| 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 |
| 14.2.312145214074303896.1 |
$x^{14} - 6 x^{13} + 15 x^{12} - 21 x^{11} + 5 x^{10} + 23 x^{9} - 34 x^{8} - 3 x^{7} + 36 x^{6} - 23 x^{5} - 21 x^{4} + 24 x^{3} + 9 x^{2} - 16 x - 6$ |
$14$ |
[2,6] |
$2^{3}\cdot 3^{3}\cdot 11^{6}\cdot 13^{8}$ |
$4$ |
$17.7662965009$ |
$89.83195783382237$ |
|
|
? |
$C_2\wr F_7$ (as 14T48) |
trivial |
$2$ |
$7$ |
$4213.63772224$ |
| 14.0.936435642222911688.1 |
$x^{14} - 4 x^{13} + 8 x^{12} - 14 x^{11} + 29 x^{10} - 52 x^{9} + 83 x^{8} - 97 x^{7} + 124 x^{6} - 108 x^{5} + 108 x^{4} - 56 x^{3} + 54 x^{2} - 13 x + 11$ |
$14$ |
[0,7] |
$-\,2^{3}\cdot 3^{4}\cdot 11^{6}\cdot 13^{8}$ |
$4$ |
$19.2166196959$ |
$89.83195783382237$ |
|
|
? |
$C_2\wr F_7$ (as 14T48) |
trivial |
$2$ |
$6$ |
$3619.99301644$ |
| 14.0.284...096.1 |
$x^{14} - 7 x^{12} + 7 x^{10} + 35 x^{8} - 49 x^{6} - 49 x^{4} + 49 x^{2} + 49$ |
$14$ |
[0,7] |
$-\,2^{22}\cdot 7^{14}$ |
$2$ |
$20.8039200479$ |
|
|
|
? |
$C_2\wr F_7$ (as 14T48) |
trivial |
$2$ |
$6$ |
$13691.4390163$ |
| 14.2.103...568.1 |
$x^{14} - 3 x^{13} - 4 x^{12} + 13 x^{11} + 21 x^{10} - 39 x^{9} - 53 x^{8} + 47 x^{7} + 95 x^{6} - 25 x^{5} - 71 x^{4} - 22 x^{3} + 26 x^{2} + 7 x + 1$ |
$14$ |
[2,6] |
$2^{3}\cdot 3^{4}\cdot 11^{7}\cdot 13^{8}$ |
$4$ |
$22.8066862043$ |
$89.83195783382237$ |
|
|
? |
$C_2\wr F_7$ (as 14T48) |
trivial |
$2$ |
$7$ |
$22855.5172753$ |
| 14.2.199...672.1 |
$x^{14} - 14 x^{10} - 14 x^{9} + 14 x^{8} - 88 x^{7} + 98 x^{6} - 84 x^{5} + 14 x^{4} - 84 x^{3} - 112 x^{2} - 84 x - 38$ |
$14$ |
[2,6] |
$2^{22}\cdot 7^{15}$ |
$2$ |
$23.906132473361374$ |
|
|
|
? |
$C_2\wr F_7$ (as 14T48) |
trivial |
$2$ |
$7$ |
$25107.183319967484$ |
| 14.4.463...867.1 |
$x^{14} - 9 x^{12} - 6 x^{11} + 36 x^{10} + 32 x^{9} - 34 x^{8} - 54 x^{7} - 116 x^{6} - 143 x^{5} + 192 x^{4} + 289 x^{3} + 125 x^{2} - 24 x - 21$ |
$14$ |
[4,5] |
$-\,3\cdot 7^{8}\cdot 173^{6}$ |
$3$ |
$29.9333877161$ |
$83.36473467247461$ |
|
|
? |
$C_2\wr F_7$ (as 14T48) |
trivial |
$2$ |
$8$ |
$688484.776641$ |
| 14.8.618...156.1 |
$x^{14} - 6 x^{12} - 25 x^{10} + 196 x^{8} - 313 x^{6} + 17 x^{4} + 173 x^{2} + 4$ |
$14$ |
[8,3] |
$-\,2^{2}\cdot 7^{8}\cdot 173^{6}$ |
$3$ |
$30.5548436978$ |
$96.26130400814988$ |
|
|
? |
$C_2\wr F_7$ (as 14T48) |
trivial |
$2$ |
$10$ |
$540448.408326$ |
| 14.10.772...445.1 |
$x^{14} - 7 x^{13} + 6 x^{12} + 55 x^{11} - 168 x^{10} + 169 x^{9} + 182 x^{8} - 851 x^{7} + 1059 x^{6} - 394 x^{5} - 318 x^{4} + 416 x^{3} - 185 x^{2} + 35 x - 2$ |
$14$ |
[10,2] |
$5\cdot 7^{8}\cdot 173^{6}$ |
$3$ |
$31.0457538803$ |
$107.62340968249805$ |
|
|
? |
$C_2\wr F_7$ (as 14T48) |
trivial |
$2$ |
$11$ |
$1491513.19697$ |
| 14.8.108...023.1 |
$x^{14} - 19 x^{12} + 87 x^{10} - 68 x^{8} - 213 x^{6} + 142 x^{4} + 153 x^{2} + 28$ |
$14$ |
[8,3] |
$-\,7^{9}\cdot 173^{6}$ |
$2$ |
$31.8009377765$ |
$66.56890576566373$ |
|
|
? |
$C_2\wr F_7$ (as 14T48) |
trivial |
$2$ |
$10$ |
$2366493.0282$ |
| 14.8.123...312.1 |
$x^{14} - 11 x^{12} - 5 x^{11} + 16 x^{10} + 106 x^{9} + 98 x^{8} - 326 x^{7} - 1116 x^{6} + 1552 x^{5} + 1784 x^{4} - 3304 x^{3} + 885 x^{2} + 579 x - 127$ |
$14$ |
[8,3] |
$-\,2^{3}\cdot 7^{8}\cdot 173^{6}$ |
$3$ |
$32.1057048585$ |
$136.13404166004514$ |
|
|
? |
$C_2\wr F_7$ (as 14T48) |
trivial |
$2$ |
$10$ |
$1006131.18405$ |
| 14.6.123...312.1 |
$x^{14} - x^{13} - 13 x^{12} + 23 x^{11} - 65 x^{9} + 139 x^{8} - 172 x^{7} + 139 x^{6} - 65 x^{5} + 23 x^{3} - 13 x^{2} - x + 1$ |
$14$ |
[6,4] |
$2^{3}\cdot 7^{8}\cdot 173^{6}$ |
$3$ |
$32.1057048585$ |
$136.13404166004514$ |
|
|
? |
$C_2\wr F_7$ (as 14T48) |
trivial |
$2$ |
$9$ |
$517581.430975$ |
| 14.4.170...179.1 |
$x^{14} - 7 x^{13} + 28 x^{12} - 77 x^{11} + 136 x^{10} - 141 x^{9} + 5 x^{8} + 265 x^{7} - 464 x^{6} + 419 x^{5} - 140 x^{4} - 99 x^{3} + 153 x^{2} - 79 x + 18$ |
$14$ |
[4,5] |
$-\,7^{8}\cdot 11\cdot 173^{6}$ |
$3$ |
$32.8443728152$ |
$159.63131361268375$ |
|
|
? |
$C_2\wr F_7$ (as 14T48) |
trivial |
$2$ |
$8$ |
$1070462.31054$ |
| 14.10.185...468.1 |
$x^{14} - 13 x^{12} + 45 x^{10} - 49 x^{8} - 5 x^{6} + 24 x^{4} - 2 x^{2} - 3$ |
$14$ |
[10,2] |
$2^{2}\cdot 3\cdot 7^{8}\cdot 173^{6}$ |
$4$ |
$33.0491394861$ |
$166.72946934494922$ |
|
|
? |
$C_2\wr F_7$ (as 14T48) |
trivial |
$2$ |
$11$ |
$1837714.54031$ |
| 14.6.262...913.1 |
$x^{14} - x^{13} - 6 x^{12} + 27 x^{11} + 14 x^{10} - 164 x^{9} - 5 x^{8} + 350 x^{7} - 449 x^{6} - 869 x^{5} + 1045 x^{4} + 1677 x^{3} + 77 x^{2} - 222 x - 20$ |
$14$ |
[6,4] |
$7^{8}\cdot 17\cdot 173^{6}$ |
$3$ |
$33.881684184$ |
$198.44776204264733$ |
|
|
? |
$C_2\wr F_7$ (as 14T48) |
trivial |
$2$ |
$9$ |
$926657.111518$ |
| 14.8.293...491.1 |
$x^{14} - 9 x^{12} - 12 x^{11} + 10 x^{10} + 203 x^{9} - 52 x^{8} - 740 x^{7} + 268 x^{6} + 840 x^{5} - 361 x^{4} - 279 x^{3} + 136 x^{2} + 21 x - 10$ |
$14$ |
[8,3] |
$-\,7^{8}\cdot 19\cdot 173^{6}$ |
$3$ |
$34.1519357119$ |
$209.79664817248607$ |
|
|
? |
$C_2\wr F_7$ (as 14T48) |
trivial |
$2$ |
$10$ |
$2181934.13455$ |
| 14.6.324...069.1 |
$x^{14} - x^{13} - 21 x^{12} - 12 x^{11} + 82 x^{10} + 11 x^{9} - 208 x^{8} + 80 x^{7} + 293 x^{6} - 245 x^{5} - 135 x^{4} + 305 x^{3} - 55 x^{2} - 90 x + 96$ |
$14$ |
[6,4] |
$3\cdot 7^{9}\cdot 173^{6}$ |
$3$ |
$34.3969564616$ |
$115.30072699039437$ |
|
|
? |
$C_2\wr F_7$ (as 14T48) |
trivial |
$2$ |
$9$ |
$2095369.98756$ |
| 14.6.370...936.1 |
$x^{14} - 16 x^{12} - 8 x^{11} + 76 x^{10} + 118 x^{9} - 166 x^{8} - 954 x^{7} + 565 x^{6} + 3537 x^{5} - 3007 x^{4} - 5201 x^{3} + 5678 x^{2} + 1212 x - 1089$ |
$14$ |
[6,4] |
$2^{3}\cdot 3\cdot 7^{8}\cdot 173^{6}$ |
$4$ |
$34.7266027168$ |
$235.79107679489636$ |
|
|
? |
$C_2\wr F_7$ (as 14T48) |
trivial |
$2$ |
$9$ |
$775756.186614$ |
| 14.4.802...991.1 |
$x^{14} - x^{13} - 6 x^{12} + 47 x^{11} - 53 x^{10} - 109 x^{9} + 388 x^{8} - 690 x^{7} - 332 x^{6} + 1141 x^{5} - 2421 x^{4} + 1566 x^{3} - 70 x^{2} + 516 x + 291$ |
$14$ |
[4,5] |
$-\,3\cdot 7^{8}\cdot 173^{7}$ |
$3$ |
$43.25300713896041$ |
$83.36473467247461$ |
|
|
? |
$C_2\wr F_7$ (as 14T48) |
$[2]$ |
$2$ |
$8$ |
$622759.6806653384$ |
| 14.2.108...589.1 |
$x^{14} - 14 x^{12} - 2 x^{11} + 63 x^{10} - 76 x^{9} - 315 x^{8} + 113 x^{7} - 435 x^{6} - 2835 x^{5} - 3410 x^{4} - 1550 x^{3} - 507 x^{2} - 847 x - 680$ |
$14$ |
[2,6] |
$7^{8}\cdot 173^{6}\cdot 701$ |
$3$ |
$44.1917656734$ |
$1274.3266156282273$ |
|
|
? |
$C_2\wr F_7$ (as 14T48) |
trivial |
$2$ |
$7$ |
$3702954.14277$ |
| 14.2.108...589.2 |
$x^{14} + 2 x^{12} - 12 x^{11} + 5 x^{10} - 13 x^{9} + 17 x^{8} + 301 x^{7} + 704 x^{6} - 845 x^{5} - 1336 x^{4} + 2572 x^{3} - 1061 x^{2} + 474 x - 108$ |
$14$ |
[2,6] |
$7^{8}\cdot 173^{6}\cdot 701$ |
$3$ |
$44.1917656734$ |
$1274.3266156282273$ |
|
|
? |
$C_2\wr F_7$ (as 14T48) |
trivial |
$2$ |
$7$ |
$1667252.28903$ |
| 14.6.454...949.1 |
$x^{14} - 7 x^{13} + 4 x^{12} + 63 x^{11} - 101 x^{10} - 338 x^{9} + 286 x^{8} + 1553 x^{7} + 1844 x^{6} + 1595 x^{5} - 903 x^{4} - 1509 x^{3} - 1331 x^{2} - 930 x - 64$ |
$14$ |
[6,4] |
$7^{8}\cdot 17\cdot 173^{7}$ |
$3$ |
$48.95819817620314$ |
$198.44776204264733$ |
|
|
? |
$C_2\wr F_7$ (as 14T48) |
$[2]$ |
$2$ |
$9$ |
$9449801.37860544$ |
| 14.12.633...744.1 |
$x^{14} - 24 x^{12} + 194 x^{10} - 607 x^{8} + 531 x^{6} + 127 x^{4} - 55 x^{2} + 1$ |
$14$ |
[12,1] |
$-\,2^{12}\cdot 7^{8}\cdot 173^{6}$ |
$3$ |
$50.1304371652$ |
$188.39724552501244$ |
|
|
? |
$C_2\wr F_7$ (as 14T48) |
trivial |
$2$ |
$12$ |
$126296523.288$ |
| 14.12.633...744.2 |
$x^{14} - 13 x^{12} + 52 x^{10} - 49 x^{8} - 89 x^{6} + 164 x^{4} - 65 x^{2} + 4$ |
$14$ |
[12,1] |
$-\,2^{12}\cdot 7^{8}\cdot 173^{6}$ |
$3$ |
$50.1304371652$ |
$188.39724552501244$ |
|
|
? |
$C_2\wr F_7$ (as 14T48) |
trivial |
$2$ |
$12$ |
$74552137.0255$ |
| 14.0.189...232.1 |
$x^{14} + 26 x^{12} + 256 x^{10} + 1188 x^{8} + 2658 x^{6} + 2741 x^{4} + 1081 x^{2} + 48$ |
$14$ |
[0,7] |
$-\,2^{12}\cdot 3\cdot 7^{8}\cdot 173^{6}$ |
$4$ |
$54.2227552122$ |
$235.79107679489636$ |
✓ |
|
? |
$C_2\wr F_7$ (as 14T48) |
$[30]$ |
$2$ |
$6$ |
$93324.5652468$ |
| 14.14.316...720.1 |
$x^{14} - 20 x^{12} + 144 x^{10} - 504 x^{8} + 936 x^{6} - 921 x^{4} + 441 x^{2} - 80$ |
$14$ |
[14,0] |
$2^{12}\cdot 5\cdot 7^{8}\cdot 173^{6}$ |
$4$ |
$56.2377479285$ |
$412.2421207677071$ |
|
|
? |
$C_2\wr F_7$ (as 14T48) |
trivial |
$2$ |
$13$ |
$193825673.236$ |
| 14.0.443...208.1 |
$x^{14} + 33 x^{12} + 357 x^{10} + 1717 x^{8} + 3843 x^{6} + 3555 x^{4} + 727 x^{2} + 7$ |
$14$ |
[0,7] |
$-\,2^{12}\cdot 7^{9}\cdot 173^{6}$ |
$3$ |
$57.6057237799$ |
$254.98641021485514$ |
✓ |
|
? |
$C_2\wr F_7$ (as 14T48) |
$[216]$ |
$2$ |
$6$ |
$93324.5652468$ |
| 14.14.506...952.1 |
$x^{14} - 27 x^{12} + 269 x^{10} - 1286 x^{8} + 3086 x^{6} - 3405 x^{4} + 1265 x^{2} - 128$ |
$14$ |
[14,0] |
$2^{15}\cdot 7^{8}\cdot 173^{6}$ |
$3$ |
$58.1577932964$ |
$260.72480981683105$ |
|
|
? |
$C_2\wr F_7$ (as 14T48) |
trivial |
$2$ |
$13$ |
$463836346.352$ |
| 14.0.766...984.1 |
$x^{14} + 59 x^{12} + 1344 x^{10} + 15094 x^{8} + 88991 x^{6} + 269951 x^{4} + 364517 x^{2} + 121100$ |
$14$ |
[0,7] |
$-\,2^{12}\cdot 7^{9}\cdot 173^{7}$ |
$3$ |
$83.23885039424447$ |
$254.98641021485514$ |
✓ |
|
? |
$C_2\wr F_7$ (as 14T48) |
$[2, 496]$ |
$2$ |
$6$ |
$93324.56524684995$ |
