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 |
14.2.138...000.1 |
$x^{14} - 7 x^{12} - 7 x^{10} + 70 x^{8} - 10 x^{7} + 49 x^{6} - 70 x^{5} - 98 x^{4} - 49 x^{2} - 70 x - 20$ |
$14$ |
[2,6] |
$2^{18}\cdot 5^{7}\cdot 7^{14}$ |
$3$ |
$38.1611635482$ |
$60.4266812699448$ |
|
|
? |
$D_7:F_7$ (as 14T24) |
trivial |
$2$ |
$7$ |
$420430.158225$ |
14.2.138...000.2 |
$x^{14} + 7 x^{12} - 7 x^{10} - 70 x^{8} - 6 x^{7} + 49 x^{6} + 14 x^{5} + 98 x^{4} - 56 x^{3} - 49 x^{2} - 14 x + 4$ |
$14$ |
[2,6] |
$2^{18}\cdot 5^{7}\cdot 7^{14}$ |
$3$ |
$38.1611635482$ |
$60.4266812699448$ |
|
|
? |
$D_7:F_7$ (as 14T24) |
trivial |
$2$ |
$7$ |
$443851.461318$ |
14.0.540...000.1 |
$x^{14} - 3 x^{7} + 6$ |
$14$ |
[0,7] |
$-\,2^{6}\cdot 3^{13}\cdot 5^{7}\cdot 7^{14}$ |
$4$ |
$58.4301582534$ |
$107.33728967696968$ |
|
|
✓ |
$D_7:F_7$ (as 14T24) |
$[2]$ |
$2$ |
$6$ |
$13145315.2551$ |
14.0.346...000.1 |
$x^{14} - 18 x^{7} + 1296$ |
$14$ |
[0,7] |
$-\,2^{12}\cdot 3^{13}\cdot 5^{7}\cdot 7^{14}$ |
$4$ |
$78.6411612488$ |
$107.33728967696968$ |
|
|
? |
$D_7:F_7$ (as 14T24) |
$[2]$ |
$2$ |
$6$ |
$79697104.8449$ |
14.14.219...968.1 |
$x^{14} - 70 x^{12} + 1757 x^{10} - 20090 x^{8} - 1832 x^{7} + 111622 x^{6} + 26656 x^{5} - 283220 x^{4} - 97104 x^{3} + 240737 x^{2} + 32368 x - 56066$ |
$14$ |
[14,0] |
$2^{27}\cdot 7^{14}\cdot 17^{6}$ |
$3$ |
$89.7410488011$ |
$400.34595504489795$ |
|
|
? |
$D_7:F_7$ (as 14T24) |
trivial |
$2$ |
$13$ |
$3947012497.5$ |
14.14.129...000.1 |
$x^{14} - 77 x^{12} + 2303 x^{10} - 33880 x^{8} - 734 x^{7} + 254359 x^{6} + 28014 x^{5} - 906598 x^{4} - 318304 x^{3} + 1195061 x^{2} + 938266 x + 134444$ |
$14$ |
[14,0] |
$2^{12}\cdot 5^{7}\cdot 7^{14}\cdot 29^{6}$ |
$4$ |
$120.046845326$ |
$765.9452780110433$ |
|
|
? |
$D_7:F_7$ (as 14T24) |
trivial |
$2$ |
$13$ |
$17896254443.2$ |