$ |
$368.977181234$ |
| 12.0.265720500000000.3 |
$x^{12} - 2 x^{9} + 4 x^{6} - 8 x^{3} + 16$ |
$12$ |
[0,6] |
$2^{8}\cdot 3^{12}\cdot 5^{9}$ |
$3$ |
$15.9233859542$ |
$19.122982643925198$ |
|
|
? |
$S_3 \times C_4$ (as 12T11) |
trivial |
$10$ |
$5$ |
$1053.91768271$ |
| 12.4.289132595703125.1 |
$x^{12} - 2 x^{11} + 3 x^{10} - 5 x^{9} - 6 x^{8} + 6 x^{7} - 51 x^{6} + 87 x^{5} - 104 x^{4} + 172 x^{3} - 181 x^{2} + 94 x - 19$ |
$12$ |
[4,4] |
$5^{9}\cdot 23^{6}$ |
$2$ |
$16.0358291776$ |
$16.03582917757843$ |
|
|
? |
$S_3 \times C_4$ (as 12T11) |
trivial |
$2$ |
$7$ |
$330.426451282$ |
| 12.4.307328000000000.1 |
$x^{12} - 4 x^{11} + x^{10} + 14 x^{9} - 28 x^{8} + 4 x^{7} + 61 x^{6} - 68 x^{5} - 36 x^{4} + 122 x^{3} + 53 x^{2} - 60 x - 19$ |
$12$ |
[4,4] |
$2^{16}\cdot 5^{9}\cdot 7^{4}$ |
$3$ |
$16.1175927278$ |
$22.292041906603796$ |
|
|
? |
$S_3 \times C_4$ (as 12T11) |
trivial |
$2$ |
$7$ |
$456.668824888$ |
| 12.0.357012500000000.1 |
$x^{12} - x^{11} - x^{10} + 25 x^{9} - 15 x^{8} - 86 x^{7} + 141 x^{6} + 76 x^{5} - 365 x^{4} + 195 x^{3} + 244 x^{2} - 384 x + 181$ |
$12$ |
[0,6] |
$2^{8}\cdot 5^{11}\cdot 13^{4}$ |
$3$ |
$16.3201301752$ |
$25.025389399554754$ |
✓ |
|
? |
$S_3 \times C_4$ (as 12T11) |
trivial |
$10$ |
$5$ |
$1008.69816141$ |
| 12.0.458793060873472.1 |
$x^{12} - 3 x^{11} + 9 x^{10} - 27 x^{9} + 55 x^{8} - 100 x^{7} + 157 x^{6} - 185 x^{5} + 152 x^{4} - 40 x^{3} - 36 x^{2} - 9 x + 27$ |
$12$ |
[0,6] |
$2^{8}\cdot 13^{11}$ |
$2$ |
$16.6648497871$ |
$20.99639504015924$ |
|
|
|
$S_3 \times C_4$ (as 12T11) |
$[3]$ |
$2$ |
$5$ |
$295.950151185$ |
| 12.0.461760500000000.2 |
$x^{12} - 4 x^{11} + 8 x^{10} - 5 x^{9} + x^{8} + 10 x^{7} + 7 x^{6} - 8 x^{5} + 31 x^{4} - 15 x^{3} + 35 x^{2} - 25 x + 25$ |
$12$ |
[0,6] |
$2^{8}\cdot 5^{9}\cdot 31^{4}$ |
$3$ |
$16.67380551902469$ |
$29.552553617121323$ |
|
|
? |
$S_3 \times C_4$ (as 12T11) |
trivial |
$10$ |
$5$ |
$1782.1558033475317$ |
| 12.0.503060929445888.2 |
$x^{12} - 12 x^{8} + 20 x^{6} + 4 x^{4} - 8 x^{2} + 2$ |
$12$ |
[0,6] |
$2^{35}\cdot 11^{4}$ |
$2$ |
$16.7932614352$ |
$25.04381555535815$ |
|
|
? |
$S_3 \times C_4$ (as 12T11) |
trivial |
$2$ |
$5$ |
$503.341863638$ |
| 12.4.503060929445888.6 |
$x^{12} - 12 x^{8} - 20 x^{6} + 4 x^{4} + 8 x^{2} + 2$ |
$12$ |
[4,4] |
$2^{35}\cdot 11^{4}$ |
$2$ |
$16.7932614352$ |
$25.04381555535815$ |
|
|
? |
$S_3 \times C_4$ (as 12T11) |
trivial |
$2$ |
$7$ |
$775.482114835$ |
| 12.0.575195158203125.1 |
$x^{12} + x^{10} - 5 x^{9} + x^{8} - 5 x^{7} + 16 x^{6} - 10 x^{5} + 21 x^{4} - 30 x^{3} + 15 x^{2} - 25 x + 25$ |
$12$ |
[0,6] |
$5^{9}\cdot 131^{4}$ |
$2$ |
$16.981834411852024$ |
$38.2704131838469$ |
|
|
? |
$S_3 \times C_4$ (as 12T11) |
trivial |
$10$ |
$5$ |
$1244.0220590230213$ |
| 12.0.668168000000000.1 |
$x^{12} - x^{11} - 7 x^{10} + 15 x^{9} + 21 x^{8} - 60 x^{7} - 23 x^{6} + 163 x^{5} - 54 x^{4} - 240 x^{3} + 290 x^{2} - 75 x + 25$ |
$12$ |
[0,6] |
$2^{12}\cdot 5^{9}\cdot 17^{4}$ |
$3$ |
$17.195196351170477$ |
$38.99392548461692$ |
|
|
? |
$S_3 \times C_4$ (as 12T11) |
trivial |
$10$ |
$5$ |
$2014.8871293984223$ |
| 12.0.729103595703125.1 |
$x^{12} - x^{10} - 5 x^{9} + x^{8} + 5 x^{7} + 14 x^{6} - 10 x^{5} - 19 x^{4} - 20 x^{3} + 15 x^{2} + 25 x + 25$ |
$12$ |
[0,6] |
$5^{9}\cdot 139^{4}$ |
$2$ |
$17.32071317552354$ |
$39.42165958407071$ |
|
|
? |
$S_3 \times C_4$ (as 12T11) |
trivial |
$10$ |
$5$ |
$2002.9878211135294$ |
| 12.4.885780500000000.1 |
$x^{12} - x^{11} + 3 x^{10} + x^{9} + 9 x^{8} - 18 x^{7} - 33 x^{6} + 46 x^{5} - 15 x^{4} - 21 x^{3} + 20 x^{2} - 22 x + 11$ |
$12$ |
[4,4] |
$2^{8}\cdot 5^{9}\cdot 11^{6}$ |
$3$ |
$17.603965534$ |
$17.603965534028475$ |
|
|
? |
$S_3 \times C_4$ (as 12T11) |
trivial |
$2$ |
$7$ |
$781.064333478$ |
| 12.0.937080500000000.1 |
$x^{12} - x^{11} + 4 x^{10} - 6 x^{9} + 17 x^{8} + 10 x^{7} + 35 x^{6} + 12 x^{5} + 103 x^{4} - 32 x^{3} + 10 x^{2} - 3 x + 1$ |
$12$ |
[0,6] |
$2^{8}\cdot 5^{9}\cdot 37^{4}$ |
$3$ |
$17.6867515429$ |
$32.28605847922135$ |
✓ |
|
? |
$S_3 \times C_4$ (as 12T11) |
$[2]$ |
$10$ |
$5$ |
$503.981234285$ |
| 12.4.981348487528448.4 |
$x^{12} - 4 x^{10} + 6 x^{8} + 8 x^{6} - 7 x^{4} - 4 x^{2} + 2$ |
$12$ |
[4,4] |
$2^{35}\cdot 13^{4}$ |
$2$ |
$17.7549152981$ |
$28.844410203711913$ |
|
|
? |
$S_3 \times C_4$ (as 12T11) |
trivial |
$2$ |
$7$ |
$1918.43223703$ |
| 12.0.981348487528448.5 |
$x^{12} + 4 x^{10} + 6 x^{8} - 8 x^{6} - 7 x^{4} + 4 x^{2} + 2$ |
$12$ |
[0,6] |
$2^{35}\cdot 13^{4}$ |
$2$ |
$17.7549152981$ |
$28.844410203711913$ |
|
|
? |
$S_3 \times C_4$ (as 12T11) |
trivial |
$2$ |
$5$ |
$695.749093895$ |
| 12.0.1015401564453125.2 |
$x^{12} - x^{11} + 5 x^{10} + 10 x^{9} - 9 x^{8} + 44 x^{6} + 100 x^{5} + 81 x^{4} - 40 x^{3} - 40 x^{2} + 24 x + 16$ |
$12$ |
[0,6] |
$5^{9}\cdot 151^{4}$ |
$2$ |
$17.805458126184142$ |
$41.088092228921276$ |
|
|
? |
$S_3 \times C_4$ (as 12T11) |
trivial |
$10$ |
$5$ |
$1971.95634084061$ |
| 12.4.1119448865964032.6 |
$x^{12} - 16 x^{8} - 40 x^{6} - 32 x^{4} + 8$ |
$12$ |
[4,4] |
$2^{33}\cdot 19^{4}$ |
$2$ |
$17.9507950469$ |
$29.323059968612448$ |
|
|
? |
$S_3 \times C_4$ (as 12T11) |
trivial |
$2$ |
$7$ |
$1325.92180197$ |
| 12.0.1119448865964032.15 |
$x^{12} - 16 x^{8} + 40 x^{6} - 32 x^{4} + 8$ |
$12$ |
[0,6] |
$2^{33}\cdot 19^{4}$ |
$2$ |
$17.9507950469$ |
$29.323059968612448$ |
|
|
? |
$S_3 \times C_4$ (as 12T11) |
$[2]$ |
$2$ |
$5$ |
$195.463564584$ |
| 12.0.1156720500000000.1 |
$x^{12} - 3 x^{11} - 3 x^{10} + 25 x^{9} + 11 x^{8} - 60 x^{7} - 27 x^{6} + 36 x^{5} + 71 x^{4} + 85 x^{3} + 60 x^{2} + 50 x + 25$ |
$12$ |
[0,6] |
$2^{8}\cdot 3^{4}\cdot 5^{9}\cdot 13^{4}$ |
$4$ |
$17.999856219800858$ |
$33.14717113722765$ |
|
|
? |
$S_3 \times C_4$ (as 12T11) |
trivial |
$10$ |
$5$ |
$1757.9316561444375$ |
| 12.0.1175078824045389.1 |
$x^{12} - 2 x^{11} + 3 x^{9} - 3 x^{8} + 17 x^{7} + 22 x^{6} - 25 x^{5} - 20 x^{4} + 91 x^{3} + 230 x^{2} + 228 x + 83$ |
$12$ |
[0,6] |
$3^{4}\cdot 29^{9}$ |
$2$ |
$18.02349111$ |
$21.645076535339435$ |
|
|
? |
$S_3 \times C_4$ (as 12T11) |
$[2]$ |
$2$ |
$5$ |
$142.483768915$ |
| 12.0.1381988962788733.1 |
$x^{12} - 6 x^{11} + 22 x^{10} - 52 x^{9} + 100 x^{8} - 162 x^{7} + 268 x^{6} - 382 x^{5} + 459 x^{4} - 432 x^{3} + 459 x^{2} - 405 x + 243$ |
$12$ |
[0,6] |
$13^{9}\cdot 19^{4}$ |
$2$ |
$18.268745029820636$ |
$29.84243899281031$ |
|
|
|
$S_3 \times C_4$ (as 12T11) |
$[2]$ |
$2$ |
$5$ |
$800.6377392154858$ |
| 12.4.1733405626953125.1 |
$x^{12} - 6 x^{10} - x^{9} + 11 x^{8} + 17 x^{7} - 60 x^{6} - 43 x^{5} + 118 x^{4} + 138 x^{3} - 44 x^{2} - 31 x + 31$ |
$12$ |
[4,4] |
$5^{9}\cdot 31^{6}$ |
$2$ |
$18.6169421902$ |
$18.616942190179014$ |
|
|
? |
$S_3 \times C_4$ (as 12T11) |
trivial |
$2$ |
$7$ |
$676.99391235$ |
| 12.0.2332800000000000.1 |
$x^{12} + 5 x^{10} - 10 x^{8} - 35 x^{6} + 10 x^{4} + 105 x^{2} + 45$ |
$12$ |
[0,6] |
$2^{16}\cdot 3^{6}\cdot 5^{11}$ |
$3$ |
$19.0834309966$ |
$19.083430996593624$ |
|
|
? |
$S_3 \times C_4$ (as 12T11) |
$[2, 2]$ |
$2$ |
$5$ |
$191.661453404$ |
