| 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 |
| 14.0.102...931.1 |
$x^{14} - 28 x^{11} + 280 x^{10} + 567 x^{9} + 5061 x^{8} + 2273 x^{7} - 735 x^{6} + 33908 x^{5} + 40348 x^{4} - 3192 x^{3} + 36855 x^{2} + 119196 x + 75141$ |
$14$ |
[0,7] |
$-\,3^{8}\cdot 7^{20}\cdot 11^{7}$ |
$3$ |
$100.142856201$ |
$353.2708881002367$ |
|
|
|
$C_7^2:(C_3\times S_3)$ (as 14T26) |
trivial |
$2$ |
$6$ |
$2528603759.06$ |
| 14.14.138...056.1 |
$x^{14} - 84 x^{12} + 2380 x^{10} - 350 x^{9} - 26082 x^{8} + 14714 x^{7} + 103684 x^{6} - 108388 x^{5} - 57036 x^{4} + 87024 x^{3} - 7840 x^{2} - 8036 x - 420$ |
$14$ |
[14,0] |
$2^{12}\cdot 7^{21}\cdot 67^{7}$ |
$3$ |
$274.606094735$ |
$326.1720425799972$ |
|
|
? |
$C_7^2:(C_3\times S_3)$ (as 14T26) |
$[3]$ |
$2$ |
$13$ |
$3053601932800$ |
| 14.0.311...552.1 |
$x^{14} + 42 x^{12} - 364 x^{11} - 623 x^{10} - 16044 x^{9} - 2212 x^{8} + 35808 x^{7} + 1564080 x^{6} + 5717824 x^{5} + 40943168 x^{4} + 117175296 x^{3} + 397307904 x^{2} + 540954624 x + 1476661248$ |
$14$ |
[0,7] |
$-\,2^{21}\cdot 3^{8}\cdot 7^{20}\cdot 73^{4}$ |
$4$ |
$290.968908444$ |
$5262.253202832733$ |
|
|
|
$C_7^2:(C_3\times S_3)$ (as 14T26) |
trivial |
$2$ |
$6$ |
$177351190608000$ |
| 14.0.524...928.1 |
$x^{14} + 224 x^{12} - 14 x^{11} + 15442 x^{10} + 1736 x^{9} + 330176 x^{8} + 251648 x^{7} + 1759688 x^{6} + 13153728 x^{5} + 14876988 x^{4} - 131149900 x^{3} + 208370820 x^{2} - 138679576 x + 34237572$ |
$14$ |
[0,7] |
$-\,2^{12}\cdot 7^{20}\cdot 107^{7}$ |
$3$ |
$301.9955292641533$ |
$461.2829834966581$ |
|
|
? |
$C_7^2:(C_3\times S_3)$ (as 14T26) |
$[6]$ |
$2$ |
$6$ |
$113326754984.28593$ |
| 14.14.402...472.1 |
$x^{14} - 4 x^{13} - 346 x^{12} + 146 x^{11} + 45973 x^{10} + 110038 x^{9} - 2593249 x^{8} - 11384888 x^{7} + 53650141 x^{6} + 348974586 x^{5} - 109694286 x^{4} - 2641431330 x^{3} + 223044192 x^{2} + 7815136932 x - 5730505137$ |
$14$ |
[14,0] |
$2^{21}\cdot 3^{16}\cdot 13^{8}\cdot 2719^{4}$ |
$4$ |
$411.742085119$ |
$13180.79806090641$ |
|
|
? |
$C_7^2:(C_3\times S_3)$ (as 14T26) |
trivial |
$2$ |
$13$ |
$106512528185000$ |
