| 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 |
| 12.2.419159399791.1 |
$x^{12} - 2 x^{11} + 3 x^{9} - 2 x^{8} - x^{7} + x^{6} - x^{5} + x^{4} + 2 x^{3} - 2 x^{2} + 1$ |
$12$ |
[2,5] |
$-\,11^{4}\cdot 31^{5}$ |
$2$ |
$9.30104189993$ |
$18.466185312619388$ |
|
|
? |
$C_2 \times S_4$ (as 12T22) |
trivial |
$2$ |
$6$ |
$6.24841548478$ |
| 12.2.838790656103.1 |
$x^{12} - 2 x^{11} + x^{10} + 2 x^{9} - 4 x^{8} + 4 x^{7} - 2 x^{6} - 3 x^{5} + 6 x^{4} - 7 x^{3} + 5 x^{2} - 3 x + 1$ |
$12$ |
[2,5] |
$-\,19^{4}\cdot 23^{5}$ |
$2$ |
$9.85457272032$ |
$20.904544960366874$ |
|
|
✓ |
$C_2 \times S_4$ (as 12T22) |
trivial |
$2$ |
$6$ |
$9.60375711012$ |
| 12.2.1008394404608.1 |
$x^{12} - 3 x^{11} + 4 x^{10} - 11 x^{8} + 24 x^{7} - 29 x^{6} + 24 x^{5} - 11 x^{4} + 4 x^{2} - 3 x + 1$ |
$12$ |
[2,5] |
$-\,2^{8}\cdot 83^{5}$ |
$2$ |
$10.0069685665$ |
$18.2208671582886$ |
|
|
? |
$C_2 \times S_4$ (as 12T22) |
trivial |
$2$ |
$6$ |
$10.1993004837$ |
| 12.2.1687248699392.2 |
$x^{12} - 4 x^{11} + 2 x^{10} + 10 x^{9} - 11 x^{8} - 4 x^{7} - 2 x^{6} + 14 x^{5} + 12 x^{4} - 30 x^{3} + 10 x^{2} + 2 x - 1$ |
$12$ |
[2,5] |
$-\,2^{18}\cdot 23^{5}$ |
$2$ |
$10.4455567243$ |
$16.131190144457708$ |
|
|
? |
$C_2 \times S_4$ (as 12T22) |
trivial |
$2$ |
$6$ |
$14.2298934051$ |
| 12.2.2928329928704.1 |
$x^{12} - x^{11} + x^{10} - x^{9} + x^{8} - 4 x^{7} + 7 x^{6} - x^{5} - 8 x^{4} + 8 x^{3} - 2 x^{2} - x + 1$ |
$12$ |
[2,5] |
$-\,2^{12}\cdot 59^{5}$ |
$2$ |
$10.9366672924$ |
$21.72556098240043$ |
|
|
? |
$C_2 \times S_4$ (as 12T22) |
trivial |
$2$ |
$6$ |
$19.2003177427$ |
| 12.2.3286040887296.1 |
$x^{12} - 2 x^{11} + 2 x^{10} + 2 x^{9} - 9 x^{8} + 20 x^{7} - 24 x^{6} + 20 x^{5} - 9 x^{4} + 2 x^{3} + 2 x^{2} - 2 x + 1$ |
$12$ |
[2,5] |
$-\,2^{14}\cdot 3^{4}\cdot 19^{5}$ |
$3$ |
$11.0422119827$ |
$16.948805249221287$ |
|
|
? |
$C_2 \times S_4$ (as 12T22) |
trivial |
$2$ |
$6$ |
$33.9678782736$ |
| 12.2.6335421661184.1 |
$x^{12} - 2 x^{11} + 2 x^{10} - 3 x^{8} + 8 x^{7} - 10 x^{6} + 8 x^{5} - 3 x^{4} + 2 x^{2} - 2 x + 1$ |
$12$ |
[2,5] |
$-\,2^{14}\cdot 7^{4}\cdot 11^{5}$ |
$3$ |
$11.6631168595$ |
$19.699129000227927$ |
|
|
✓ |
$C_2 \times S_4$ (as 12T22) |
trivial |
$2$ |
$6$ |
$52.7397059381$ |
| 12.2.7504960159744.1 |
$x^{12} - 6 x^{11} + 16 x^{10} - 16 x^{9} - 16 x^{8} + 64 x^{7} - 70 x^{6} + 22 x^{5} + 15 x^{4} - 6 x^{3} - 6 x^{2} + 2 x - 1$ |
$12$ |
[2,5] |
$-\,2^{18}\cdot 31^{5}$ |
$2$ |
$11.8289364683$ |
$18.727652374724588$ |
|
|
? |
$C_2 \times S_4$ (as 12T22) |
trivial |
$2$ |
$6$ |
$33.2988142487$ |
| 12.2.10807949656064.1 |
$x^{12} - 4 x^{11} + 2 x^{10} + 4 x^{9} + 3 x^{8} - 8 x^{6} - 12 x^{5} + 11 x^{4} + 8 x^{3} - 10 x^{2} + 4 x - 1$ |
$12$ |
[2,5] |
$-\,2^{26}\cdot 11^{5}$ |
$2$ |
$12.1939743202$ |
$16.714741551887755$ |
|
|
? |
$C_2 \times S_4$ (as 12T22) |
trivial |
$2$ |
$6$ |
$70.8187286134$ |
| 12.0.11095033120000.1 |
$x^{12} - 3 x^{11} + 7 x^{10} - 12 x^{9} + 19 x^{8} - 21 x^{7} + 22 x^{6} - 21 x^{5} + 19 x^{4} - 12 x^{3} + 7 x^{2} - 3 x + 1$ |
$12$ |
[0,6] |
$2^{8}\cdot 5^{4}\cdot 37^{5}$ |
$3$ |
$12.2206428017$ |
$21.590988593881082$ |
|
|
? |
$C_2 \times S_4$ (as 12T22) |
trivial |
$2$ |
$5$ |
$102.906709943$ |
| 12.2.11713319714816.1 |
$x^{12} - 2 x^{11} + 8 x^{9} - 28 x^{8} + 54 x^{7} - 62 x^{6} + 54 x^{5} - 28 x^{4} + 8 x^{3} - 2 x + 1$ |
$12$ |
[2,5] |
$-\,2^{14}\cdot 59^{5}$ |
$2$ |
$12.2759939707$ |
$21.72556098240043$ |
|
|
|
$C_2 \times S_4$ (as 12T22) |
trivial |
$2$ |
$6$ |
$96.488220713$ |
| 12.2.16325867520000.1 |
$x^{12} - 3 x^{8} - 6 x^{7} - 2 x^{6} - 6 x^{5} - 3 x^{4} + 1$ |
$12$ |
[2,5] |
$-\,2^{14}\cdot 3^{13}\cdot 5^{4}$ |
$3$ |
$12.6203971628$ |
$18.08540037460562$ |
|
|
? |
$C_2 \times S_4$ (as 12T22) |
trivial |
$2$ |
$6$ |
$115.889778794$ |
| 12.4.18178102263808.1 |
$x^{12} - 2 x^{11} - 4 x^{10} + 4 x^{9} + 2 x^{8} + 6 x^{7} + 18 x^{6} + 2 x^{4} + 12 x^{3} - 6 x^{2} - 4 x + 2$ |
$12$ |
[4,4] |
$2^{18}\cdot 37^{5}$ |
$2$ |
$12.7339276649$ |
$18.227692292212264$ |
|
|
? |
$C_2 \times S_4$ (as 12T22) |
trivial |
$2$ |
$7$ |
$120.276296525$ |
| 12.2.27406859829248.1 |
$x^{12} - 3 x^{10} - 4 x^{9} + 10 x^{8} + 8 x^{7} + 5 x^{6} - 28 x^{5} - x^{4} + 8 x^{3} - 8 x - 4$ |
$12$ |
[2,5] |
$-\,2^{16}\cdot 53^{5}$ |
$2$ |
$13.1771535458$ |
$20.591260281974$ |
|
|
? |
$C_2 \times S_4$ (as 12T22) |
trivial |
$2$ |
$6$ |
$228.02816098$ |
| 12.2.38537381281792.1 |
$x^{12} - 8 x^{9} + 6 x^{7} + 34 x^{6} + 16 x^{5} + 6 x^{4} - 20 x^{3} - 10 x^{2} - 8 x + 2$ |
$12$ |
[2,5] |
$-\,2^{18}\cdot 43^{5}$ |
$2$ |
$13.5567894155$ |
$19.65011309429094$ |
|
|
? |
$C_2 \times S_4$ (as 12T22) |
trivial |
$2$ |
$6$ |
$122.014624052$ |
| 12.2.42845606719488.1 |
$x^{12} - 3 x^{11} + 8 x^{9} - 9 x^{8} - 6 x^{7} + 17 x^{6} - 6 x^{5} - 9 x^{4} + 8 x^{3} - 3 x + 1$ |
$12$ |
[2,5] |
$-\,2^{12}\cdot 3^{21}$ |
$2$ |
$13.6770423417$ |
$21.196653174008656$ |
|
|
? |
$C_2 \times S_4$ (as 12T22) |
trivial |
$2$ |
$6$ |
$121.63723042$ |
| 12.2.43231798624256.1 |
$x^{12} - 6 x^{10} + 11 x^{8} - 4 x^{6} - x^{4} - 6 x^{2} - 11$ |
$12$ |
[2,5] |
$-\,2^{28}\cdot 11^{5}$ |
$2$ |
$13.6872733925$ |
$19.877289578936544$ |
|
|
? |
$C_2 \times S_4$ (as 12T22) |
trivial |
$2$ |
$6$ |
$141.402896817$ |
| 12.2.43231798624256.2 |
$x^{12} + 6 x^{10} + 11 x^{8} + 4 x^{6} - x^{4} + 6 x^{2} - 11$ |
$12$ |
[2,5] |
$-\,2^{28}\cdot 11^{5}$ |
$2$ |
$13.6872733925$ |
$19.877289578936544$ |
|
|
? |
$C_2 \times S_4$ (as 12T22) |
trivial |
$2$ |
$6$ |
$148.120097366$ |
| 12.2.55351463182336.1 |
$x^{12} - 4 x^{11} + 4 x^{10} + 4 x^{9} - 12 x^{8} + 12 x^{7} - 8 x^{5} + 7 x^{4} - 12 x^{3} + 4 x^{2} - 4$ |
$12$ |
[2,5] |
$-\,2^{16}\cdot 61^{5}$ |
$2$ |
$13.9720701937$ |
$22.090722034374522$ |
|
|
? |
$C_2 \times S_4$ (as 12T22) |
trivial |
$2$ |
$6$ |
$334.571274244$ |
| 12.2.56192894500864.1 |
$x^{12} - 3 x^{11} + 2 x^{10} + 9 x^{9} - 32 x^{8} + 55 x^{7} - 62 x^{6} + 55 x^{5} - 32 x^{4} + 9 x^{3} + 2 x^{2} - 3 x + 1$ |
$12$ |
[2,5] |
$-\,2^{18}\cdot 11^{8}$ |
$2$ |
$13.9896478859$ |
$19.784349772994805$ |
|
|
|
$C_2 \times S_4$ (as 12T22) |
trivial |
$2$ |
$6$ |
$246.479323144$ |
| 12.2.86029994295296.1 |
$x^{12} - 4 x^{10} + 4 x^{8} - 12 x^{7} + 12 x^{6} - 25 x^{4} + 12 x^{3} + 16 x^{2} - 8 x - 4$ |
$12$ |
[2,5] |
$-\,2^{22}\cdot 29^{5}$ |
$2$ |
$14.4950869386$ |
$21.540659228538015$ |
|
|
? |
$C_2 \times S_4$ (as 12T22) |
trivial |
$2$ |
$6$ |
$449.241210256$ |
| 12.2.86029994295296.2 |
$x^{12} - 6 x^{11} + 17 x^{10} - 28 x^{9} + 23 x^{8} + 4 x^{7} - 34 x^{6} + 32 x^{5} + 2 x^{4} - 16 x^{3} + 6 x^{2} - 2$ |
$12$ |
[2,5] |
$-\,2^{22}\cdot 29^{5}$ |
$2$ |
$14.4950869386$ |
$25.616305216426433$ |
|
|
? |
$C_2 \times S_4$ (as 12T22) |
trivial |
$2$ |
$6$ |
$238.080953447$ |
| 12.2.86029994295296.3 |
$x^{12} + 5 x^{10} - 2 x^{9} + x^{8} + 4 x^{7} - 26 x^{6} + 24 x^{5} - 17 x^{4} + 44 x^{3} - 35 x^{2} + 10 x - 1$ |
$12$ |
[2,5] |
$-\,2^{22}\cdot 29^{5}$ |
$2$ |
$14.4950869386$ |
$25.616305216426433$ |
|
|
? |
$C_2 \times S_4$ (as 12T22) |
trivial |
$2$ |
$6$ |
$250.170138042$ |
| 12.2.102241426653184.2 |
$x^{12} - 2 x^{11} + 6 x^{9} - 23 x^{8} + 42 x^{7} - 46 x^{6} + 42 x^{5} - 23 x^{4} + 6 x^{3} - 2 x + 1$ |
$12$ |
[2,5] |
$-\,2^{14}\cdot 7^{5}\cdot 13^{5}$ |
$3$ |
$14.7051313608$ |
$21.415210999701447$ |
|
|
? |
$C_2 \times S_4$ (as 12T22) |
trivial |
$2$ |
$6$ |
$303.966776362$ |
| 12.2.106993205379072.1 |
$x^{12} - 8 x^{9} + 12 x^{7} + 20 x^{6} - 54 x^{4} + 12 x^{3} + 24 x^{2} - 6$ |
$12$ |
[2,5] |
$-\,2^{26}\cdot 3^{13}$ |
$2$ |
$14.7609060669$ |
$18.157028993074817$ |
|
|
? |
$C_2 \times S_4$ (as 12T22) |
trivial |
$2$ |
$6$ |
$321.190145319$ |
| 12.2.107983916761088.2 |
$x^{12} + 6 x^{10} + 10 x^{8} - 6 x^{6} - 39 x^{4} - 50 x^{2} - 23$ |
$12$ |
[2,5] |
$-\,2^{24}\cdot 23^{5}$ |
$2$ |
$14.772247986$ |
$22.812947879511295$ |
|
|
? |
$C_2 \times S_4$ (as 12T22) |
trivial |
$2$ |
$6$ |
$131.495914081$ |
| 12.2.107983916761088.5 |
$x^{12} - 6 x^{10} + 10 x^{8} + 6 x^{6} - 39 x^{4} + 50 x^{2} - 23$ |
$12$ |
[2,5] |
$-\,2^{24}\cdot 23^{5}$ |
$2$ |
$14.772247986$ |
$22.812947879511295$ |
|
|
? |
$C_2 \times S_4$ (as 12T22) |
trivial |
$2$ |
$6$ |
$114.796116528$ |
| 12.0.164499237983257.1 |
$x^{12} - 3 x^{11} + 8 x^{10} - 16 x^{9} + 21 x^{8} - 17 x^{7} + 9 x^{6} + 11 x^{5} - 19 x^{4} + 5 x^{3} + 20 x^{2} - 20 x + 8$ |
$12$ |
[0,6] |
$17^{5}\cdot 41^{5}$ |
$2$ |
$15.2996087241$ |
$26.40075756488817$ |
|
|
|
$C_2 \times S_4$ (as 12T22) |
trivial |
$2$ |
$5$ |
$183.111680618$ |
| 12.2.166168191041536.1 |
$x^{12} - 12 x^{9} - 6 x^{8} + 20 x^{6} + 16 x^{5} - 16 x^{4} - 16 x^{3} + 16 x^{2} - 4$ |
$12$ |
[2,5] |
$-\,2^{26}\cdot 19^{5}$ |
$2$ |
$15.3124843439$ |
$21.967474133325677$ |
|
|
? |
$C_2 \times S_4$ (as 12T22) |
trivial |
$2$ |
$6$ |
$286.929116619$ |
| 12.2.171382426877952.2 |
$x^{12} - 6 x^{11} + 18 x^{10} - 32 x^{9} + 45 x^{8} - 78 x^{7} + 146 x^{6} - 180 x^{5} + 99 x^{4} + 30 x^{3} - 72 x^{2} + 36 x - 6$ |
$12$ |
[2,5] |
$-\,2^{14}\cdot 3^{21}$ |
$2$ |
$15.3519609617$ |
$21.196653174008656$ |
|
|
|
$C_2 \times S_4$ (as 12T22) |
trivial |
$2$ |
$6$ |
$635.742109669$ |
| 12.2.180551034077184.5 |
$x^{12} - 6 x^{11} + 9 x^{10} + 4 x^{9} - 9 x^{8} - 12 x^{7} + 10 x^{6} + 6 x^{4} - 6 x^{2} + 2$ |
$12$ |
[2,5] |
$-\,2^{22}\cdot 3^{16}$ |
$2$ |
$15.4187795211$ |
$20.58160140743025$ |
|
|
? |
$C_2 \times S_4$ (as 12T22) |
trivial |
$2$ |
$6$ |
$699.749160748$ |
| 12.2.199336411529216.1 |
$x^{12} - 2 x^{10} - 8 x^{9} - 18 x^{8} - 20 x^{7} - 10 x^{6} + 8 x^{5} + 11 x^{4} + 4 x^{3} - 8 x^{2} - 8 x - 2$ |
$12$ |
[2,5] |
$-\,2^{29}\cdot 13^{5}$ |
$2$ |
$15.546485268$ |
$24.255161140409015$ |
|
|
|
$C_2 \times S_4$ (as 12T22) |
trivial |
$2$ |
$6$ |
$1091.06965821$ |
| 12.2.199336411529216.2 |
$x^{12} - 2 x^{10} + 12 x^{8} - 24 x^{7} + 4 x^{6} + 20 x^{5} - 4 x^{4} - 12 x^{3} + 6 x^{2} - 4 x + 1$ |
$12$ |
[2,5] |
$-\,2^{29}\cdot 13^{5}$ |
$2$ |
$15.546485268$ |
$24.255161140409015$ |
|
|
? |
$C_2 \times S_4$ (as 12T22) |
trivial |
$2$ |
$6$ |
$379.671550328$ |
| 12.4.201657968164864.1 |
$x^{12} - 2 x^{11} - 7 x^{10} + 10 x^{9} + 18 x^{8} - 6 x^{7} - 21 x^{6} - 30 x^{5} - 24 x^{4} + 2 x^{3} + 11 x^{2} + 6 x + 1$ |
$12$ |
[4,4] |
$2^{16}\cdot 79^{5}$ |
$2$ |
$15.5614937361$ |
$25.13961017995307$ |
|
|
|
$C_2 \times S_4$ (as 12T22) |
trivial |
$2$ |
$7$ |
$398.451552343$ |
| 12.2.209715200000000.2 |
$x^{12} + 2 x^{10} + 2 x^{8} - 24 x^{6} - 4 x^{4} + 8 x^{2} - 8$ |
$12$ |
[2,5] |
$-\,2^{29}\cdot 5^{8}$ |
$2$ |
$15.6123816451$ |
$19.670368273611786$ |
|
|
? |
$C_2 \times S_4$ (as 12T22) |
trivial |
$2$ |
$6$ |
$532.390119928$ |
| 12.2.427972821516288.3 |
$x^{12} - 4 x^{9} - 3 x^{8} + 12 x^{7} - 16 x^{6} + 24 x^{5} - 45 x^{4} + 52 x^{3} - 24 x^{2} + 12 x - 3$ |
$12$ |
[2,5] |
$-\,2^{28}\cdot 3^{13}$ |
$2$ |
$16.5685568588$ |
$21.592468065875266$ |
|
|
? |
$C_2 \times S_4$ (as 12T22) |
trivial |
$2$ |
$6$ |
$1199.61371106$ |
| 12.2.427972821516288.4 |
$x^{12} - 8 x^{9} - 3 x^{8} - 12 x^{7} - 20 x^{6} - 24 x^{5} - 27 x^{4} - 12 x^{3} - 1$ |
$12$ |
[2,5] |
$-\,2^{28}\cdot 3^{13}$ |
$2$ |
$16.5685568588$ |
$21.592468065875266$ |
|
|
? |
$C_2 \times S_4$ (as 12T22) |
trivial |
$2$ |
$6$ |
$628.001481873$ |
| 12.4.439022168653824.1 |
$x^{12} - 6 x^{10} - 6 x^{9} + 9 x^{8} + 12 x^{7} + 20 x^{6} - 21 x^{4} + 8 x^{3} - 6 x^{2} - 6 x - 1$ |
$12$ |
[4,4] |
$2^{14}\cdot 3^{13}\cdot 7^{5}$ |
$3$ |
$16.6037889417$ |
$21.398934305093306$ |
|
|
? |
$C_2 \times S_4$ (as 12T22) |
trivial |
$2$ |
$7$ |
$1055.13048188$ |
| 12.2.457884390703104.2 |
$x^{12} - 2 x^{11} - 2 x^{10} + 4 x^{9} + 7 x^{8} - 2 x^{7} - 26 x^{6} + 4 x^{5} + 31 x^{4} + 30 x^{3} - 54 x^{2} - 54 x + 81$ |
$12$ |
[2,5] |
$-\,2^{14}\cdot 3^{9}\cdot 17^{5}$ |
$3$ |
$16.6620968003$ |
$21.09925220183081$ |
|
|
? |
$C_2 \times S_4$ (as 12T22) |
trivial |
$2$ |
$6$ |
$1246.20671404$ |
| 12.2.480317450223616.2 |
$x^{12} - 2 x^{10} + 2 x^{8} - 30 x^{6} + 13 x^{4} - 20 x^{2} - 31$ |
$12$ |
[2,5] |
$-\,2^{24}\cdot 31^{5}$ |
$2$ |
$16.728642382$ |
$26.484899979744217$ |
|
|
? |
$C_2 \times S_4$ (as 12T22) |
trivial |
$2$ |
$6$ |
$305.160935314$ |
| 12.2.480317450223616.5 |
$x^{12} + 2 x^{10} + 2 x^{8} + 30 x^{6} + 13 x^{4} + 20 x^{2} - 31$ |
$12$ |
[2,5] |
$-\,2^{24}\cdot 31^{5}$ |
$2$ |
$16.728642382$ |
$26.484899979744217$ |
|
|
? |
$C_2 \times S_4$ (as 12T22) |
trivial |
$2$ |
$6$ |
$249.163848876$ |
| 12.2.537824000000000.2 |
$x^{12} - 2 x^{11} + 2 x^{10} - 6 x^{9} + 15 x^{8} - 28 x^{7} + 32 x^{6} - 28 x^{5} + 15 x^{4} - 6 x^{3} + 2 x^{2} - 2 x + 1$ |
$12$ |
[2,5] |
$-\,2^{14}\cdot 5^{9}\cdot 7^{5}$ |
$3$ |
$16.8870328498$ |
$19.85995155932405$ |
|
|
? |
$C_2 \times S_4$ (as 12T22) |
$[2]$ |
$2$ |
$6$ |
$398.24134756$ |
| 12.2.618121839509504.1 |
$x^{12} - 4 x^{10} - 2 x^{9} + 17 x^{8} + 6 x^{7} - 30 x^{6} - 6 x^{5} + 31 x^{4} - 26 x^{3} - 4 x^{2} + 28 x - 13$ |
$12$ |
[2,5] |
$-\,2^{18}\cdot 11^{9}$ |
$2$ |
$17.0839978211$ |
$18.09986519556776$ |
|
|
? |
$C_2 \times S_4$ (as 12T22) |
trivial |
$2$ |
$6$ |
$696.143544995$ |
| 12.2.664672764166144.1 |
$x^{12} + 2 x^{10} + 7 x^{8} + 16 x^{6} - 17 x^{4} - 42 x^{2} - 19$ |
$12$ |
[2,5] |
$-\,2^{28}\cdot 19^{5}$ |
$2$ |
$17.1876825414$ |
$26.123876537989126$ |
|
|
? |
$C_2 \times S_4$ (as 12T22) |
trivial |
$2$ |
$6$ |
$714.514529701$ |
| 12.2.664672764166144.2 |
$x^{12} - 2 x^{10} + 7 x^{8} - 16 x^{6} - 17 x^{4} + 42 x^{2} - 19$ |
$12$ |
[2,5] |
$-\,2^{28}\cdot 19^{5}$ |
$2$ |
$17.1876825414$ |
$26.123876537989126$ |
|
|
? |
$C_2 \times S_4$ (as 12T22) |
trivial |
$2$ |
$6$ |
$502.906276556$ |
| 12.2.797345646116864.3 |
$x^{12} - 2 x^{10} + 16 x^{8} - 24 x^{7} - 8 x^{6} + 16 x^{5} - 18 x^{4} - 8 x^{3} + 12 x^{2} - 4$ |
$12$ |
[2,5] |
$-\,2^{31}\cdot 13^{5}$ |
$2$ |
$17.4503396979$ |
$24.255161140409015$ |
|
|
? |
$C_2 \times S_4$ (as 12T22) |
trivial |
$2$ |
$6$ |
$1372.2435544$ |
| 12.2.855945643032576.1 |
$x^{12} - 8 x^{9} + 3 x^{8} + 12 x^{7} - 12 x^{6} - 48 x^{5} + 6 x^{4} + 32 x^{3} - 4$ |
$12$ |
[2,5] |
$-\,2^{29}\cdot 3^{13}$ |
$2$ |
$17.5537745187$ |
$24.23672593327708$ |
|
|
? |
$C_2 \times S_4$ (as 12T22) |
trivial |
$2$ |
$6$ |
$2145.51696839$ |
| 12.2.855945643032576.2 |
$x^{12} - 6 x^{10} - 12 x^{9} - 12 x^{8} + 14 x^{6} + 12 x^{5} - 9 x^{4} - 8 x^{3} + 12 x^{2} - 4$ |
$12$ |
[2,5] |
$-\,2^{29}\cdot 3^{13}$ |
$2$ |
$17.5537745187$ |
$24.23672593327708$ |
|
|
|
$C_2 \times S_4$ (as 12T22) |
trivial |
$2$ |
$6$ |
$3094.46806616$ |
| 12.2.1276813346484375.1 |
$x^{12} - 5 x^{11} + 8 x^{10} - x^{9} - 9 x^{8} - 2 x^{7} + 44 x^{6} - 93 x^{5} + 118 x^{4} - 105 x^{3} + 40 x^{2} + 24 x - 19$ |
$12$ |
[2,5] |
$-\,3^{4}\cdot 5^{8}\cdot 7^{9}$ |
$3$ |
$18.1486343654$ |
$21.795365695370254$ |
|
|
? |
$C_2 \times S_4$ (as 12T22) |
trivial |
$2$ |
$6$ |
$656.404897984$ |
| 12.2.1329345528332288.1 |
$x^{12} + 4 x^{10} - 4 x^{9} + 2 x^{8} - 4 x^{7} - 48 x^{6} + 4 x^{5} + 43 x^{4} - 4 x^{3} - 16 x^{2} + 8 x - 2$ |
$12$ |
[2,5] |
$-\,2^{29}\cdot 19^{5}$ |
$2$ |
$18.2097153301$ |
$29.323059968612448$ |
|
|
|
$C_2 \times S_4$ (as 12T22) |
trivial |
$2$ |
$6$ |
$3128.31378321$ |
