| 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 |
| 14.0.3332000199986667.1 |
$x^{14} - 2 x^{13} - 3 x^{12} + 8 x^{11} + 3 x^{10} - 11 x^{9} - x^{8} + 7 x^{7} + 5 x^{6} + x^{5} - 5 x^{4} - 3 x^{3} + 4 x^{2} + 4 x + 1$ |
$14$ |
[0,7] |
$-\,3^{7}\cdot 11^{4}\cdot 101^{4}$ |
$3$ |
$12.8459031741$ |
$57.73214009544424$ |
|
|
? |
$\PGL(2,7)$ (as 14T16) |
trivial |
$6$ |
$6$ |
$358.769387668$ |
| 14.0.146081389744226304.1 |
$x^{14} - 2 x^{13} + 2 x^{12} + 8 x^{11} - 7 x^{10} - 14 x^{9} + 38 x^{8} - 16 x^{7} - 35 x^{6} + 46 x^{5} - 2 x^{4} - 40 x^{3} + 37 x^{2} - 14 x + 2$ |
$14$ |
[0,7] |
$-\,2^{38}\cdot 3^{12}$ |
$2$ |
$16.8283870546$ |
$31.63696468726565$ |
|
|
|
$\PGL(2,7)$ (as 14T16) |
trivial |
$4$ |
$6$ |
$7065.07089747$ |
| 14.6.926...597.1 |
$x^{14} - 6 x^{13} + 12 x^{12} - 8 x^{11} - 11 x^{10} + 61 x^{9} - 142 x^{8} + 239 x^{7} - 391 x^{6} + 486 x^{5} - 382 x^{4} + 203 x^{3} - 70 x^{2} + 13 x - 1$ |
$14$ |
[6,4] |
$53^{11}$ |
$1$ |
$22.6354005083$ |
$27.346173066268356$ |
|
|
? |
$\PGL(2,7)$ (as 14T16) |
trivial |
$2$ |
$9$ |
$25636.9775584$ |
| 14.6.551...381.1 |
$x^{14} - 7 x^{13} + 7 x^{12} + 35 x^{11} - 77 x^{10} + 35 x^{9} + 147 x^{8} - 309 x^{7} + 21 x^{6} + 308 x^{5} - 203 x^{4} + 140 x^{3} + 49 x^{2} - 322 x - 68$ |
$14$ |
[6,4] |
$3^{19}\cdot 7^{15}$ |
$2$ |
$35.7259584307$ |
$45.85501413123854$ |
|
|
? |
$\PGL(2,7)$ (as 14T16) |
trivial |
$2$ |
$9$ |
$2315086.73291$ |
| 14.14.252...000.1 |
$x^{14} - 52 x^{12} - 52 x^{11} + 932 x^{10} + 1864 x^{9} - 5660 x^{8} - 19688 x^{7} - 4939 x^{6} + 48280 x^{5} + 71236 x^{4} + 29324 x^{3} - 11918 x^{2} - 12912 x - 2788$ |
$14$ |
[14,0] |
$2^{33}\cdot 3^{4}\cdot 5^{4}\cdot 491^{4}$ |
$4$ |
$65.2344799301$ |
$577.323005240646$ |
|
|
|
$\PGL(2,7)$ (as 14T16) |
trivial |
$2$ |
$13$ |
$1490540782.35$ |
| 14.14.140...408.1 |
$x^{14} - 126 x^{12} - 70 x^{11} + 5208 x^{10} + 3864 x^{9} - 96992 x^{8} - 79686 x^{7} + 889644 x^{6} + 737478 x^{5} - 3976098 x^{4} - 3152520 x^{3} + 7393869 x^{2} + 5217534 x - 2795274$ |
$14$ |
[14,0] |
$2^{18}\cdot 3^{8}\cdot 7^{15}\cdot 29^{7}$ |
$4$ |
$197.852010386$ |
$306.4007916309987$ |
|
|
|
$\PGL(2,7)$ (as 14T16) |
$[2]$ |
$2$ |
$13$ |
$758587333915$ |
