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 |
12.0.389136420864.1 |
$x^{12} - x^{10} + x^{8} - 2 x^{6} + 4 x^{4} - 3 x^{2} + 1$ |
$12$ |
[0,6] |
$2^{12}\cdot 3^{6}\cdot 19^{4}$ |
$3$ |
$9.24361446117$ |
$45.23704936610096$ |
|
|
✓ |
$A_4\wr C_2$ (as 12T126) |
trivial |
$6$ |
$5$ |
$13.5657970125$ |
12.0.479174066176.2 |
$x^{12} - 2 x^{10} + 3 x^{8} - 4 x^{6} + 4 x^{4} - 2 x^{2} + 1$ |
$12$ |
[0,6] |
$2^{24}\cdot 13^{4}$ |
$2$ |
$9.40533875088$ |
$35.616153539817454$ |
|
|
✓ |
$A_4\wr C_2$ (as 12T126) |
trivial |
$4$ |
$5$ |
$10.6558694116$ |
12.4.5832828765625.1 |
$x^{12} - x^{11} - 2 x^{10} + 2 x^{8} + x^{7} - x^{6} + x^{5} + 2 x^{4} - 2 x^{2} - x + 1$ |
$12$ |
[4,4] |
$5^{6}\cdot 139^{4}$ |
$2$ |
$11.5830590114$ |
$60.001420981750954$ |
|
|
✓ |
$A_4\wr C_2$ (as 12T126) |
trivial |
$2$ |
$7$ |
$39.2351086262$ |
12.0.7044820107264.1 |
$x^{12} - 2 x^{10} + 3 x^{8} - 2 x^{6} + 2 x^{4} + 1$ |
$12$ |
[0,6] |
$2^{30}\cdot 3^{8}$ |
$2$ |
$11.7667310137$ |
$39.41801805957117$ |
|
|
✓ |
$A_4\wr C_2$ (as 12T126) |
trivial |
$2$ |
$5$ |
$42.4156653636$ |
12.4.8340544000000.1 |
$x^{12} - 2 x^{11} - x^{8} + 2 x^{7} - 4 x^{6} + 2 x^{5} - x^{4} - 2 x + 1$ |
$12$ |
[4,4] |
$2^{12}\cdot 5^{6}\cdot 19^{4}$ |
$3$ |
$11.9334549556$ |
$38.97784406822943$ |
|
|
? |
$A_4\wr C_2$ (as 12T126) |
trivial |
$2$ |
$7$ |
$53.7277629388$ |
12.0.128536820158464.3 |
$x^{12} - 6 x^{10} + 15 x^{8} - 17 x^{6} + 6 x^{4} + 3 x^{2} + 1$ |
$12$ |
[0,6] |
$2^{12}\cdot 3^{22}$ |
$2$ |
$14.9882971978$ |
$39.64550556709086$ |
|
|
✓ |
$A_4\wr C_2$ (as 12T126) |
trivial |
$6$ |
$5$ |
$647.283288233$ |
12.0.139931108245504.2 |
$x^{12} - 4 x^{10} + 6 x^{8} - 6 x^{6} + 7 x^{4} - 2 x^{2} + 1$ |
$12$ |
[0,6] |
$2^{30}\cdot 19^{4}$ |
$2$ |
$15.0947592059$ |
$64.86874738888089$ |
|
|
? |
$A_4\wr C_2$ (as 12T126) |
trivial |
$2$ |
$5$ |
$224.833464865$ |
12.0.406239826673664.6 |
$x^{12} - 3 x^{10} + 25 x^{6} + 30 x^{4} + 9 x^{2} + 1$ |
$12$ |
[0,6] |
$2^{20}\cdot 3^{18}$ |
$2$ |
$16.496755644$ |
$38.621286224735144$ |
|
|
? |
$A_4\wr C_2$ (as 12T126) |
trivial |
$6$ |
$5$ |
$1448.71010922$ |
12.8.612593437890625.1 |
$x^{12} - 5 x^{11} + 3 x^{10} + 29 x^{9} - 76 x^{8} + 51 x^{7} + 76 x^{6} - 174 x^{5} + 126 x^{4} - 55 x^{2} + 30 x - 5$ |
$12$ |
[8,2] |
$5^{8}\cdot 199^{4}$ |
$2$ |
$17.0712122359$ |
$113.97148864113937$ |
|
|
? |
$A_4\wr C_2$ (as 12T126) |
trivial |
$2$ |
$9$ |
$1221.67129336$ |
12.8.657980213765625.1 |
$x^{12} - 4 x^{11} + 4 x^{10} - x^{9} - 14 x^{8} + 37 x^{7} + 12 x^{6} - 38 x^{5} + 29 x^{4} + 21 x^{3} - 54 x^{2} - 45 x - 9$ |
$12$ |
[8,2] |
$3^{4}\cdot 5^{6}\cdot 151^{4}$ |
$3$ |
$17.1731937419$ |
$109.82391660725793$ |
|
|
? |
$A_4\wr C_2$ (as 12T126) |
trivial |
$2$ |
$9$ |
$1118.90813104$ |
12.0.722204136308736.5 |
$x^{12} + 3 x^{8} - 16 x^{6} + 18 x^{4} - 6 x^{2} + 1$ |
$12$ |
[0,6] |
$2^{24}\cdot 3^{16}$ |
$2$ |
$17.3069948437$ |
$45.418593103914915$ |
|
|
? |
$A_4\wr C_2$ (as 12T126) |
trivial |
$4$ |
$5$ |
$857.829664175$ |
12.12.23891266624000000.1 |
$x^{12} - 12 x^{10} + 48 x^{8} - 80 x^{6} + 54 x^{4} - 13 x^{2} + 1$ |
$12$ |
[12,0] |
$2^{12}\cdot 5^{6}\cdot 139^{4}$ |
$3$ |
$23.1661180228$ |
$220.08618255316486$ |
|
|
✓ |
$A_4\wr C_2$ (as 12T126) |
trivial |
$2$ |
$11$ |
$14867.0875378$ |
12.12.32020222185570304.1 |
$x^{12} - 4 x^{11} - 10 x^{10} + 36 x^{9} + 50 x^{8} - 108 x^{7} - 136 x^{6} + 104 x^{5} + 151 x^{4} - 8 x^{3} - 52 x^{2} - 16 x - 1$ |
$12$ |
[12,0] |
$2^{24}\cdot 7^{2}\cdot 79^{4}$ |
$3$ |
$23.7384319679$ |
$231.71344694380466$ |
|
|
✓ |
$A_4\wr C_2$ (as 12T126) |
trivial |
$2$ |
$11$ |
$20009.6779227$ |
12.0.32905425960566784.15 |
$x^{12} - 9 x^{10} + 36 x^{8} - 75 x^{6} + 54 x^{4} + 27 x^{2} + 9$ |
$12$ |
[0,6] |
$2^{20}\cdot 3^{22}$ |
$2$ |
$23.792438739$ |
$62.93331724301113$ |
|
|
? |
$A_4\wr C_2$ (as 12T126) |
trivial |
$6$ |
$5$ |
$12776.1839726$ |
12.0.32905425960566784.16 |
$x^{12} + 45 x^{8} + 6 x^{6} + 81 x^{4} + 54 x^{2} + 9$ |
$12$ |
[0,6] |
$2^{20}\cdot 3^{22}$ |
$2$ |
$23.792438739$ |
$62.93331724301113$ |
|
|
? |
$A_4\wr C_2$ (as 12T126) |
trivial |
$6$ |
$5$ |
$24484.3727346$ |
12.0.415989582513831936.5 |
$x^{12} - 6 x^{8} - 2 x^{6} + 63 x^{4} + 6 x^{2} + 1$ |
$12$ |
[0,6] |
$2^{30}\cdot 3^{18}$ |
$2$ |
$29.3938769134$ |
$60.428517356777206$ |
|
|
? |
$A_4\wr C_2$ (as 12T126) |
$[2]$ |
$2$ |
$5$ |
$19062.5830688$ |
12.4.526...544.37 |
$x^{12} + 12 x^{10} + 42 x^{8} + 22 x^{6} - 75 x^{4} - 42 x^{2} + 25$ |
$12$ |
[4,4] |
$2^{24}\cdot 3^{22}$ |
$2$ |
$29.9765943956$ |
$51.413859783540225$ |
|
|
? |
$A_4\wr C_2$ (as 12T126) |
trivial |
$2$ |
$7$ |
$47813.887436$ |
12.0.335...896.4 |
$x^{12} + x^{10} + 3 x^{8} + 11 x^{6} + 13 x^{4} + 5 x^{2} + 1$ |
$12$ |
[0,6] |
$2^{12}\cdot 31^{10}$ |
$2$ |
$34.9809344929$ |
$49.470511984396374$ |
|
|
✓ |
$A_4\wr C_2$ (as 12T126) |
$[9]$ |
$2$ |
$5$ |
$3931.0189663$ |
12.0.642...376.5 |
$x^{12} - 4 x^{10} + 13 x^{8} + 18 x^{6} + 29 x^{4} + 10 x^{2} + 1$ |
$12$ |
[0,6] |
$2^{20}\cdot 19^{10}$ |
$2$ |
$36.9270538929$ |
$67.72451544679102$ |
|
|
? |
$A_4\wr C_2$ (as 12T126) |
$[3]$ |
$2$ |
$5$ |
$16708.8751726$ |
12.4.336...816.16 |
$x^{12} - 6 x^{10} - 57 x^{8} - 74 x^{6} - 12 x^{4} + 12 x^{2} + 1$ |
$12$ |
[4,4] |
$2^{30}\cdot 3^{22}$ |
$2$ |
$42.393306348$ |
$98.46816160418916$ |
|
|
? |
$A_4\wr C_2$ (as 12T126) |
trivial |
$2$ |
$7$ |
$337725.05099$ |
12.4.336...816.17 |
$x^{12} + 12 x^{10} + 6 x^{8} - 182 x^{6} - 273 x^{4} + 30 x^{2} + 1$ |
$12$ |
[4,4] |
$2^{30}\cdot 3^{22}$ |
$2$ |
$42.393306348$ |
$98.46816160418916$ |
|
|
|
$A_4\wr C_2$ (as 12T126) |
trivial |
$2$ |
$7$ |
$705221.710959$ |
12.8.336...816.18 |
$x^{12} - 6 x^{10} - 21 x^{8} + 130 x^{6} + 42 x^{4} - 312 x^{2} + 25$ |
$12$ |
[8,2] |
$2^{30}\cdot 3^{22}$ |
$2$ |
$42.393306348$ |
$98.46816160418916$ |
|
|
? |
$A_4\wr C_2$ (as 12T126) |
trivial |
$2$ |
$9$ |
$904126.959513$ |
12.8.336...816.19 |
$x^{12} - 6 x^{10} - 21 x^{8} + 130 x^{6} - 102 x^{4} - 24 x^{2} + 25$ |
$12$ |
[8,2] |
$2^{30}\cdot 3^{22}$ |
$2$ |
$42.393306348$ |
$98.46816160418916$ |
|
|
? |
$A_4\wr C_2$ (as 12T126) |
trivial |
$2$ |
$9$ |
$831630.42521$ |
12.0.102...016.4 |
$x^{12} - 4 x^{10} - 6 x^{8} + 18 x^{6} + 181 x^{4} + 10 x^{2} + 1$ |
$12$ |
[0,6] |
$2^{24}\cdot 19^{10}$ |
$2$ |
$46.5251725102$ |
$55.32806617588871$ |
|
|
? |
$A_4\wr C_2$ (as 12T126) |
$[18]$ |
$2$ |
$5$ |
$19317.6466425$ |
12.0.148...576.3 |
$x^{12} + 8 x^{10} + 18 x^{8} + 6 x^{6} + 19 x^{4} - 2 x^{2} + 1$ |
$12$ |
[0,6] |
$2^{30}\cdot 13^{10}$ |
$2$ |
$47.9580058227$ |
$77.23590471702916$ |
|
|
? |
$A_4\wr C_2$ (as 12T126) |
$[18]$ |
$2$ |
$5$ |
$24050.3532795$ |