| 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 |
| 12.0.48737056617.1 |
$x^{12} - 2 x^{11} + 5 x^{10} - 10 x^{9} + 16 x^{8} - 22 x^{7} + 30 x^{6} - 31 x^{5} + 28 x^{4} - 27 x^{3} + 19 x^{2} - 7 x + 1$ |
$12$ |
[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 |
$6$ |
$5$ |
$3.95685086216$ |
| 12.0.84687918336.1 |
$x^{12} - 4 x^{11} + 8 x^{10} - 11 x^{9} + 13 x^{8} - 14 x^{7} + 15 x^{6} - 14 x^{5} + 7 x^{4} + 3 x^{3} - 5 x^{2} + x + 1$ |
$12$ |
[0,6] |
$2^{8}\cdot 3^{9}\cdot 7^{5}$ |
$3$ |
$8.1405132619$ |
$18.313694764355912$ |
|
|
✓ |
$C_6\wr C_2$ (as 12T42) |
trivial |
$6$ |
$5$ |
$5.6892134587$ |
| 12.0.97332232192.1 |
$x^{12} - 4 x^{11} + 6 x^{10} - 4 x^{9} + 4 x^{8} - 18 x^{7} + 44 x^{6} - 64 x^{5} + 63 x^{4} - 42 x^{3} + 20 x^{2} - 6 x + 1$ |
$12$ |
[0,6] |
$2^{18}\cdot 13^{5}$ |
$2$ |
$8.23546369422$ |
$23.97900291135148$ |
|
|
? |
$C_6\wr C_2$ (as 12T42) |
trivial |
$4$ |
$5$ |
$4.09180173939$ |
| 12.0.241162079949.1 |
$x^{12} - 6 x^{11} + 18 x^{10} - 35 x^{9} + 54 x^{8} - 72 x^{7} + 84 x^{6} - 81 x^{5} + 66 x^{4} - 44 x^{3} + 21 x^{2} - 6 x + 1$ |
$12$ |
[0,6] |
$3^{15}\cdot 7^{5}$ |
$2$ |
$8.882306429$ |
$19.9825052193603$ |
|
|
? |
$C_6\wr C_2$ (as 12T42) |
trivial |
$6$ |
$5$ |
$13.4276872379$ |
| 12.0.3833392529408.2 |
$x^{12} - 6 x^{10} + 18 x^{8} - 36 x^{6} + 48 x^{4} - 32 x^{2} + 8$ |
$12$ |
[0,6] |
$2^{27}\cdot 13^{4}$ |
$2$ |
$11.1848957616$ |
$37.1930153725407$ |
|
|
? |
$C_6\wr C_2$ (as 12T42) |
trivial |
$4$ |
$5$ |
$28.3263340908$ |
| 12.0.3833392529408.5 |
$x^{12} - 2 x^{10} + 2 x^{8} - 12 x^{6} + 16 x^{4} + 8$ |
$12$ |
[0,6] |
$2^{27}\cdot 13^{4}$ |
$2$ |
$11.1848957616$ |
$37.1930153725407$ |
|
|
? |
$C_6\wr C_2$ (as 12T42) |
trivial |
$4$ |
$5$ |
$32.0173476193$ |
| 12.0.4149707998464.1 |
$x^{12} - 3 x^{11} + 5 x^{10} - x^{9} - 15 x^{8} + 6 x^{7} + 11 x^{6} + 6 x^{5} + 19 x^{4} + 9 x^{3} - 6 x^{2} - 2 x + 1$ |
$12$ |
[0,6] |
$2^{8}\cdot 3^{9}\cdot 7^{7}$ |
$3$ |
$11.2590425779$ |
$18.313694764355912$ |
|
|
? |
$C_6\wr C_2$ (as 12T42) |
trivial |
$6$ |
$5$ |
$49.9438027112$ |
| 12.0.6229262860288.5 |
$x^{12} + 6 x^{8} - 4 x^{6} + 13 x^{4} + 13$ |
$12$ |
[0,6] |
$2^{24}\cdot 13^{5}$ |
$2$ |
$11.6467044488$ |
$33.911431129417196$ |
|
|
? |
$C_6\wr C_2$ (as 12T42) |
trivial |
$4$ |
$5$ |
$41.1757969799$ |
| 12.6.9904396000000.1 |
$x^{12} - 3 x^{11} - x^{10} + 7 x^{9} - x^{8} - 2 x^{7} + 7 x^{6} - 16 x^{5} - 9 x^{4} + 19 x^{3} + 4 x^{2} - 4 x - 1$ |
$12$ |
[6,3] |
$-\,2^{8}\cdot 5^{6}\cdot 19^{5}$ |
$3$ |
$12.1055817906$ |
$41.28570135662403$ |
|
|
? |
$C_6\wr C_2$ (as 12T42) |
trivial |
$2$ |
$8$ |
$67.9024659123$ |
| 12.0.11816941917501.1 |
$x^{12} - 6 x^{11} + 18 x^{10} - 30 x^{9} + 30 x^{8} - 24 x^{7} + 30 x^{6} - 36 x^{5} + 21 x^{4} + 9 x^{2} - 9 x + 3$ |
$12$ |
[0,6] |
$3^{15}\cdot 7^{7}$ |
$2$ |
$12.2850074751$ |
$19.9825052193603$ |
|
|
? |
$C_6\wr C_2$ (as 12T42) |
trivial |
$6$ |
$5$ |
$137.93869321$ |
| 12.0.16449147240448.2 |
$x^{12} - 2 x^{11} - 8 x^{10} + 20 x^{9} + 34 x^{8} - 100 x^{7} + 8 x^{6} + 72 x^{5} + 40 x^{4} - 56 x^{3} - 32 x^{2} + 16 x + 8$ |
$12$ |
[0,6] |
$2^{18}\cdot 13^{7}$ |
$2$ |
$12.6283113934$ |
$23.97900291135148$ |
|
|
? |
$C_6\wr C_2$ (as 12T42) |
trivial |
$4$ |
$5$ |
$54.2662492894$ |
| 12.0.21134460321792.2 |
$x^{12} + 2 x^{10} + 3 x^{8} - 2 x^{6} - 6 x^{4} + 3$ |
$12$ |
[0,6] |
$2^{30}\cdot 3^{9}$ |
$2$ |
$12.8948391819$ |
$34.955407562927284$ |
|
|
? |
$C_6\wr C_2$ (as 12T42) |
trivial |
$2$ |
$5$ |
$66.6052959539$ |
| 12.0.21134460321792.3 |
$x^{12} - 2 x^{10} + 3 x^{8} + 2 x^{6} - 6 x^{4} + 3$ |
$12$ |
[0,6] |
$2^{30}\cdot 3^{9}$ |
$2$ |
$12.8948391819$ |
$34.955407562927284$ |
|
|
? |
$C_6\wr C_2$ (as 12T42) |
trivial |
$2$ |
$5$ |
$46.2693030491$ |
| 12.6.24321556876032.1 |
$x^{12} - 6 x^{11} + 12 x^{10} - 5 x^{9} - 31 x^{8} + 88 x^{7} - 105 x^{6} + 52 x^{5} + 23 x^{4} - 53 x^{3} + 35 x^{2} - 11 x + 1$ |
$12$ |
[6,3] |
$-\,2^{8}\cdot 3^{9}\cdot 13^{6}$ |
$3$ |
$13.0466580859$ |
$29.739949176590752$ |
|
|
? |
$C_6\wr C_2$ (as 12T42) |
trivial |
$2$ |
$8$ |
$148.752171087$ |
| 12.0.49834102882304.4 |
$x^{12} + 8 x^{8} - 20 x^{6} + 52 x^{4} - 104 x^{2} + 104$ |
$12$ |
[0,6] |
$2^{27}\cdot 13^{5}$ |
$2$ |
$13.8503437968$ |
$57.032001745700285$ |
|
|
? |
$C_6\wr C_2$ (as 12T42) |
trivial |
$4$ |
$5$ |
$144.303729424$ |
| 12.0.49834102882304.5 |
$x^{12} - 8 x^{8} - 4 x^{6} + 52 x^{4} - 104 x^{2} + 104$ |
$12$ |
[0,6] |
$2^{27}\cdot 13^{5}$ |
$2$ |
$13.8503437968$ |
$57.032001745700285$ |
|
|
? |
$C_6\wr C_2$ (as 12T42) |
trivial |
$4$ |
$5$ |
$139.543058404$ |
| 12.0.56358560858112.2 |
$x^{12} - 8 x^{10} + 26 x^{8} - 48 x^{6} + 56 x^{4} - 32 x^{2} + 8$ |
$12$ |
[0,6] |
$2^{33}\cdot 3^{8}$ |
$2$ |
$13.9930802419$ |
$34.6139896873778$ |
|
|
? |
$C_6\wr C_2$ (as 12T42) |
trivial |
$2$ |
$5$ |
$154.73210613$ |
| 12.0.56358560858112.5 |
$x^{12} + 8 x^{10} + 26 x^{8} + 48 x^{6} + 56 x^{4} + 32 x^{2} + 8$ |
$12$ |
[0,6] |
$2^{33}\cdot 3^{8}$ |
$2$ |
$13.9930802419$ |
$34.6139896873778$ |
|
|
? |
$C_6\wr C_2$ (as 12T42) |
trivial |
$2$ |
$5$ |
$57.8552485125$ |
| 12.0.69205338429957.1 |
$x^{12} - 2 x^{10} - 8 x^{9} - 8 x^{8} - 22 x^{7} + 40 x^{6} + 114 x^{5} + 123 x^{4} - 72 x^{3} - 45 x^{2} - 27 x + 27$ |
$12$ |
[0,6] |
$3^{6}\cdot 37^{7}$ |
$2$ |
$14.234590123$ |
$35.10713565663159$ |
|
|
? |
$C_6\wr C_2$ (as 12T42) |
trivial |
$6$ |
$5$ |
$236.525829412$ |
| 12.0.76169967501312.2 |
$x^{12} - 8 x^{9} + 30 x^{6} - 20 x^{3} + 4$ |
$12$ |
[0,6] |
$2^{16}\cdot 3^{19}$ |
$2$ |
$14.3487911438$ |
$21.71095140107369$ |
|
|
? |
$C_6\wr C_2$ (as 12T42) |
trivial |
$6$ |
$5$ |
$599.804026491$ |
| 12.0.76169967501312.3 |
$x^{12} - 10 x^{9} + 30 x^{6} - 16 x^{3} + 4$ |
$12$ |
[0,6] |
$2^{16}\cdot 3^{19}$ |
$2$ |
$14.3487911438$ |
$21.71095140107369$ |
|
|
? |
$C_6\wr C_2$ (as 12T42) |
trivial |
$6$ |
$5$ |
$287.874847139$ |
| 12.0.169075682574336.3 |
$x^{12} - 4 x^{10} + 6 x^{8} - 8 x^{6} + 24 x^{4} + 24$ |
$12$ |
[0,6] |
$2^{33}\cdot 3^{9}$ |
$2$ |
$15.3346345019$ |
$34.955407562927284$ |
|
|
? |
$C_6\wr C_2$ (as 12T42) |
trivial |
$2$ |
$5$ |
$137.794131547$ |
| 12.0.169075682574336.4 |
$x^{12} + 4 x^{10} + 6 x^{8} + 8 x^{6} + 24 x^{4} + 24$ |
$12$ |
[0,6] |
$2^{33}\cdot 3^{9}$ |
$2$ |
$15.3346345019$ |
$34.955407562927284$ |
|
|
? |
$C_6\wr C_2$ (as 12T42) |
trivial |
$2$ |
$5$ |
$210.057438007$ |
| 12.0.190210142896128.2 |
$x^{12} - 6 x^{10} + 15 x^{8} - 26 x^{6} + 66 x^{4} - 36 x^{2} + 27$ |
$12$ |
[0,6] |
$2^{30}\cdot 3^{11}$ |
$2$ |
$15.4858889046$ |
$34.955407562927284$ |
|
|
? |
$C_6\wr C_2$ (as 12T42) |
trivial |
$2$ |
$5$ |
$167.590181576$ |
| 12.0.190210142896128.5 |
$x^{12} + 6 x^{10} + 15 x^{8} + 26 x^{6} + 66 x^{4} + 36 x^{2} + 27$ |
$12$ |
[0,6] |
$2^{30}\cdot 3^{11}$ |
$2$ |
$15.4858889046$ |
$34.955407562927284$ |
|
|
? |
$C_6\wr C_2$ (as 12T42) |
trivial |
$2$ |
$5$ |
$223.577561584$ |
| 12.0.385610460475392.2 |
$x^{12} - 3 x^{6} + 3$ |
$12$ |
[0,6] |
$2^{12}\cdot 3^{23}$ |
$2$ |
$16.4252655857$ |
$31.518176284013194$ |
|
|
✓ |
$C_6\wr C_2$ (as 12T42) |
trivial |
$6$ |
$5$ |
$361.488304208$ |
| 12.0.385610460475392.4 |
$x^{12} + 3 x^{6} + 3$ |
$12$ |
[0,6] |
$2^{12}\cdot 3^{23}$ |
$2$ |
$16.4252655857$ |
$31.518176284013194$ |
|
|
✓ |
$C_6\wr C_2$ (as 12T42) |
trivial |
$6$ |
$5$ |
$1232.65239988$ |
| 12.0.1052745423388672.9 |
$x^{12} - 16 x^{10} + 133 x^{8} - 664 x^{6} + 2106 x^{4} - 3380 x^{2} + 2197$ |
$12$ |
[0,6] |
$2^{24}\cdot 13^{7}$ |
$2$ |
$17.8591292425$ |
$33.911431129417196$ |
|
|
? |
$C_6\wr C_2$ (as 12T42) |
trivial |
$4$ |
$5$ |
$440.470798883$ |
| 12.0.1119448865964032.21 |
$x^{12} - 8 x^{10} + 18 x^{8} - 24 x^{4} - 32 x^{2} + 72$ |
$12$ |
[0,6] |
$2^{33}\cdot 19^{4}$ |
$2$ |
$17.9507950469$ |
$56.96293887121595$ |
|
|
|
$C_6\wr C_2$ (as 12T42) |
trivial |
$2$ |
$5$ |
$2107.68308501$ |
| 12.0.1119448865964032.22 |
$x^{12} + 8 x^{10} + 18 x^{8} - 24 x^{4} + 32 x^{2} + 72$ |
$12$ |
[0,6] |
$2^{33}\cdot 19^{4}$ |
$2$ |
$17.9507950469$ |
$56.96293887121595$ |
|
|
? |
$C_6\wr C_2$ (as 12T42) |
trivial |
$2$ |
$5$ |
$360.009751011$ |
| 12.0.1521681143169024.4 |
$x^{12} - 12 x^{10} + 78 x^{8} - 296 x^{6} + 600 x^{4} - 576 x^{2} + 216$ |
$12$ |
[0,6] |
$2^{33}\cdot 3^{11}$ |
$2$ |
$18.4159292675$ |
$34.955407562927284$ |
|
|
? |
$C_6\wr C_2$ (as 12T42) |
trivial |
$2$ |
$5$ |
$458.496033215$ |
| 12.0.1521681143169024.7 |
$x^{12} + 12 x^{10} + 78 x^{8} + 296 x^{6} + 600 x^{4} + 576 x^{2} + 216$ |
$12$ |
[0,6] |
$2^{33}\cdot 3^{11}$ |
$2$ |
$18.4159292675$ |
$34.955407562927284$ |
|
|
? |
$C_6\wr C_2$ (as 12T42) |
trivial |
$2$ |
$5$ |
$539.987638583$ |
| 12.0.2535525376000000.1 |
$x^{12} - 2 x^{11} + 4 x^{10} + 3 x^{8} - 24 x^{7} + 70 x^{6} - 12 x^{5} + 33 x^{4} + 82 x^{3} + 134 x^{2} - 44 x + 71$ |
$12$ |
[0,6] |
$2^{16}\cdot 5^{6}\cdot 19^{5}$ |
$3$ |
$19.2164132691$ |
$82.57140271324806$ |
✓ |
|
? |
$C_6\wr C_2$ (as 12T42) |
$[2]$ |
$2$ |
$5$ |
$205.215798368$ |
| 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 |
$2$ |
$11$ |
$4759.10509283$ |
| 12.0.2658691056664576.6 |
$x^{12} - 10 x^{8} - 2 x^{6} + 57 x^{4} - 38 x^{2} + 19$ |
$12$ |
[0,6] |
$2^{30}\cdot 19^{5}$ |
$2$ |
$19.2925213511$ |
$78.24570156581791$ |
|
|
|
$C_6\wr C_2$ (as 12T42) |
trivial |
$2$ |
$5$ |
$3556.44215772$ |
| 12.0.2658691056664576.18 |
$x^{12} - 10 x^{8} + 2 x^{6} + 57 x^{4} + 38 x^{2} + 19$ |
$12$ |
[0,6] |
$2^{30}\cdot 19^{5}$ |
$2$ |
$19.2925213511$ |
$78.24570156581791$ |
|
|
? |
$C_6\wr C_2$ (as 12T42) |
trivial |
$2$ |
$5$ |
$551.472883789$ |
| 12.0.3378385204000000.1 |
$x^{12} - 3 x^{11} + 7 x^{10} - 5 x^{9} + 13 x^{8} + 10 x^{7} + 29 x^{6} + 76 x^{5} + 127 x^{4} + 169 x^{3} + 166 x^{2} + 108 x + 31$ |
$12$ |
[0,6] |
$2^{8}\cdot 5^{6}\cdot 61^{5}$ |
$3$ |
$19.6815409067$ |
$109.13059635449413$ |
✓ |
|
|
$C_6\wr C_2$ (as 12T42) |
trivial |
$2$ |
$5$ |
$902.071846456$ |
| 12.0.4565043429507072.30 |
$x^{12} + 18 x^{8} - 48 x^{6} - 72 x^{4} + 648$ |
$12$ |
[0,6] |
$2^{33}\cdot 3^{12}$ |
$2$ |
$20.1815139661$ |
$41.569219381653056$ |
|
|
? |
$C_6\wr C_2$ (as 12T42) |
$[2]$ |
$2$ |
$5$ |
$624.397980596$ |
| 12.0.4565043429507072.31 |
$x^{12} + 18 x^{8} + 48 x^{6} - 72 x^{4} + 648$ |
$12$ |
[0,6] |
$2^{33}\cdot 3^{12}$ |
$2$ |
$20.1815139661$ |
$41.569219381653056$ |
|
|
? |
$C_6\wr C_2$ (as 12T42) |
$[2]$ |
$2$ |
$5$ |
$255.08110436$ |
| 12.0.4874877920083968.11 |
$x^{12} - 18 x^{6} + 108$ |
$12$ |
[0,6] |
$2^{22}\cdot 3^{19}$ |
$2$ |
$20.2922550392$ |
$30.703921923421564$ |
|
|
? |
$C_6\wr C_2$ (as 12T42) |
trivial |
$6$ |
$5$ |
$7037.93412524$ |
| 12.0.4874877920083968.12 |
$x^{12} + 18 x^{6} + 108$ |
$12$ |
[0,6] |
$2^{22}\cdot 3^{19}$ |
$2$ |
$20.2922550392$ |
$30.703921923421564$ |
|
|
? |
$C_6\wr C_2$ (as 12T42) |
trivial |
$6$ |
$5$ |
$3642.2444614$ |
| 12.0.5777633090469888.26 |
$x^{12} - 12 x^{10} + 72 x^{8} - 212 x^{6} + 468 x^{4} - 504 x^{2} + 200$ |
$12$ |
[0,6] |
$2^{27}\cdot 3^{16}$ |
$2$ |
$20.5816014074$ |
$47.429446013156884$ |
|
|
? |
$C_6\wr C_2$ (as 12T42) |
trivial |
$4$ |
$5$ |
$1537.26471655$ |
| 12.0.5777633090469888.27 |
$x^{12} - 12 x^{10} + 72 x^{8} - 188 x^{6} + 180 x^{4} - 72 x^{2} + 200$ |
$12$ |
[0,6] |
$2^{27}\cdot 3^{16}$ |
$2$ |
$20.5816014074$ |
$47.429446013156884$ |
|
|
|
$C_6\wr C_2$ (as 12T42) |
trivial |
$4$ |
$5$ |
$3903.06692197$ |
| 12.0.6169767367606272.2 |
$x^{12} - 6 x^{9} + 42 x^{6} + 12$ |
$12$ |
[0,6] |
$2^{16}\cdot 3^{23}$ |
$2$ |
$20.6945378615$ |
$35.37795671072935$ |
|
|
? |
$C_6\wr C_2$ (as 12T42) |
trivial |
$6$ |
$5$ |
$7162.0802986$ |
| 12.0.6169767367606272.3 |
$x^{12} - 12 x^{9} + 30 x^{6} + 36 x^{3} + 12$ |
$12$ |
[0,6] |
$2^{16}\cdot 3^{23}$ |
$2$ |
$20.6945378615$ |
$35.37795671072935$ |
|
|
? |
$C_6\wr C_2$ (as 12T42) |
trivial |
$6$ |
$5$ |
$4231.86504907$ |
| 12.0.6169767367606272.8 |
$x^{12} - 12 x^{6} + 48$ |
$12$ |
[0,6] |
$2^{16}\cdot 3^{23}$ |
$2$ |
$20.6945378615$ |
$35.37795671072935$ |
|
|
? |
$C_6\wr C_2$ (as 12T42) |
trivial |
$6$ |
$5$ |
$3299.12016116$ |
| 12.0.6169767367606272.10 |
$x^{12} + 12 x^{6} + 48$ |
$12$ |
[0,6] |
$2^{16}\cdot 3^{23}$ |
$2$ |
$20.6945378615$ |
$35.37795671072935$ |
|
|
? |
$C_6\wr C_2$ (as 12T42) |
trivial |
$6$ |
$5$ |
$3880.06275603$ |
| 12.12.6226318560264192.1 |
$x^{12} - 13 x^{10} + 60 x^{8} - 125 x^{6} + 120 x^{4} - 45 x^{2} + 3$ |
$12$ |
[12,0] |
$2^{16}\cdot 3^{9}\cdot 13^{6}$ |
$3$ |
$20.7102787703$ |
$59.479898353181504$ |
|
|
? |
$C_6\wr C_2$ (as 12T42) |
trivial |
$2$ |
$11$ |
$10362.9088206$ |
| 12.0.8421963387109376.23 |
$x^{12} - 14 x^{10} + 74 x^{8} - 612 x^{6} + 5200 x^{4} - 16224 x^{2} + 17576$ |
$12$ |
[0,6] |
$2^{27}\cdot 13^{7}$ |
$2$ |
$21.2382035629$ |
$57.032001745700285$ |
|
|
? |
$C_6\wr C_2$ (as 12T42) |
trivial |
$4$ |
$5$ |
$2282.33854171$ |
