| 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 |
| 12.2.3851755393646592.6 |
$x^{12} + 6 x^{10} + 9 x^{8} + 6 x^{6} + 3 x^{4} - 3$ |
$12$ |
[2,5] |
$-\,2^{28}\cdot 3^{15}$ |
$2$ |
$19.8977922257$ |
$33.95070887724191$ |
|
|
? |
$C_2^4:S_4$ (as 12T145) |
trivial |
$2$ |
$6$ |
$2394.74657786$ |
| 12.2.239...984.16 |
$x^{12} + 10 x^{10} + 38 x^{8} + 160 x^{6} + 180 x^{4} - 76$ |
$12$ |
[2,5] |
$-\,2^{28}\cdot 19^{7}$ |
$2$ |
$28.0764971448$ |
$78.25506903819789$ |
|
|
|
$C_2^4:S_4$ (as 12T145) |
trivial |
$2$ |
$6$ |
$13617.6757974$ |
| 12.2.239...984.26 |
$x^{12} + 10 x^{10} + 25 x^{8} + 10 x^{6} - 49 x^{4} - 60 x^{2} - 19$ |
$12$ |
[2,5] |
$-\,2^{28}\cdot 19^{7}$ |
$2$ |
$28.0764971448$ |
$78.25506903819789$ |
|
|
? |
$C_2\wr S_4$ (as 12T223) |
trivial |
$2$ |
$6$ |
$13918.366008$ |
| 12.2.239...984.28 |
$x^{12} + 7 x^{8} - 26 x^{6} + 5 x^{4} - 26 x^{2} - 19$ |
$12$ |
[2,5] |
$-\,2^{28}\cdot 19^{7}$ |
$2$ |
$28.0764971448$ |
$78.25506903819789$ |
|
|
? |
$C_2\wr S_4$ (as 12T223) |
trivial |
$2$ |
$6$ |
$13965.6733549$ |
| 12.2.239...984.38 |
$x^{12} - 8 x^{10} + 15 x^{8} + 38 x^{6} - 171 x^{4} + 190 x^{2} - 19$ |
$12$ |
[2,5] |
$-\,2^{28}\cdot 19^{7}$ |
$2$ |
$28.0764971448$ |
$113.07241789343452$ |
|
|
? |
$C_2\wr S_4$ (as 12T223) |
trivial |
$2$ |
$6$ |
$13213.0179464$ |
| 12.2.311...952.30 |
$x^{12} - 21 x^{8} - 6 x^{6} - 27 x^{4} - 18 x^{2} - 3$ |
$12$ |
[2,5] |
$-\,2^{28}\cdot 3^{19}$ |
$2$ |
$28.6975822875$ |
$58.804352728362694$ |
|
|
? |
$A_4^2:D_4$ (as 12T196) |
trivial |
$2$ |
$6$ |
$20635.7813149$ |
| 12.2.252...112.12 |
$x^{12} - 45 x^{8} - 246 x^{6} - 603 x^{4} - 738 x^{2} - 363$ |
$12$ |
[2,5] |
$-\,2^{28}\cdot 3^{23}$ |
$2$ |
$41.389075723$ |
$70.62032031669557$ |
|
|
? |
$C_2^4:S_4$ (as 12T145) |
trivial |
$2$ |
$6$ |
$187882.582648$ |
| 12.2.252...112.34 |
$x^{12} - 9 x^{8} - 18 x^{6} + 189 x^{4} - 162 x^{2} - 27$ |
$12$ |
[2,5] |
$-\,2^{28}\cdot 3^{23}$ |
$2$ |
$41.389075723$ |
$95.82158822959698$ |
|
|
? |
$A_4^2:D_4$ (as 12T196) |
trivial |
$2$ |
$6$ |
$163935.416397$ |
| 12.2.252...112.48 |
$x^{12} - 9 x^{8} - 6 x^{6} + 45 x^{4} - 54 x^{2} - 3$ |
$12$ |
[2,5] |
$-\,2^{28}\cdot 3^{23}$ |
$2$ |
$41.389075723$ |
$95.82158822959698$ |
|
|
? |
$A_4^2:D_4$ (as 12T196) |
trivial |
$2$ |
$6$ |
$205492.963913$ |
| 12.2.765...616.5 |
$x^{12} - 33 x^{8} - 110 x^{6} - 187 x^{4} - 286 x^{2} - 275$ |
$12$ |
[2,5] |
$-\,2^{28}\cdot 11^{11}$ |
$2$ |
$45.3955502459$ |
$77.45638778619025$ |
|
|
? |
$A_4^2:D_4$ (as 12T196) |
trivial |
$2$ |
$6$ |
$570023.329222$ |
| 12.2.866...224.6 |
$x^{12} - 38 x^{10} + 570 x^{8} - 4332 x^{6} + 11552 x^{4} - 27436$ |
$12$ |
[2,5] |
$-\,2^{28}\cdot 19^{9}$ |
$2$ |
$45.8636404311$ |
$78.25506903819789$ |
|
|
|
$C_2^4:S_4$ (as 12T145) |
$[2]$ |
$2$ |
$6$ |
$492143.366785$ |
| 12.2.866...224.20 |
$x^{12} + 19 x^{8} + 418 x^{6} - 3667 x^{4} + 19494 x^{2} - 6859$ |
$12$ |
[2,5] |
$-\,2^{28}\cdot 19^{9}$ |
$2$ |
$45.8636404311$ |
$113.07241789343452$ |
|
|
? |
$C_2\wr S_4$ (as 12T223) |
$[2, 2]$ |
$2$ |
$6$ |
$51387.2889194$ |
