| Label |
Polynomial |
Degree |
Signature |
Discriminant |
Ram. prime count |
Root discriminant |
Galois root discriminant |
CM field |
Galois |
Monogenic |
Galois group |
Class group |
Narrow class group |
Unit group torsion |
Unit group rank |
Regulator |
Unit signature rank |
Max $p$ |
| 12.0.1136131391488.1 |
$x^{12} - 2 x^{11} + 4 x^{10} - 6 x^{9} + 9 x^{8} - 10 x^{7} + 10 x^{6} - 10 x^{5} + 9 x^{4} - 6 x^{3} + 4 x^{2} - 2 x + 1$ |
$12$ |
(0, 6) |
$2^{14}\cdot 37^{5}$ |
$2$ |
$10.1069250855$ |
$13.655340178276088$ |
|
|
✓ |
$S_4$ (as 12T8) |
trivial |
trivial |
$2$ |
$5$ |
$13.5537942867$ |
$0$ |
$37$ |
| 12.2.2408586330112.1 |
$x^{12} - 2 x^{11} + 2 x^{10} - 4 x^{9} + 9 x^{8} - 16 x^{7} + 18 x^{6} - 16 x^{5} + 9 x^{4} - 4 x^{3} + 2 x^{2} - 2 x + 1$ |
$12$ |
(2, 5) |
$-\,2^{14}\cdot 43^{5}$ |
$2$ |
$10.7600308898$ |
$14.720951755301632$ |
|
|
? |
$S_4$ (as 12T8) |
trivial |
trivial |
$2$ |
$6$ |
$28.1348461967$ |
$2$ |
$43$ |
| 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 |
trivial |
$2$ |
$6$ |
$33.9678782736$ |
$2$ |
$19$ |
| 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 |
trivial |
$2$ |
$6$ |
$52.7397059381$ |
$2$ |
$11$ |
| 12.0.12150547628032.1 |
$x^{12} - 2 x^{11} + 2 x^{10} - 2 x^{9} + 6 x^{7} - 8 x^{6} + 4 x^{5} - 2 x^{3} + 4 x^{2} - 4 x + 2$ |
$12$ |
(0, 6) |
$2^{14}\cdot 11^{4}\cdot 37^{3}$ |
$3$ |
$12.31354176261322$ |
$45.2896397560066$ |
|
|
✓ |
$S_3\times S_4$ (as 12T83) |
trivial |
trivial |
$2$ |
$5$ |
$57.54186953098291$ |
$0$ |
$37$ |
| 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 |
trivial |
$2$ |
$6$ |
$115.889778794$ |
$2$ |
$5$ |
| 12.4.28403284787200.1 |
$x^{12} - 2 x^{11} - 2 x^{10} + 6 x^{9} + 9 x^{8} - 14 x^{7} - 18 x^{6} + 14 x^{5} + 9 x^{4} - 6 x^{3} - 2 x^{2} + 2 x + 1$ |
$12$ |
(4, 4) |
$2^{14}\cdot 5^{2}\cdot 37^{5}$ |
$3$ |
$13.2164265693$ |
$30.53426889450943$ |
|
|
? |
$C_2^3:S_4$ (as 12T100) |
trivial |
$[2]$ |
$2$ |
$7$ |
$155.861619562$ |
$3$ |
$37$ |
| 12.2.29574367985664.1 |
$x^{12} - 4 x^{11} + 4 x^{10} + 4 x^{9} - 14 x^{8} + 20 x^{7} - 22 x^{6} + 26 x^{5} - 20 x^{4} + 10 x^{3} - 8 x^{2} - 4 x - 2$ |
$12$ |
(2, 5) |
$-\,2^{14}\cdot 3^{6}\cdot 19^{5}$ |
$3$ |
$13.2610004369$ |
$16.948805249221287$ |
|
|
? |
$S_4$ (as 12T8) |
trivial |
$[2]$ |
$2$ |
$6$ |
$129.16714716$ |
$1$ |
$19$ |
| 12.2.38632614969344.1 |
$x^{12} - 2 x^{11} + 6 x^{9} - 9 x^{8} + 6 x^{7} + 2 x^{6} - 12 x^{5} + 15 x^{4} - 14 x^{3} + 8 x^{2} - 4 x + 1$ |
$12$ |
(2, 5) |
$-\,2^{14}\cdot 11^{9}$ |
$2$ |
$13.5595780565$ |
$13.559578056516557$ |
|
|
✓ |
$S_4$ (as 12T8) |
trivial |
$[2]$ |
$2$ |
$6$ |
$148.220008484$ |
$1$ |
$11$ |
| 12.0.80636724854784.1 |
$x^{12} - 4 x^{9} - 3 x^{8} + 6 x^{5} + 9 x^{4} + 2 x^{3} + 6 x^{2} + 1$ |
$12$ |
(0, 6) |
$2^{14}\cdot 3^{15}\cdot 7^{3}$ |
$3$ |
$14.41709432962182$ |
$27.316124971259402$ |
|
|
? |
$S_3\times S_4$ (as 12T83) |
trivial |
trivial |
$2$ |
$5$ |
$294.843804874118$ |
$0$ |
$7$ |
| 12.2.102241426653184.1 |
$x^{12} - 4 x^{11} + 10 x^{10} - 24 x^{9} + 43 x^{8} - 64 x^{7} + 72 x^{6} - 64 x^{5} + 43 x^{4} - 24 x^{3} + 10 x^{2} - 4 x + 1$ |
$12$ |
(2, 5) |
$-\,2^{14}\cdot 7^{5}\cdot 13^{5}$ |
$3$ |
$14.7051313608$ |
$21.415210999701447$ |
|
|
? |
$S_4$ (as 12T8) |
trivial |
trivial |
$2$ |
$6$ |
$223.476590192$ |
$2$ |
$13$ |
| 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 |
trivial |
$2$ |
$6$ |
$303.966776362$ |
$2$ |
$13$ |
| 12.2.125971200000000.1 |
$x^{12} - 4 x^{11} + 8 x^{10} - 12 x^{9} + 13 x^{8} - 26 x^{7} + 22 x^{6} - 26 x^{5} + 13 x^{4} - 12 x^{3} + 8 x^{2} - 4 x + 1$ |
$12$ |
(2, 5) |
$-\,2^{14}\cdot 3^{9}\cdot 5^{8}$ |
$3$ |
$14.9631353895$ |
$14.963135389464592$ |
|
|
? |
$S_4$ (as 12T8) |
trivial |
$[2]$ |
$2$ |
$6$ |
$458.531539034$ |
$1$ |
$5$ |
| 12.2.171382426877952.1 |
$x^{12} + 6 x^{10} - 4 x^{9} + 18 x^{8} - 18 x^{7} + 30 x^{6} - 54 x^{5} + 36 x^{4} - 50 x^{3} + 36 x^{2} - 12 x + 2$ |
$12$ |
(2, 5) |
$-\,2^{14}\cdot 3^{21}$ |
$2$ |
$15.3519609617$ |
$21.475876974362272$ |
|
|
? |
$C_3:S_4$ (as 12T44) |
trivial |
trivial |
$2$ |
$6$ |
$529.332182878$ |
$2$ |
$3$ |
| 12.2.171382426877952.3 |
$x^{12} - 9 x^{8} - 30 x^{6} - 18 x^{5} - 45 x^{4} - 22 x^{3} - 36 x^{2} - 3$ |
$12$ |
(2, 5) |
$-\,2^{14}\cdot 3^{21}$ |
$2$ |
$15.3519609617$ |
$16.82379477331321$ |
|
|
? |
$S_4$ (as 12T8) |
trivial |
trivial |
$2$ |
$6$ |
$721.332827695$ |
$2$ |
$3$ |
| 12.4.192006205161472.1 |
$x^{12} - 4 x^{11} + 12 x^{10} - 32 x^{9} + 67 x^{8} - 94 x^{7} + 72 x^{6} + 2 x^{5} - 85 x^{4} + 96 x^{3} - 46 x^{2} + 8 x + 1$ |
$12$ |
(4, 4) |
$2^{14}\cdot 13^{2}\cdot 37^{5}$ |
$3$ |
$15.49802196311259$ |
$49.235029196678006$ |
|
|
? |
$C_2^3:S_4$ (as 12T100) |
trivial |
$[2]$ |
$2$ |
$7$ |
$453.721831435661$ |
$3$ |
$37$ |
| 12.2.232753523245056.1 |
$x^{12} - 6 x^{10} + 18 x^{8} - 2 x^{7} - 38 x^{6} + 48 x^{4} + 18 x^{3} - 20 x^{2} - 16 x - 14$ |
$12$ |
(2, 5) |
$-\,2^{14}\cdot 3^{6}\cdot 11^{7}$ |
$3$ |
$15.748578346$ |
$23.485878123082728$ |
|
|
? |
$\GL(2,\mathbb{Z}/4)$ (as 12T49) |
trivial |
$[2]$ |
$2$ |
$6$ |
$460.319309354$ |
$1$ |
$11$ |
| 12.2.232753523245056.2 |
$x^{12} - 2 x^{11} + 4 x^{10} + 4 x^{9} - 7 x^{8} + 28 x^{7} - 34 x^{6} + 28 x^{5} - 7 x^{4} + 4 x^{3} + 4 x^{2} - 2 x + 1$ |
$12$ |
(2, 5) |
$-\,2^{14}\cdot 3^{6}\cdot 11^{7}$ |
$3$ |
$15.748578346$ |
$23.485878123082728$ |
|
|
? |
$\GL(2,\mathbb{Z}/4)$ (as 12T49) |
trivial |
$[2]$ |
$2$ |
$6$ |
$460.319309354$ |
$1$ |
$11$ |
| 12.2.310435661398016.1 |
$x^{12} + 2 x^{10} - 4 x^{9} - 10 x^{8} - 8 x^{7} + 6 x^{6} + 32 x^{5} + 4 x^{4} - 18 x^{3} - 64 x^{2} - 40 x - 26$ |
$12$ |
(2, 5) |
$-\,2^{14}\cdot 7^{6}\cdot 11^{5}$ |
$3$ |
$16.1311117724$ |
$19.699129000227927$ |
|
|
? |
$S_4$ (as 12T8) |
trivial |
$[2]$ |
$2$ |
$6$ |
$430.047821956$ |
$1$ |
$11$ |
| 12.2.408146688000000.1 |
$x^{12} - 6 x^{10} + 12 x^{8} - 6 x^{7} - 30 x^{6} - 12 x^{5} + 24 x^{4} + 26 x^{3} - 12 x - 6$ |
$12$ |
(2, 5) |
$-\,2^{14}\cdot 3^{13}\cdot 5^{6}$ |
$3$ |
$16.5031946876$ |
$18.08540037460562$ |
|
|
? |
$S_4$ (as 12T8) |
$[2]$ |
$[2]$ |
$2$ |
$6$ |
$600.997650083$ |
$2$ |
$5$ |
| 12.0.410143432327168.1 |
$x^{12} - 4 x^{11} + 4 x^{10} - 2 x^{8} + 6 x^{7} + 24 x^{6} + 12 x^{5} + 48 x^{4} + 46 x^{3} + 44 x^{2} + 56 x + 58$ |
$12$ |
(0, 6) |
$2^{14}\cdot 19^{2}\cdot 37^{5}$ |
$3$ |
$16.5099077564$ |
$59.522247876776156$ |
|
|
? |
$C_2^3:S_4$ (as 12T100) |
$[2]$ |
$[2]$ |
$2$ |
$5$ |
$128.76655262$ |
$0$ |
$37$ |
| 12.0.439022168653824.1 |
$x^{12} - 6 x^{11} + 18 x^{10} - 34 x^{9} + 48 x^{8} - 54 x^{7} + 38 x^{6} + 12 x^{5} - 60 x^{4} + 46 x^{3} + 12 x^{2} - 36 x + 18$ |
$12$ |
(0, 6) |
$2^{14}\cdot 3^{13}\cdot 7^{5}$ |
$3$ |
$16.6037889417$ |
$21.398934305093306$ |
|
|
? |
$S_4$ (as 12T8) |
trivial |
trivial |
$2$ |
$5$ |
$894.033156281$ |
$0$ |
$7$ |
| 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 |
trivial |
$2$ |
$7$ |
$1055.13048188$ |
$4$ |
$7$ |
| 12.2.457884390703104.1 |
$x^{12} - 4 x^{11} + 10 x^{10} - 8 x^{9} - 5 x^{8} + 32 x^{7} - 40 x^{6} + 32 x^{5} - 5 x^{4} - 8 x^{3} + 10 x^{2} - 4 x + 1$ |
$12$ |
(2, 5) |
$-\,2^{14}\cdot 3^{9}\cdot 17^{5}$ |
$3$ |
$16.6620968003$ |
$21.09925220183081$ |
|
|
? |
$S_4$ (as 12T8) |
trivial |
$[2]$ |
$2$ |
$6$ |
$768.349367832$ |
$1$ |
$17$ |
| 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 |
$[2]$ |
$2$ |
$6$ |
$1246.20671404$ |
$1$ |
$17$ |
| 12.2.537824000000000.1 |
$x^{12} - 4 x^{11} + 10 x^{10} - 10 x^{9} + x^{8} + 20 x^{7} - 26 x^{6} + 20 x^{5} + x^{4} - 10 x^{3} + 10 x^{2} - 4 x + 1$ |
$12$ |
(2, 5) |
$-\,2^{14}\cdot 5^{9}\cdot 7^{5}$ |
$3$ |
$16.8870328498$ |
$19.85995155932405$ |
|
|
✓ |
$S_4$ (as 12T8) |
$[2]$ |
$[4]$ |
$2$ |
$6$ |
$466.841389207$ |
$1$ |
$7$ |
| 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) |
$[2]$ |
$[4]$ |
$2$ |
$6$ |
$398.24134756$ |
$1$ |
$7$ |
| 12.4.601013506097152.1 |
$x^{12} - 4 x^{11} + 2 x^{10} + 2 x^{9} + 8 x^{8} + 30 x^{7} - 90 x^{6} - 22 x^{5} + 84 x^{4} + 34 x^{3} - 12 x^{2} - 8 x + 2$ |
$12$ |
(4, 4) |
$2^{14}\cdot 23^{2}\cdot 37^{5}$ |
$3$ |
$17.0440847874$ |
$65.4887108885352$ |
|
|
? |
$C_2^3:S_4$ (as 12T100) |
trivial |
$[2]$ |
$2$ |
$7$ |
$819.571798386$ |
$3$ |
$37$ |
| 12.4.601013506097152.2 |
$x^{12} - 4 x^{11} - 2 x^{10} + 14 x^{9} + 24 x^{8} - 76 x^{7} + 48 x^{6} + 64 x^{5} - 196 x^{4} + 8 x^{3} + 136 x^{2} + 40 x + 4$ |
$12$ |
(4, 4) |
$2^{14}\cdot 23^{2}\cdot 37^{5}$ |
$3$ |
$17.0440847874$ |
$65.4887108885352$ |
|
|
? |
$C_2^5:S_4$ (as 12T190) |
trivial |
$[2]$ |
$2$ |
$7$ |
$792.557510465$ |
$3$ |
$37$ |
| 12.4.601013506097152.3 |
$x^{12} - 6 x^{11} + 6 x^{10} + 16 x^{9} - 5 x^{8} - 68 x^{7} + 44 x^{6} + 58 x^{5} - 39 x^{4} + 60 x^{3} - 96 x^{2} + 8 x + 23$ |
$12$ |
(4, 4) |
$2^{14}\cdot 23^{2}\cdot 37^{5}$ |
$3$ |
$17.0440847874$ |
$65.4887108885352$ |
|
|
? |
$C_2^5:S_4$ (as 12T190) |
trivial |
$[2]$ |
$2$ |
$7$ |
$761.880916978$ |
$3$ |
$37$ |
| 12.2.766586021003264.1 |
$x^{12} - 4 x^{11} + 4 x^{10} + 8 x^{9} - 16 x^{8} - 14 x^{7} + 44 x^{6} - 2 x^{5} - 68 x^{4} + 82 x^{3} - 44 x^{2} + 12 x - 2$ |
$12$ |
(2, 5) |
$-\,2^{14}\cdot 7^{4}\cdot 11^{7}$ |
$3$ |
$17.393223380511614$ |
$35.87527142051133$ |
|
|
? |
$C_2^3:S_4$ (as 12T100) |
trivial |
$[2]$ |
$2$ |
$6$ |
$740.2763700444449$ |
$1$ |
$11$ |
| 12.0.913094028509184.1 |
$x^{12} - 4 x^{11} + 6 x^{10} - 50 x^{7} + 172 x^{6} - 296 x^{5} + 320 x^{4} - 230 x^{3} + 112 x^{2} - 36 x + 6$ |
$12$ |
(0, 6) |
$2^{14}\cdot 3^{5}\cdot 47^{5}$ |
$3$ |
$17.6485742011$ |
$69.79682741791062$ |
|
|
? |
$C_2^5:S_4$ (as 12T190) |
trivial |
trivial |
$2$ |
$5$ |
$618.477177673$ |
$0$ |
$47$ |
| 12.0.955486500241408.1 |
$x^{12} - 2 x^{11} + 8 x^{10} - 14 x^{9} + 24 x^{8} - 38 x^{7} + 78 x^{6} - 136 x^{5} + 232 x^{4} - 274 x^{3} + 276 x^{2} - 200 x + 74$ |
$12$ |
(0, 6) |
$2^{14}\cdot 29^{2}\cdot 37^{5}$ |
$3$ |
$17.7154441962$ |
$73.5362573575022$ |
|
|
? |
$C_2^3:S_4$ (as 12T100) |
$[2]$ |
$[2]$ |
$2$ |
$5$ |
$190.282971716$ |
$0$ |
$37$ |
| 12.2.1025934419738624.1 |
$x^{12} - 4 x^{11} + 12 x^{10} - 22 x^{9} + 34 x^{8} - 48 x^{7} + 52 x^{6} - 56 x^{5} + 44 x^{4} - 40 x^{3} + 40 x^{2} - 8 x - 8$ |
$12$ |
(2, 5) |
$-\,2^{14}\cdot 11^{3}\cdot 19^{6}$ |
$3$ |
$17.820776904665728$ |
$32.454491179374756$ |
|
|
? |
$S_3\times S_4$ (as 12T83) |
trivial |
$[2]$ |
$2$ |
$6$ |
$1197.7008606316144$ |
$1$ |
$19$ |
| 12.0.1091822267219968.1 |
$x^{12} - 2 x^{11} + 2 x^{10} - 12 x^{9} + 12 x^{8} - 6 x^{7} + 28 x^{6} - 12 x^{5} + 48 x^{4} + 38 x^{3} + 132 x^{2} + 52 x + 62$ |
$12$ |
(0, 6) |
$2^{14}\cdot 31^{2}\cdot 37^{5}$ |
$3$ |
$17.9134538394$ |
$76.02971640692657$ |
|
|
? |
$C_2^5:S_4$ (as 12T190) |
$[2]$ |
$[2]$ |
$2$ |
$5$ |
$163.284712017$ |
$0$ |
$37$ |
| 12.2.1859069183311872.1 |
$x^{12} - 2 x^{11} + 4 x^{10} - 10 x^{9} - 11 x^{8} - 14 x^{7} - 34 x^{6} - 14 x^{5} - 11 x^{4} - 10 x^{3} + 4 x^{2} - 2 x + 1$ |
$12$ |
(2, 5) |
$-\,2^{14}\cdot 3^{9}\cdot 7^{8}$ |
$3$ |
$18.7258394691$ |
$18.725839469079336$ |
|
|
? |
$S_4$ (as 12T8) |
$[3]$ |
$[6]$ |
$2$ |
$6$ |
$761.905614584$ |
$1$ |
$7$ |
| 12.2.2066104678400000.1 |
$x^{12} - 4 x^{9} - 7 x^{8} - 14 x^{7} - 22 x^{6} - 14 x^{5} - 7 x^{4} - 4 x^{3} + 1$ |
$12$ |
(2, 5) |
$-\,2^{14}\cdot 5^{5}\cdot 7^{9}$ |
$3$ |
$18.8913369136$ |
$21.602807404215152$ |
|
|
? |
$C_2 \times S_4$ (as 12T22) |
trivial |
$[2]$ |
$2$ |
$6$ |
$2313.68880713$ |
$1$ |
$7$ |
| 12.2.2066104678400000.2 |
$x^{12} - 4 x^{11} + 10 x^{10} - 12 x^{9} + 7 x^{8} + 8 x^{7} + 2 x^{6} - 6 x^{5} - 21 x^{4} + 10 x^{3} + 2 x^{2} + 4 x + 1$ |
$12$ |
(2, 5) |
$-\,2^{14}\cdot 5^{5}\cdot 7^{9}$ |
$3$ |
$18.8913369136$ |
$21.602807404215152$ |
|
|
? |
$S_4$ (as 12T8) |
trivial |
$[2]$ |
$2$ |
$6$ |
$1445.16454904$ |
$1$ |
$7$ |
| 12.0.2203992115200000.1 |
$x^{12} - 2 x^{9} + 15 x^{8} + 16 x^{6} - 42 x^{5} + 45 x^{4} - 42 x^{3} + 54 x^{2} - 54 x + 27$ |
$12$ |
(0, 6) |
$2^{14}\cdot 3^{16}\cdot 5^{5}$ |
$3$ |
$18.9933178599$ |
$21.719425659017812$ |
|
|
? |
$S_4$ (as 12T8) |
trivial |
trivial |
$2$ |
$5$ |
$1889.04965926$ |
$0$ |
$5$ |
| 12.6.2441362122784768.1 |
$x^{12} - 2 x^{11} - 2 x^{10} + 16 x^{9} - 8 x^{8} - 22 x^{7} - 6 x^{6} + 32 x^{5} - 18 x^{3} + 8 x^{2} + 4 x - 2$ |
$12$ |
(6, 3) |
$-\,2^{14}\cdot 37^{4}\cdot 43^{3}$ |
$3$ |
$19.1559053947$ |
$89.54405374747657$ |
|
|
? |
$S_3\times S_4$ (as 12T83) |
trivial |
$[2]$ |
$2$ |
$8$ |
$2614.53092349$ |
$5$ |
$43$ |
| 12.2.3149280000000000.1 |
$x^{12} - 6 x^{10} - 10 x^{9} - 15 x^{8} - 60 x^{7} - 90 x^{6} - 60 x^{5} - 15 x^{4} - 10 x^{3} - 6 x^{2} + 1$ |
$12$ |
(2, 5) |
$-\,2^{14}\cdot 3^{9}\cdot 5^{10}$ |
$3$ |
$19.5667008956$ |
$19.56670089564809$ |
|
|
? |
$C_2 \times S_4$ (as 12T22) |
$[2]$ |
$[2, 2]$ |
$2$ |
$6$ |
$2357.18699584$ |
$1$ |
$5$ |
| 12.2.3673320192000000.1 |
$x^{12} - 6 x^{10} - 10 x^{9} + 24 x^{8} + 54 x^{7} - 66 x^{6} - 108 x^{5} + 96 x^{4} + 98 x^{3} - 60 x^{2} - 36 x + 10$ |
$12$ |
(2, 5) |
$-\,2^{14}\cdot 3^{15}\cdot 5^{6}$ |
$3$ |
$19.81929637877742$ |
$25.916910735084592$ |
|
|
? |
$C_3:S_4$ (as 12T44) |
trivial |
$[2]$ |
$2$ |
$6$ |
$2638.9704191086867$ |
$1$ |
$5$ |
| 12.4.5254607685632000.1 |
$x^{12} - 4 x^{10} - 6 x^{9} - 3 x^{8} + 4 x^{7} + 6 x^{6} + 4 x^{5} - 3 x^{4} - 6 x^{3} - 4 x^{2} + 1$ |
$12$ |
(4, 4) |
$2^{14}\cdot 5^{3}\cdot 37^{6}$ |
$3$ |
$20.4194962927$ |
$112.61090738722997$ |
|
|
✓ |
$C_4^3:S_4$ (as 12T225) |
trivial |
$[2, 2]$ |
$2$ |
$7$ |
$2871.96749853$ |
$2$ |
$37$ |
| 12.8.5254607685632000.1 |
$x^{12} - 6 x^{10} - 8 x^{9} + 4 x^{8} + 16 x^{7} + 38 x^{6} + 72 x^{5} - 84 x^{4} - 150 x^{3} + 24 x^{2} + 24 x + 2$ |
$12$ |
(8, 2) |
$2^{14}\cdot 5^{3}\cdot 37^{6}$ |
$3$ |
$20.4194962927$ |
$112.61090738722997$ |
|
|
? |
$C_4^3:S_4$ (as 12T225) |
trivial |
$[2, 2]$ |
$2$ |
$9$ |
$6360.27323099$ |
$6$ |
$37$ |
| 12.2.6528911929819136.1 |
$x^{12} + 2 x^{10} - 4 x^{9} + 7 x^{8} + 38 x^{7} + 56 x^{6} + 162 x^{5} + 191 x^{4} + 276 x^{3} + 128 x^{2} + 20 x + 1$ |
$12$ |
(2, 5) |
$-\,2^{14}\cdot 11^{9}\cdot 13^{2}$ |
$3$ |
$20.792341563173032$ |
$48.889753956426794$ |
|
|
? |
$C_2^3:S_4$ (as 12T100) |
$[2]$ |
$[2, 2]$ |
$2$ |
$6$ |
$1309.4586215013092$ |
$1$ |
$13$ |
| 12.0.21512086264037376.1 |
$x^{12} + 6 x^{10} - 8 x^{9} + 21 x^{8} - 6 x^{7} + 14 x^{6} - 6 x^{5} + 21 x^{4} - 8 x^{3} + 6 x^{2} + 1$ |
$12$ |
(0, 6) |
$2^{14}\cdot 3^{13}\cdot 7^{7}$ |
$3$ |
$22.96449383894824$ |
$34.80700498597547$ |
|
|
? |
$C_2^3:S_4$ (as 12T100) |
$[2]$ |
$[2]$ |
$2$ |
$5$ |
$2123.658265021706$ |
$0$ |
$7$ |
| 12.0.98871834344243200.1 |
$x^{12} + 4 x^{10} - 4 x^{9} + 15 x^{8} + 16 x^{7} + 60 x^{6} + 56 x^{5} + 59 x^{4} + 42 x^{3} + 22 x^{2} + 6 x + 1$ |
$12$ |
(0, 6) |
$2^{14}\cdot 5^{2}\cdot 37^{5}\cdot 59^{2}$ |
$4$ |
$26.0769052679$ |
$605.1325779927694$ |
|
|
? |
$A_4^3:S_3$ (as 12T276) |
$[2]$ |
$[2]$ |
$2$ |
$5$ |
$4052.77245489$ |
$0$ |
$59$ |
| 12.2.124937789194027008.1 |
$x^{12} - 8 x^{9} + 48 x^{3} + 48$ |
$12$ |
(2, 5) |
$-\,2^{14}\cdot 3^{27}$ |
$2$ |
$26.5903763815$ |
$64.42763092308682$ |
|
|
? |
$C_3^3:S_4$ (as 12T177) |
trivial |
trivial |
$2$ |
$6$ |
$22066.253967$ |
$2$ |
$3$ |
| 12.2.124937789194027008.2 |
$x^{12} - 10 x^{9} - 36 x^{6} - 24 x^{3} - 12$ |
$12$ |
(2, 5) |
$-\,2^{14}\cdot 3^{27}$ |
$2$ |
$26.5903763815$ |
$71.8117067983391$ |
|
|
? |
$C_3^4:S_4$ (as 12T233) |
trivial |
trivial |
$2$ |
$6$ |
$27035.5109157$ |
$2$ |
$3$ |
| 12.4.145937850711228416.1 |
$x^{12} - 2 x^{11} - 2 x^{9} + 14 x^{8} - 2 x^{7} - 6 x^{6} - 16 x^{5} - 16 x^{4} - 18 x^{3} - 52 x^{2} - 20 x - 2$ |
$12$ |
(4, 4) |
$2^{14}\cdot 389^{5}$ |
$2$ |
$26.9368823113$ |
$44.27682411416183$ |
|
|
? |
$C_2^2:S_4$ (as 12T66) |
$[2]$ |
$[4]$ |
$2$ |
$7$ |
$9176.00410337$ |
$3$ |
$389$ |
