| 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 |
| 14.6.241...648.1 |
$x^{14} - 5 x^{12} - 14 x^{11} - 29 x^{10} - 26 x^{9} + 7 x^{8} + 250 x^{7} + 877 x^{6} + 1766 x^{5} + 2427 x^{4} + 2404 x^{3} + 1535 x^{2} + 516 x + 67$ |
$14$ |
[6,4] |
$2^{12}\cdot 73^{9}$ |
$2$ |
$28.5677555262$ |
$64.68368606819884$ |
|
|
? |
$F_8:C_6$ (as 14T18) |
trivial |
$2$ |
$9$ |
$411958.953606$ |
| 14.6.412...000.1 |
$x^{14} - 2 x^{13} - 3 x^{12} - 10 x^{11} + 13 x^{10} + 12 x^{9} - 165 x^{8} + 94 x^{7} - 35 x^{6} - 360 x^{5} + 205 x^{4} + 464 x^{3} + 109 x^{2} - 42 x - 13$ |
$14$ |
[6,4] |
$2^{12}\cdot 5^{3}\cdot 73^{8}$ |
$3$ |
$29.686631204$ |
$70.74991995054486$ |
|
|
? |
$F_8:C_6$ (as 14T18) |
trivial |
$2$ |
$9$ |
$148510.390471$ |
| 14.8.845...656.1 |
$x^{14} - 6 x^{13} + 12 x^{12} - 26 x^{11} + 110 x^{10} - 234 x^{9} + 248 x^{8} - 342 x^{7} + 538 x^{6} - 356 x^{5} + 186 x^{4} - 256 x^{3} + 64 x^{2} + 48 x - 10$ |
$14$ |
[8,3] |
$-\,2^{20}\cdot 73^{8}$ |
$2$ |
$31.246312436$ |
$55.91335985267225$ |
|
|
? |
$F_8:C_6$ (as 14T18) |
trivial |
$2$ |
$10$ |
$638290.116569$ |
| 14.8.845...656.2 |
$x^{14} - x^{12} - 27 x^{10} + 51 x^{8} + 67 x^{6} - 115 x^{4} - 41 x^{2} + 1$ |
$14$ |
[8,3] |
$-\,2^{20}\cdot 73^{8}$ |
$2$ |
$31.246312436$ |
$60.97395127863427$ |
|
|
? |
$F_8:C_6$ (as 14T18) |
trivial |
$2$ |
$10$ |
$445200.518323$ |
| 14.8.845...656.3 |
$x^{14} - 4 x^{12} - 40 x^{10} + 84 x^{8} + 136 x^{6} - 240 x^{4} + 4 x^{2} + 4$ |
$14$ |
[8,3] |
$-\,2^{20}\cdot 73^{8}$ |
$2$ |
$31.246312435962817$ |
$47.01734386490306$ |
|
|
? |
$F_8:C_6$ (as 14T18) |
trivial |
$2$ |
$10$ |
$581750.6075640706$ |
| 14.8.228...672.1 |
$x^{14} - 21 x^{12} - 14 x^{11} + 119 x^{10} + 238 x^{9} - 147 x^{8} - 652 x^{7} - 441 x^{6} + 84 x^{5} - 483 x^{4} - 966 x^{3} - 511 x^{2} - 98 x - 5$ |
$14$ |
[8,3] |
$-\,2^{12}\cdot 7^{21}$ |
$2$ |
$33.54847401063839$ |
$36.805738348396915$ |
|
|
? |
$F_8:C_6$ (as 14T18) |
trivial |
$2$ |
$10$ |
$2012636.134734509$ |
| 14.14.660...000.1 |
$x^{14} - 2 x^{13} - 21 x^{12} + 38 x^{11} + 175 x^{10} - 278 x^{9} - 733 x^{8} + 974 x^{7} + 1599 x^{6} - 1640 x^{5} - 1661 x^{4} + 1150 x^{3} + 597 x^{2} - 258 x - 47$ |
$14$ |
[14,0] |
$2^{16}\cdot 5^{3}\cdot 73^{8}$ |
$3$ |
$36.188408785$ |
$100.05549633087136$ |
|
|
? |
$F_8:C_6$ (as 14T18) |
trivial |
$2$ |
$13$ |
$3521147.55218$ |
| 14.14.154...472.1 |
$x^{14} - 23 x^{12} + 189 x^{10} - 723 x^{8} + 1363 x^{6} - 1241 x^{4} + 511 x^{2} - 73$ |
$14$ |
[14,0] |
$2^{18}\cdot 73^{9}$ |
$2$ |
$38.4493476658$ |
$108.78455948029008$ |
|
|
? |
$F_8:C_6$ (as 14T18) |
trivial |
$2$ |
$13$ |
$6393971.60344$ |
| 14.0.226...584.1 |
$x^{14} - 2 x^{13} + 22 x^{12} - 54 x^{11} + 240 x^{10} - 648 x^{9} + 1498 x^{8} - 4160 x^{7} + 6684 x^{6} - 13264 x^{5} + 20352 x^{4} - 22164 x^{3} + 30700 x^{2} - 15156 x + 14300$ |
$14$ |
[0,7] |
$-\,2^{12}\cdot 19^{3}\cdot 73^{8}$ |
$3$ |
$39.5184824981$ |
$137.91698393393153$ |
✓ |
|
? |
$F_8:C_6$ (as 14T18) |
$[18]$ |
$2$ |
$6$ |
$22194.7968555$ |
| 14.0.541...984.1 |
$x^{14} + 22 x^{12} + 188 x^{10} + 780 x^{8} + 1584 x^{6} + 1352 x^{4} + 288 x^{2} + 16$ |
$14$ |
[0,7] |
$-\,2^{26}\cdot 73^{8}$ |
$2$ |
$42.0544179266$ |
$111.8267197053445$ |
✓ |
|
? |
$F_8:C_6$ (as 14T18) |
$[48]$ |
$2$ |
$6$ |
$11097.3984277$ |
| 14.14.108...968.2 |
$x^{14} - 24 x^{12} + 176 x^{10} - 502 x^{8} + 564 x^{6} - 260 x^{4} + 42 x^{2} - 2$ |
$14$ |
[14,0] |
$2^{27}\cdot 73^{8}$ |
$2$ |
$44.18895882108572$ |
$121.94790255726853$ |
|
|
? |
$F_8:C_6$ (as 14T18) |
trivial |
$2$ |
$13$ |
$25995509.59983374$ |
| 14.6.258...000.1 |
$x^{14} - x^{13} + 6 x^{12} - 29 x^{11} + 43 x^{10} - 146 x^{9} + 267 x^{8} - 317 x^{7} - 1813 x^{6} + 732 x^{5} + 4485 x^{4} + 16021 x^{3} - 1150 x^{2} - 11589 x + 1031$ |
$14$ |
[6,4] |
$2^{12}\cdot 5^{7}\cdot 73^{8}$ |
$3$ |
$47.018268619046374$ |
$70.74991995054486$ |
|
|
? |
$F_8:C_6$ (as 14T18) |
$[2]$ |
$2$ |
$9$ |
$1633711.8617625309$ |
| 14.0.257...976.1 |
$x^{14} + 32 x^{12} + 392 x^{10} + 2428 x^{8} + 8228 x^{6} + 15052 x^{4} + 13232 x^{2} + 3844$ |
$14$ |
[0,7] |
$-\,2^{20}\cdot 199^{8}$ |
$2$ |
$55.42084974121413$ |
$118.9865348040865$ |
✓ |
|
? |
$F_8:C_6$ (as 14T18) |
$[80]$ |
$2$ |
$6$ |
$113339.86168168049$ |
