| 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 |
| 14.0.407483719072587.1 |
$x^{14} - x^{13} + 4 x^{12} - x^{11} + 4 x^{10} + 2 x^{9} - 6 x^{8} + 3 x^{7} - 6 x^{6} + 2 x^{5} + 4 x^{4} - x^{3} + 4 x^{2} - x + 1$ |
$14$ |
[0,7] |
$-\,3^{15}\cdot 73^{4}$ |
$2$ |
$11.0555233042$ |
$80.3310880644573$ |
|
|
? |
$A_7\times C_2$ (as 14T47) |
trivial |
$6$ |
$6$ |
$96.5294199023$ |
| 14.0.1667731600838171.1 |
$x^{14} - 3 x^{13} + 5 x^{12} - 5 x^{11} + 3 x^{10} - 6 x^{9} + 12 x^{8} - 21 x^{7} + 25 x^{6} - 19 x^{5} + 14 x^{4} - 5 x^{3} + 4 x^{2} - x + 1$ |
$14$ |
[0,7] |
$-\,11^{9}\cdot 29^{4}$ |
$2$ |
$12.2262909234$ |
$69.62404259846498$ |
|
|
? |
$A_7\times C_2$ (as 14T47) |
trivial |
$2$ |
$6$ |
$84.1958965155$ |
| 14.6.120844706781744833.1 |
$x^{14} - 7 x^{13} + 20 x^{12} - 19 x^{11} - 36 x^{10} + 112 x^{9} - 84 x^{8} - 65 x^{7} + 167 x^{6} - 113 x^{5} - 11 x^{4} + 80 x^{3} - 55 x^{2} + 12 x - 1$ |
$14$ |
[6,4] |
$17^{7}\cdot 131^{4}$ |
$2$ |
$16.6019505744$ |
$106.35028493145434$ |
|
|
? |
$A_7\times C_2$ (as 14T47) |
trivial |
$2$ |
$9$ |
$1409.11802093$ |
| 14.6.155277354533203125.1 |
$x^{14} - 10 x^{12} + 41 x^{10} - 90 x^{8} + 114 x^{6} - 85 x^{4} + 35 x^{2} - 5$ |
$14$ |
[6,4] |
$3^{8}\cdot 5^{9}\cdot 59^{4}$ |
$3$ |
$16.9019298365$ |
$70.72908067166546$ |
|
|
? |
$A_7\times C_2$ (as 14T47) |
trivial |
$2$ |
$9$ |
$2122.32991912$ |
| 14.0.104...027.1 |
$x^{14} - x^{13} + 10 x^{12} - 19 x^{11} + 22 x^{10} - 46 x^{9} + 23 x^{8} + 223 x^{7} - 394 x^{6} - 152 x^{5} + 734 x^{4} - 191 x^{3} - 473 x^{2} + 185 x + 169$ |
$14$ |
[0,7] |
$-\,3^{19}\cdot 547^{4}$ |
$2$ |
$26.9031910709$ |
$501.24168878521635$ |
✓ |
|
? |
$A_7\times C_2$ (as 14T47) |
$[2, 2]$ |
$6$ |
$6$ |
$18139.3317602$ |
| 14.0.122...987.1 |
$x^{14} - 3 x^{13} - 2 x^{12} + 3 x^{11} + 29 x^{10} + 25 x^{9} - 69 x^{8} - 93 x^{7} + 579 x^{6} + 1357 x^{5} + 2826 x^{4} + 2263 x^{3} + 2130 x^{2} + 494 x + 361$ |
$14$ |
[0,7] |
$-\,3^{15}\cdot 29^{4}\cdot 59^{4}$ |
$3$ |
$27.2262019366$ |
$611.6307435196422$ |
✓ |
|
? |
$A_7\times C_2$ (as 14T47) |
$[2]$ |
$6$ |
$6$ |
$22888.2323492$ |
| 14.14.155...125.1 |
$x^{14} - 7 x^{13} + 3 x^{12} + 72 x^{11} - 114 x^{10} - 223 x^{9} + 438 x^{8} + 377 x^{7} - 659 x^{6} - 448 x^{5} + 383 x^{4} + 290 x^{3} - 20 x^{2} - 31 x - 1$ |
$14$ |
[14,0] |
$5^{7}\cdot 6679^{4}$ |
$2$ |
$27.6859672163$ |
$793.0355042500815$ |
|
|
? |
$A_7\times C_2$ (as 14T47) |
trivial |
$2$ |
$13$ |
$296155.532655$ |
| 14.14.763...125.1 |
$x^{14} - 3 x^{13} - 22 x^{12} + 65 x^{11} + 160 x^{10} - 475 x^{9} - 423 x^{8} + 1351 x^{7} + 329 x^{6} - 1444 x^{5} - 76 x^{4} + 608 x^{3} - 20 x^{2} - 81 x + 11$ |
$14$ |
[14,0] |
$5^{7}\cdot 149^{4}\cdot 211^{4}$ |
$3$ |
$43.099880506$ |
$2227.3962524896715$ |
|
|
|
$A_7\times C_2$ (as 14T47) |
trivial |
$2$ |
$13$ |
$13136792.584$ |
