| Label |
$n$ |
Polynomial |
$p$ |
$e$ |
$f$ |
$c$ |
Galois group |
$u$ |
$t$ |
Visible slopes |
Slope content |
Unram. Ext. |
Eisen. Poly. |
Ind. of Insep. |
Assoc. Inertia |
| 2.14.14.1 |
$14$ |
$x^{14} + 14 x^{13} + 86 x^{12} + 312 x^{11} + 644 x^{10} - 520 x^{9} - 11432 x^{8} - 52608 x^{7} - 119376 x^{6} - 50400 x^{5} + 566816 x^{4} + 1929856 x^{3} + 3246784 x^{2} + 2999424 x + 1331328$ |
$2$ |
$2$ |
$7$ |
$14$ |
$C_2 \wr C_7$ (as 14T29) |
$7$ |
$1$ |
$[2]$ |
$[2, 2, 2, 2, 2, 2, 2]^{7}$ |
$t^{7} + t + 1$ |
$x^{2} + \left(2 t^{3} + 2 t^{2} + 2\right) x + 4 t^{6} + 4 t^{5} + 4 t^{3} + 4 t^{2} + 2$ |
$[1, 0]$ |
$[1]$ |
| 2.14.14.10 |
$14$ |
$x^{14} - 12 x^{13} + 74 x^{12} - 304 x^{11} + 1116 x^{10} - 912 x^{9} + 6104 x^{8} - 1536 x^{7} + 12208 x^{6} - 3648 x^{5} + 8928 x^{4} - 4864 x^{3} + 2368 x^{2} - 768 x + 128$ |
$2$ |
$2$ |
$7$ |
$14$ |
$C_2 \wr C_7$ (as 14T29) |
$7$ |
$1$ |
$[2]$ |
$[2, 2, 2, 2, 2, 2, 2]^{7}$ |
$t^{7} + t + 1$ |
$x^{2} + \left(2 t^{6} + 2 t^{5}\right) x + 2$ |
$[1, 0]$ |
$[1]$ |
| 2.14.14.11 |
$14$ |
$x^{14} + 78 x^{12} + 32 x^{11} + 1220 x^{10} + 2944 x^{9} + 16664 x^{8} + 33152 x^{7} + 97520 x^{6} + 211712 x^{5} + 308000 x^{4} + 480256 x^{3} + 827328 x^{2} + 903168 x + 382592$ |
$2$ |
$2$ |
$7$ |
$14$ |
$C_2 \wr C_7$ (as 14T29) |
$14$ |
$1$ |
$[2]$ |
$[2, 2, 2, 2, 2, 2]^{14}$ |
$t^{7} + t + 1$ |
$x^{2} + \left(2 t^{5} + 2 t^{3} + 2 t^{2} + 2 t\right) x + 4 t^{5} + 4 t^{2} + 2$ |
$[1, 0]$ |
$[1]$ |
| 2.14.14.12 |
$14$ |
$x^{14} + 2 x^{13} + 66 x^{12} + 496 x^{11} + 3092 x^{10} + 16296 x^{9} + 66568 x^{8} + 234688 x^{7} + 669424 x^{6} + 1649632 x^{5} + 3193312 x^{4} + 5403648 x^{3} + 6433984 x^{2} + 6444416 x + 3453824$ |
$2$ |
$2$ |
$7$ |
$14$ |
$C_2 \wr C_7$ (as 14T29) |
$7$ |
$1$ |
$[2]$ |
$[2, 2, 2, 2, 2, 2, 2]^{7}$ |
$t^{7} + t + 1$ |
$x^{2} + \left(2 t^{6} + 2 t^{4} + 2 t^{2} + 2\right) x + 4 t^{5} + 4 t^{4} + 4 t^{3} + 4 t^{2} + 4 t + 6$ |
$[1, 0]$ |
$[1]$ |
| 2.14.14.13 |
$14$ |
$x^{14} + 110 x^{12} + 608 x^{11} + 3212 x^{10} + 8992 x^{9} + 26568 x^{8} + 49792 x^{7} + 109936 x^{6} + 183168 x^{5} + 302112 x^{4} + 136704 x^{3} - 176320 x^{2} - 190464 x + 117632$ |
$2$ |
$2$ |
$7$ |
$14$ |
$C_2 \wr C_7$ (as 14T29) |
$7$ |
$1$ |
$[2]$ |
$[2, 2, 2, 2, 2, 2, 2]^{7}$ |
$t^{7} + t + 1$ |
$x^{2} + \left(2 t^{5} + 2 t^{4} + 2 t^{3} + 2 t^{2}\right) x + 4 t^{6} + 4 t^{4} + 4 t^{2} + 4 t + 6$ |
$[1, 0]$ |
$[1]$ |
| 2.14.14.16 |
$14$ |
$x^{14} + 2 x^{13} + 42 x^{12} + 216 x^{11} + 1444 x^{10} + 6120 x^{9} + 31016 x^{8} + 117248 x^{7} + 421168 x^{6} + 1164128 x^{5} + 2968544 x^{4} + 5580928 x^{3} + 9331904 x^{2} + 10179456 x + 11438976$ |
$2$ |
$2$ |
$7$ |
$14$ |
$C_2 \wr C_7$ (as 14T29) |
$14$ |
$1$ |
$[2]$ |
$[2, 2, 2, 2, 2, 2]^{14}$ |
$t^{7} + t + 1$ |
$x^{2} + \left(2 t^{6} + 2 t^{2} + 2\right) x + 4 t^{5} + 4 t^{4} + 4 t^{2} + 6$ |
$[1, 0]$ |
$[1]$ |
| 2.14.14.17 |
$14$ |
$x^{14} - 12 x^{13} + 90 x^{12} + 112 x^{11} - 1924 x^{10} - 544 x^{9} + 37720 x^{8} + 38592 x^{7} + 6064 x^{6} + 319936 x^{5} + 553440 x^{4} - 259584 x^{3} - 1264320 x^{2} - 1064448 x - 301952$ |
$2$ |
$2$ |
$7$ |
$14$ |
$C_2 \wr C_7$ (as 14T29) |
$14$ |
$1$ |
$[2]$ |
$[2, 2, 2, 2, 2, 2]^{14}$ |
$t^{7} + t + 1$ |
$x^{2} + \left(2 t^{6} + 2 t^{5} + 2 t^{3} + 2 t^{2}\right) x + 4 t^{6} + 4 t^{3} + 4 t + 2$ |
$[1, 0]$ |
$[1]$ |
| 2.14.14.18 |
$14$ |
$x^{14} + 2 x^{13} + 18 x^{12} + 152 x^{11} + 740 x^{10} + 2504 x^{9} + 9768 x^{8} + 30336 x^{7} + 78256 x^{6} + 170976 x^{5} + 351072 x^{4} + 558208 x^{3} + 627904 x^{2} + 397184 x + 190336$ |
$2$ |
$2$ |
$7$ |
$14$ |
$C_2 \wr C_7$ (as 14T29) |
$7$ |
$1$ |
$[2]$ |
$[2, 2, 2, 2, 2, 2, 2]^{7}$ |
$t^{7} + t + 1$ |
$x^{2} + \left(2 t^{6} + 2 t^{4} + 2\right) x + 4 t^{6} + 4 t + 6$ |
$[1, 0]$ |
$[1]$ |
| 2.14.14.21 |
$14$ |
$x^{14} + 14 x^{13} + 150 x^{12} + 920 x^{11} + 4732 x^{10} + 18168 x^{9} + 62696 x^{8} + 168768 x^{7} + 416560 x^{6} + 837152 x^{5} + 1445152 x^{4} + 1942400 x^{3} + 2164544 x^{2} + 1809536 x + 827264$ |
$2$ |
$2$ |
$7$ |
$14$ |
$C_2 \wr C_7$ (as 14T29) |
$14$ |
$1$ |
$[2]$ |
$[2, 2, 2, 2, 2, 2]^{14}$ |
$t^{7} + t + 1$ |
$x^{2} + \left(2 t^{4} + 2 t^{2} + 2 t + 2\right) x + 4 t^{3} + 6$ |
$[1, 0]$ |
$[1]$ |
| 2.14.14.22 |
$14$ |
$x^{14} + 38 x^{12} - 8 x^{11} + 388 x^{10} - 80 x^{9} + 1624 x^{8} + 3712 x^{7} + 28336 x^{6} + 66048 x^{5} + 221984 x^{4} + 196736 x^{3} + 431808 x^{2} + 91392 x + 204928$ |
$2$ |
$2$ |
$7$ |
$14$ |
$C_2 \wr C_7$ (as 14T29) |
$7$ |
$1$ |
$[2]$ |
$[2, 2, 2, 2, 2, 2, 2]^{7}$ |
$t^{7} + t + 1$ |
$x^{2} + \left(2 t^{4} + 2 t^{2} + 2 t\right) x + 4 t^{5} + 4 t^{4} + 2$ |
$[1, 0]$ |
$[1]$ |
| 2.14.14.25 |
$14$ |
$x^{14} + 14 x^{13} + 114 x^{12} + 1200 x^{11} + 11164 x^{10} + 66232 x^{9} + 256408 x^{8} + 687104 x^{7} + 1311088 x^{6} + 1763360 x^{5} + 1573600 x^{4} + 803584 x^{3} + 184384 x^{2} + 90240 x + 130688$ |
$2$ |
$2$ |
$7$ |
$14$ |
$C_2 \wr C_7$ (as 14T29) |
$14$ |
$1$ |
$[2]$ |
$[2, 2, 2, 2, 2, 2]^{14}$ |
$t^{7} + t + 1$ |
$x^{2} + \left(2 t^{5} + 2 t^{4} + 2 t^{3} + 2\right) x + 4 t^{6} + 4 t^{5} + 4 t^{4} + 4 t^{3} + 4 t^{2} + 2$ |
$[1, 0]$ |
$[1]$ |
| 2.14.14.27 |
$14$ |
$x^{14} + 70 x^{12} + 464 x^{11} + 3436 x^{10} + 18112 x^{9} + 84008 x^{8} + 302144 x^{7} + 956912 x^{6} + 2396160 x^{5} + 4775072 x^{4} + 7114240 x^{3} + 6744896 x^{2} + 2924544 x + 1574272$ |
$2$ |
$2$ |
$7$ |
$14$ |
$C_2 \wr C_7$ (as 14T29) |
$7$ |
$1$ |
$[2]$ |
$[2, 2, 2, 2, 2, 2, 2]^{7}$ |
$t^{7} + t + 1$ |
$x^{2} + \left(2 t^{5} + 2 t^{4} + 2 t^{2}\right) x + 4 t^{6} + 4 t^{5} + 4 t^{4} + 4 t^{2} + 4 t + 6$ |
$[1, 0]$ |
$[1]$ |
| 2.14.14.28 |
$14$ |
$x^{14} + 14 x^{13} + 162 x^{12} + 1224 x^{11} + 6876 x^{10} + 30936 x^{9} + 112792 x^{8} + 325440 x^{7} + 782704 x^{6} + 1551008 x^{5} + 2508512 x^{4} + 3324544 x^{3} + 3534912 x^{2} + 2744448 x + 1389184$ |
$2$ |
$2$ |
$7$ |
$14$ |
$C_2 \wr C_7$ (as 14T29) |
$14$ |
$1$ |
$[2]$ |
$[2, 2, 2, 2, 2, 2]^{14}$ |
$t^{7} + t + 1$ |
$x^{2} + \left(2 t^{5} + 2 t^{3} + 2 t^{2} + 2 t + 2\right) x + 4 t^{5} + 4 t^{4} + 4 t^{2} + 2$ |
$[1, 0]$ |
$[1]$ |
| 2.14.14.29 |
$14$ |
$x^{14} + 42 x^{12} + 336 x^{11} + 1572 x^{10} + 1104 x^{9} + 9160 x^{8} + 21760 x^{7} + 63088 x^{6} + 116224 x^{5} + 493152 x^{4} + 727296 x^{3} + 1236928 x^{2} + 742144 x + 194432$ |
$2$ |
$2$ |
$7$ |
$14$ |
$C_2 \wr C_7$ (as 14T29) |
$14$ |
$1$ |
$[2]$ |
$[2, 2, 2, 2, 2, 2]^{14}$ |
$t^{7} + t + 1$ |
$x^{2} + \left(2 t^{5} + 2 t^{4} + 2 t\right) x + 4 t^{6} + 4 t^{4} + 4 t^{3} + 4 t^{2} + 4 t + 6$ |
$[1, 0]$ |
$[1]$ |
| 2.14.14.30 |
$14$ |
$x^{14} + 14 x^{13} + 190 x^{12} + 1848 x^{11} + 11548 x^{10} + 54664 x^{9} + 205352 x^{8} + 564736 x^{7} + 1424048 x^{6} + 2409760 x^{5} + 3832224 x^{4} + 3554944 x^{3} + 2750784 x^{2} + 604032 x + 998272$ |
$2$ |
$2$ |
$7$ |
$14$ |
$C_2 \wr C_7$ (as 14T29) |
$7$ |
$1$ |
$[2]$ |
$[2, 2, 2, 2, 2, 2, 2]^{7}$ |
$t^{7} + t + 1$ |
$x^{2} + \left(2 t^{5} + 2 t^{4} + 2 t^{3} + 2 t + 2\right) x + 4 t^{3} + 4 t^{2} + 6$ |
$[1, 0]$ |
$[1]$ |
| 2.14.14.33 |
$14$ |
$x^{14} + 54 x^{12} + 48 x^{11} + 1212 x^{10} + 2016 x^{9} + 14888 x^{8} + 30400 x^{7} + 110384 x^{6} + 189824 x^{5} + 486944 x^{4} + 467456 x^{3} + 1346880 x^{2} + 270336 x + 1659776$ |
$2$ |
$2$ |
$7$ |
$14$ |
$C_2 \wr C_7$ (as 14T29) |
$7$ |
$1$ |
$[2]$ |
$[2, 2, 2, 2, 2, 2, 2]^{7}$ |
$t^{7} + t + 1$ |
$x^{2} + 2 t^{3} x + 4 t^{5} + 4 t^{3} + 6$ |
$[1, 0]$ |
$[1]$ |
| 2.14.14.35 |
$14$ |
$x^{14} + 14 x^{12} + 48 x^{11} - 124 x^{10} + 640 x^{9} + 5272 x^{8} - 9472 x^{7} - 36944 x^{6} + 63744 x^{5} + 138912 x^{4} - 23808 x^{3} + 110272 x^{2} - 181248 x + 62592$ |
$2$ |
$2$ |
$7$ |
$14$ |
$C_2 \wr C_7$ (as 14T29) |
$7$ |
$1$ |
$[2]$ |
$[2, 2, 2, 2, 2, 2, 2]^{7}$ |
$t^{7} + t + 1$ |
$x^{2} + \left(2 t^{4} + 2 t^{2} + 2 t\right) x + 4 t^{6} + 4 t^{5} + 4 t^{2} + 4 t + 2$ |
$[1, 0]$ |
$[1]$ |
| 2.14.14.4 |
$14$ |
$x^{14} + 2 x^{13} + 38 x^{12} + 240 x^{11} + 884 x^{10} + 4840 x^{9} + 13432 x^{8} + 46528 x^{7} + 102384 x^{6} + 227552 x^{5} + 361632 x^{4} + 465408 x^{3} + 432832 x^{2} + 199040 x + 22656$ |
$2$ |
$2$ |
$7$ |
$14$ |
$C_2 \wr C_7$ (as 14T29) |
$7$ |
$1$ |
$[2]$ |
$[2, 2, 2, 2, 2, 2, 2]^{7}$ |
$t^{7} + t + 1$ |
$x^{2} + \left(2 t^{6} + 2 t^{4} + 2 t^{2} + 2\right) x + 4 t^{5} + 2$ |
$[1, 0]$ |
$[1]$ |
| 2.14.14.5 |
$14$ |
$x^{14} + 2 x^{13} + 70 x^{12} + 808 x^{11} + 7772 x^{10} + 51528 x^{9} + 259720 x^{8} + 1006080 x^{7} + 3047152 x^{6} + 7154528 x^{5} + 12862880 x^{4} + 17283456 x^{3} + 16442432 x^{2} + 9668992 x + 2866048$ |
$2$ |
$2$ |
$7$ |
$14$ |
$C_2 \wr C_7$ (as 14T29) |
$7$ |
$1$ |
$[2]$ |
$[2, 2, 2, 2, 2, 2, 2]^{7}$ |
$t^{7} + t + 1$ |
$x^{2} + \left(2 t^{6} + 2 t^{5} + 2 t^{4} + 2 t^{2} + 2\right) x + 4 t^{6} + 4 t^{5} + 4 t^{4} + 4 t^{3} + 4 t^{2} + 6$ |
$[1, 0]$ |
$[1]$ |
| 2.14.14.7 |
$14$ |
$x^{14} + 2 x^{13} + 42 x^{12} + 704 x^{11} + 3660 x^{10} + 11000 x^{9} + 40152 x^{8} + 158272 x^{7} + 362736 x^{6} + 302048 x^{5} - 214176 x^{4} - 417536 x^{3} - 79552 x^{2} + 172160 x + 89728$ |
$2$ |
$2$ |
$7$ |
$14$ |
$C_2 \wr C_7$ (as 14T29) |
$7$ |
$1$ |
$[2]$ |
$[2, 2, 2, 2, 2, 2, 2]^{7}$ |
$t^{7} + t + 1$ |
$x^{2} + \left(2 t^{6} + 2 t^{5} + 2 t^{4} + 2 t^{2} + 2\right) x + 4 t^{6} + 4 t^{2} + 4 t + 2$ |
$[1, 0]$ |
$[1]$ |
| 2.14.14.9 |
$14$ |
$x^{14} + 14 x^{13} + 162 x^{12} + 1560 x^{11} + 9596 x^{10} + 36936 x^{9} + 91768 x^{8} + 146816 x^{7} + 150832 x^{6} + 89120 x^{5} + 59488 x^{4} + 95872 x^{3} + 61760 x^{2} + 257920 x + 457344$ |
$2$ |
$2$ |
$7$ |
$14$ |
$C_2 \wr C_7$ (as 14T29) |
$7$ |
$1$ |
$[2]$ |
$[2, 2, 2, 2, 2, 2, 2]^{7}$ |
$t^{7} + t + 1$ |
$x^{2} + \left(2 t^{5} + 2 t^{4} + 2 t^{3} + 2 t + 2\right) x + 4 t^{5} + 4 t^{4} + 4 t^{2} + 4 t + 2$ |
$[1, 0]$ |
$[1]$ |
| 2.14.21.1 |
$14$ |
$x^{14} - 24 x^{13} + 310 x^{12} - 448 x^{11} + 31892 x^{10} - 21856 x^{9} + 718648 x^{8} - 960512 x^{7} + 7507504 x^{6} - 4420736 x^{5} + 55408160 x^{4} + 18013184 x^{3} + 137399744 x^{2} + 37318144 x + 94078592$ |
$2$ |
$2$ |
$7$ |
$21$ |
$C_2 \wr C_7$ (as 14T29) |
$7$ |
$1$ |
$[3]$ |
$[2, 2, 2, 2, 2, 2, 3]^{7}$ |
$t^{7} + t + 1$ |
$x^{2} + \left(4 t^{6} + 4 t^{5} + 4 t^{4}\right) x + 8 t^{4} + 8 t^{2} + 10$ |
$[2, 0]$ |
$[1]$ |
| 2.14.21.11 |
$14$ |
$x^{14} + 28 x^{13} + 510 x^{12} + 8384 x^{11} + 101460 x^{10} + 783408 x^{9} + 3431320 x^{8} + 5962240 x^{7} - 2627792 x^{6} + 14709056 x^{5} + 55863200 x^{4} - 173569024 x^{3} - 154837568 x^{2} + 514519296 x - 215357312$ |
$2$ |
$2$ |
$7$ |
$21$ |
$C_2 \wr C_7$ (as 14T29) |
$7$ |
$1$ |
$[3]$ |
$[2, 2, 2, 2, 2, 2, 3]^{7}$ |
$t^{7} + t + 1$ |
$x^{2} + \left(4 t^{5} + 4 t^{4} + 4 t^{2} + 4\right) x + 8 t^{6} + 4 t^{5} + 4 t^{4} + 8 t^{3} + 8 t^{2} + 12 t + 2$ |
$[2, 0]$ |
$[1]$ |
| 2.14.21.12 |
$14$ |
$x^{14} - 24 x^{13} + 786 x^{12} - 5616 x^{11} + 38196 x^{10} + 61888 x^{9} + 86184 x^{8} + 2682752 x^{7} + 10850864 x^{6} + 34114176 x^{5} + 87284576 x^{4} + 177201408 x^{3} + 308454336 x^{2} + 311934976 x + 122913664$ |
$2$ |
$2$ |
$7$ |
$21$ |
$C_2 \wr C_7$ (as 14T29) |
$7$ |
$1$ |
$[3]$ |
$[2, 2, 2, 2, 2, 2, 3]^{7}$ |
$t^{7} + t + 1$ |
$x^{2} + \left(4 t^{6} + 4 t^{5} + 4 t^{4} + 4 t^{3} + 4 t^{2} + 4 t\right) x + 12 t^{6} + 4 t^{5} + 4 t^{3} + 4 t^{2} + 4 t + 6$ |
$[2, 0]$ |
$[1]$ |
| 2.14.21.13 |
$14$ |
$x^{14} + 28 x^{13} + 690 x^{12} + 7888 x^{11} + 70564 x^{10} + 437328 x^{9} + 2540296 x^{8} + 11475584 x^{7} + 48388016 x^{6} + 163996224 x^{5} + 484180064 x^{4} + 1217939712 x^{3} + 2468243136 x^{2} + 3992333056 x + 3284656512$ |
$2$ |
$2$ |
$7$ |
$21$ |
$C_2 \wr C_7$ (as 14T29) |
$7$ |
$1$ |
$[3]$ |
$[2, 2, 2, 2, 2, 2, 3]^{7}$ |
$t^{7} + t + 1$ |
$x^{2} + \left(4 t^{4} + 4 t^{3} + 4 t^{2} + 4 t + 4\right) x + 12 t^{5} + 4 t^{4} + 12 t^{2} + 12 t + 14$ |
$[2, 0]$ |
$[1]$ |
| 2.14.21.14 |
$14$ |
$x^{14} - 24 x^{13} + 578 x^{12} - 4816 x^{11} + 30356 x^{10} + 155392 x^{9} + 85544 x^{8} + 2565760 x^{7} + 10082096 x^{6} + 13385856 x^{5} + 45529696 x^{4} + 148247296 x^{3} + 232446400 x^{2} + 174429184 x + 53748608$ |
$2$ |
$2$ |
$7$ |
$21$ |
$C_2 \wr C_7$ (as 14T29) |
$7$ |
$1$ |
$[3]$ |
$[2, 2, 2, 2, 2, 2, 3]^{7}$ |
$t^{7} + t + 1$ |
$x^{2} + \left(4 t^{6} + 4 t^{5} + 4 t^{3} + 4 t^{2} + 4 t\right) x + 12 t^{6} + 4 t^{4} + 4 t + 6$ |
$[2, 0]$ |
$[1]$ |
| 2.14.21.15 |
$14$ |
$x^{14} + 28 x^{13} + 594 x^{12} + 8032 x^{11} + 83732 x^{10} + 640112 x^{9} + 3689704 x^{8} + 15420416 x^{7} + 49152048 x^{6} + 122918208 x^{5} + 239944544 x^{4} + 388045312 x^{3} + 473533888 x^{2} + 297688320 x + 70766464$ |
$2$ |
$2$ |
$7$ |
$21$ |
$C_2 \wr C_7$ (as 14T29) |
$7$ |
$1$ |
$[3]$ |
$[2, 2, 2, 2, 2, 2, 3]^{7}$ |
$t^{7} + t + 1$ |
$x^{2} + \left(4 t^{5} + 4 t^{2} + 4 t + 4\right) x + 8 t^{6} + 4 t^{4} + 8 t^{3} + 4 t^{2} + 8 t + 14$ |
$[2, 0]$ |
$[1]$ |
| 2.14.21.16 |
$14$ |
$x^{14} - 58 x^{12} + 96 x^{11} + 996 x^{10} + 4736 x^{9} - 24168 x^{8} - 361728 x^{7} + 2560944 x^{6} + 8902656 x^{5} - 28504032 x^{4} + 5074432 x^{3} + 241889984 x^{2} + 98285568 x - 755960704$ |
$2$ |
$2$ |
$7$ |
$21$ |
$C_2 \wr C_7$ (as 14T29) |
$7$ |
$1$ |
$[3]$ |
$[2, 2, 2, 2, 2, 2, 3]^{7}$ |
$t^{7} + t + 1$ |
$x^{2} + 4 t^{2} x + 12 t^{6} + 8 t^{5} + 12 t^{3} + 4 t + 2$ |
$[2, 0]$ |
$[1]$ |
| 2.14.21.18 |
$14$ |
$x^{14} - 24 x^{13} + 342 x^{12} + 768 x^{11} - 23596 x^{10} - 11680 x^{9} + 863032 x^{8} + 2247168 x^{7} + 7158576 x^{6} + 29476224 x^{5} + 63538720 x^{4} + 113563648 x^{3} + 154097088 x^{2} + 117418496 x + 81600128$ |
$2$ |
$2$ |
$7$ |
$21$ |
$C_2 \wr C_7$ (as 14T29) |
$7$ |
$1$ |
$[3]$ |
$[2, 2, 2, 2, 2, 2, 3]^{7}$ |
$t^{7} + t + 1$ |
$x^{2} + \left(4 t^{6} + 4 t^{5} + 4 t^{3} + 4 t^{2}\right) x + 12 t^{6} + 8 t^{4} + 12 t^{3} + 2$ |
$[2, 0]$ |
$[1]$ |
| 2.14.21.2 |
$14$ |
$x^{14} + 4 x^{13} + 42 x^{12} + 256 x^{11} + 4788 x^{10} + 35664 x^{9} + 193928 x^{8} + 461056 x^{7} + 204336 x^{6} - 3373376 x^{5} - 1338400 x^{4} + 26864640 x^{3} + 73898944 x^{2} - 22860032 x + 16452992$ |
$2$ |
$2$ |
$7$ |
$21$ |
$C_2 \wr C_7$ (as 14T29) |
$7$ |
$1$ |
$[3]$ |
$[2, 2, 2, 2, 2, 2, 3]^{7}$ |
$t^{7} + t + 1$ |
$x^{2} + \left(4 t^{6} + 4\right) x + 12 t^{4} + 12 t^{3} + 12 t^{2} + 4 t + 6$ |
$[2, 0]$ |
$[1]$ |
| 2.14.21.20 |
$14$ |
$x^{14} + 28 x^{13} + 458 x^{12} + 5600 x^{11} + 55220 x^{10} + 446640 x^{9} + 2993416 x^{8} + 16632832 x^{7} + 75974192 x^{6} + 279485248 x^{5} + 817828320 x^{4} + 1797079552 x^{3} + 2825079744 x^{2} + 2847056128 x + 1501721984$ |
$2$ |
$2$ |
$7$ |
$21$ |
$C_2 \wr C_7$ (as 14T29) |
$7$ |
$1$ |
$[3]$ |
$[2, 2, 2, 2, 2, 2, 3]^{7}$ |
$t^{7} + t + 1$ |
$x^{2} + \left(4 t^{3} + 4\right) x + 4 t^{6} + 4 t^{5} + 12 t^{4} + 12 t^{3} + 12 t^{2} + 14$ |
$[2, 0]$ |
$[1]$ |
| 2.14.21.22 |
$14$ |
$x^{14} + 28 x^{13} + 422 x^{12} + 4896 x^{11} + 41252 x^{10} + 139376 x^{9} + 108312 x^{8} - 150784 x^{7} + 925104 x^{6} + 4176704 x^{5} + 3222048 x^{4} - 6475264 x^{3} - 18786624 x^{2} - 18160384 x - 6259584$ |
$2$ |
$2$ |
$7$ |
$21$ |
$C_2 \wr C_7$ (as 14T29) |
$7$ |
$1$ |
$[3]$ |
$[2, 2, 2, 2, 2, 2, 3]^{7}$ |
$t^{7} + t + 1$ |
$x^{2} + \left(4 t^{5} + 4 t^{4} + 4 t + 4\right) x + 4 t^{6} + 4 t^{5} + 8 t + 2$ |
$[2, 0]$ |
$[1]$ |
| 2.14.21.23 |
$14$ |
$x^{14} + 28 x^{13} + 354 x^{12} + 3328 x^{11} + 25540 x^{10} + 129712 x^{9} + 475848 x^{8} + 1959424 x^{7} + 6270896 x^{6} + 10683712 x^{5} + 29122400 x^{4} + 44046336 x^{3} + 9184448 x^{2} + 133839104 x - 62685824$ |
$2$ |
$2$ |
$7$ |
$21$ |
$C_2 \wr C_7$ (as 14T29) |
$7$ |
$1$ |
$[3]$ |
$[2, 2, 2, 2, 2, 2, 3]^{7}$ |
$t^{7} + t + 1$ |
$x^{2} + \left(4 t^{4} + 4 t + 4\right) x + 4 t^{6} + 12 t^{5} + 4 t^{4} + 8 t^{3} + 12 t^{2} + 12 t + 6$ |
$[2, 0]$ |
$[1]$ |
| 2.14.21.24 |
$14$ |
$x^{14} + 118 x^{12} - 448 x^{11} + 7012 x^{10} - 6464 x^{9} + 117080 x^{8} + 233728 x^{7} + 1416624 x^{6} + 2361344 x^{5} + 29156640 x^{4} - 50792448 x^{3} + 365138624 x^{2} - 452447232 x + 1020360832$ |
$2$ |
$2$ |
$7$ |
$21$ |
$C_2 \wr C_7$ (as 14T29) |
$7$ |
$1$ |
$[3]$ |
$[2, 2, 2, 2, 2, 2, 3]^{7}$ |
$t^{7} + t + 1$ |
$x^{2} + \left(4 t^{3} + 4 t^{2} + 4 t\right) x + 12 t^{5} + 12 t^{4} + 4 t^{3} + 4 t^{2} + 4 t + 10$ |
$[2, 0]$ |
$[1]$ |
| 2.14.21.27 |
$14$ |
$x^{14} + 4 x^{13} + 86 x^{12} + 1536 x^{11} + 4500 x^{10} + 13136 x^{9} + 37624 x^{8} - 147456 x^{7} - 1187024 x^{6} - 1620800 x^{5} + 944160 x^{4} + 9543680 x^{3} + 21477824 x^{2} + 18102016 x + 4070016$ |
$2$ |
$2$ |
$7$ |
$21$ |
$C_2 \wr C_7$ (as 14T29) |
$7$ |
$1$ |
$[3]$ |
$[2, 2, 2, 2, 2, 2, 3]^{7}$ |
$t^{7} + t + 1$ |
$x^{2} + \left(4 t^{6} + 4 t^{4} + 4 t^{2} + 4\right) x + 4 t^{6} + 8 t^{4} + 4 t + 2$ |
$[2, 0]$ |
$[1]$ |
| 2.14.21.28 |
$14$ |
$x^{14} - 24 x^{13} + 282 x^{12} - 1808 x^{11} + 8644 x^{10} - 32256 x^{9} + 126376 x^{8} - 112000 x^{7} + 920240 x^{6} + 106624 x^{5} + 2576352 x^{4} - 2898176 x^{3} + 997568 x^{2} - 5954560 x + 4480896$ |
$2$ |
$2$ |
$7$ |
$21$ |
$C_2 \wr C_7$ (as 14T29) |
$7$ |
$1$ |
$[3]$ |
$[2, 2, 2, 2, 2, 2, 3]^{7}$ |
$t^{7} + t + 1$ |
$x^{2} + 4 t^{6} x + 4 t^{5} + 4 t^{4} + 4 t^{3} + 12 t^{2} + 12 t + 6$ |
$[2, 0]$ |
$[1]$ |
| 2.14.21.29 |
$14$ |
$x^{14} + 28 x^{13} + 334 x^{12} + 2720 x^{11} + 18836 x^{10} + 103472 x^{9} + 518424 x^{8} + 2310400 x^{7} + 8718640 x^{6} + 30512448 x^{5} + 85527712 x^{4} + 194830848 x^{3} + 435061184 x^{2} + 413663488 x + 915417216$ |
$2$ |
$2$ |
$7$ |
$21$ |
$C_2 \wr C_7$ (as 14T29) |
$7$ |
$1$ |
$[3]$ |
$[2, 2, 2, 2, 2, 2, 3]^{7}$ |
$t^{7} + t + 1$ |
$x^{2} + \left(4 t + 4\right) x + 12 t^{6} + 8 t^{5} + 8 t^{4} + 4 t^{3} + 12 t^{2} + 10$ |
$[2, 0]$ |
$[1]$ |
| 2.14.21.3 |
$14$ |
$x^{14} + 28 x^{13} + 378 x^{12} + 3664 x^{11} + 32500 x^{10} + 273168 x^{9} + 1874504 x^{8} + 9363072 x^{7} + 32697904 x^{6} + 76914752 x^{5} + 115280608 x^{4} + 93905152 x^{3} + 46798784 x^{2} + 116983552 x + 185864576$ |
$2$ |
$2$ |
$7$ |
$21$ |
$C_2 \wr C_7$ (as 14T29) |
$7$ |
$1$ |
$[3]$ |
$[2, 2, 2, 2, 2, 2, 3]^{7}$ |
$t^{7} + t + 1$ |
$x^{2} + \left(4 t^{5} + 4\right) x + 4 t^{5} + 12 t^{4} + 8 t^{2} + 8 t + 6$ |
$[2, 0]$ |
$[1]$ |
| 2.14.21.30 |
$14$ |
$x^{14} + 322 x^{12} + 992 x^{11} + 24148 x^{10} + 8064 x^{9} + 317928 x^{8} + 478720 x^{7} - 3399120 x^{6} + 4096512 x^{5} + 29321824 x^{4} - 2311680 x^{3} - 71904832 x^{2} - 80338944 x - 49698944$ |
$2$ |
$2$ |
$7$ |
$21$ |
$C_2 \wr C_7$ (as 14T29) |
$7$ |
$1$ |
$[3]$ |
$[2, 2, 2, 2, 2, 2, 3]^{7}$ |
$t^{7} + t + 1$ |
$x^{2} + \left(4 t^{5} + 4 t^{4} + 4 t^{2} + 4 t\right) x + 4 t^{6} + 8 t^{5} + 4 t^{4} + 12 t^{3} + 4 t + 6$ |
$[2, 0]$ |
$[1]$ |
| 2.14.21.31 |
$14$ |
$x^{14} + 4 x^{13} + 14 x^{12} + 2128 x^{11} + 52820 x^{10} + 576624 x^{9} + 3828760 x^{8} + 17907072 x^{7} + 57734448 x^{6} + 129816512 x^{5} + 175769760 x^{4} + 75629824 x^{3} - 125368896 x^{2} - 178349824 x - 67479424$ |
$2$ |
$2$ |
$7$ |
$21$ |
$C_2 \wr C_7$ (as 14T29) |
$7$ |
$1$ |
$[3]$ |
$[2, 2, 2, 2, 2, 2, 3]^{7}$ |
$t^{7} + t + 1$ |
$x^{2} + \left(4 t^{6} + 4 t^{5} + 4 t^{4} + 4\right) x + 12 t^{5} + 8 t^{3} + 2$ |
$[2, 0]$ |
$[1]$ |
| 2.14.21.32 |
$14$ |
$x^{14} - 24 x^{13} + 418 x^{12} + 1840 x^{11} + 15268 x^{10} + 49216 x^{9} + 181896 x^{8} + 872320 x^{7} + 2279088 x^{6} + 3532928 x^{5} + 26386784 x^{4} - 17133824 x^{3} + 26938048 x^{2} + 52731904 x + 102902144$ |
$2$ |
$2$ |
$7$ |
$21$ |
$C_2 \wr C_7$ (as 14T29) |
$7$ |
$1$ |
$[3]$ |
$[2, 2, 2, 2, 2, 2, 3]^{7}$ |
$t^{7} + t + 1$ |
$x^{2} + \left(4 t^{6} + 4 t^{5} + 4 t^{4} + 4 t^{3}\right) x + 4 t^{6} + 4 t^{5} + 4 t^{4} + 12 t^{2} + 4 t + 6$ |
$[2, 0]$ |
$[1]$ |
| 2.14.21.36 |
$14$ |
$x^{14} - 24 x^{13} + 318 x^{12} - 2240 x^{11} + 8276 x^{10} + 5280 x^{9} - 118824 x^{8} + 253952 x^{7} + 1583664 x^{6} + 1514368 x^{5} - 2190432 x^{4} - 11588608 x^{3} - 13098560 x^{2} - 10711552 x + 1152$ |
$2$ |
$2$ |
$7$ |
$21$ |
$C_2 \wr C_7$ (as 14T29) |
$7$ |
$1$ |
$[3]$ |
$[2, 2, 2, 2, 2, 2, 3]^{7}$ |
$t^{7} + t + 1$ |
$x^{2} + \left(4 t^{6} + 4 t\right) x + 8 t^{6} + 8 t^{3} + 2$ |
$[2, 0]$ |
$[1]$ |
| 2.14.21.37 |
$14$ |
$x^{14} - 24 x^{13} + 566 x^{12} - 4720 x^{11} + 27300 x^{10} - 73664 x^{9} - 43752 x^{8} + 2067840 x^{7} - 8352848 x^{6} + 34541184 x^{5} - 27340000 x^{4} + 140902656 x^{3} + 149096128 x^{2} - 8656896 x - 499526528$ |
$2$ |
$2$ |
$7$ |
$21$ |
$C_2 \wr C_7$ (as 14T29) |
$7$ |
$1$ |
$[3]$ |
$[2, 2, 2, 2, 2, 2, 3]^{7}$ |
$t^{7} + t + 1$ |
$x^{2} + \left(4 t^{6} + 4 t^{4} + 4 t^{3} + 4 t^{2}\right) x + 12 t^{5} + 4 t^{3} + 12 t + 10$ |
$[2, 0]$ |
$[1]$ |
| 2.14.21.39 |
$14$ |
$x^{14} + 4 x^{13} - 34 x^{12} + 80 x^{11} + 4372 x^{10} + 25328 x^{9} + 120280 x^{8} + 1136512 x^{7} + 7151920 x^{6} + 20307904 x^{5} + 15339424 x^{4} - 29721344 x^{3} - 17585728 x^{2} + 134123776 x + 90221696$ |
$2$ |
$2$ |
$7$ |
$21$ |
$C_2 \wr C_7$ (as 14T29) |
$7$ |
$1$ |
$[3]$ |
$[2, 2, 2, 2, 2, 2, 3]^{7}$ |
$t^{7} + t + 1$ |
$x^{2} + \left(4 t^{6} + 4\right) x + 8 t^{6} + 8 t^{5} + 12 t^{4} + 4 t^{3} + 8 t^{2} + 8 t + 2$ |
$[2, 0]$ |
$[1]$ |
| 2.14.21.4 |
$14$ |
$x^{14} + 28 x^{13} + 382 x^{12} + 5040 x^{11} + 67924 x^{10} + 654608 x^{9} + 3941912 x^{8} + 13991552 x^{7} + 24218160 x^{6} - 6224320 x^{5} - 104638048 x^{4} - 129754368 x^{3} + 125379008 x^{2} + 420916992 x + 285988992$ |
$2$ |
$2$ |
$7$ |
$21$ |
$C_2 \wr C_7$ (as 14T29) |
$7$ |
$1$ |
$[3]$ |
$[2, 2, 2, 2, 2, 2, 3]^{7}$ |
$t^{7} + t + 1$ |
$x^{2} + \left(4 t^{5} + 4 t^{4} + 4\right) x + 4 t^{6} + 4 t^{5} + 12 t^{4} + 12 t + 10$ |
$[2, 0]$ |
$[1]$ |
| 2.14.21.5 |
$14$ |
$x^{14} - 10 x^{12} + 2320 x^{11} + 23044 x^{10} + 85408 x^{9} + 334168 x^{8} + 1354880 x^{7} + 4478640 x^{6} + 17039616 x^{5} + 66434336 x^{4} + 154381568 x^{3} + 171738304 x^{2} + 91275776 x + 46291072$ |
$2$ |
$2$ |
$7$ |
$21$ |
$C_2 \wr C_7$ (as 14T29) |
$7$ |
$1$ |
$[3]$ |
$[2, 2, 2, 2, 2, 2, 3]^{7}$ |
$t^{7} + t + 1$ |
$x^{2} + \left(4 t^{5} + 4 t^{4}\right) x + 4 t^{6} + 12 t^{5} + 8 t^{4} + 12 t^{2} + 12 t + 2$ |
$[2, 0]$ |
$[1]$ |
| 2.14.21.7 |
$14$ |
$x^{14} - 24 x^{13} + 698 x^{12} - 5728 x^{11} + 75284 x^{10} - 134432 x^{9} - 657400 x^{8} - 2235136 x^{7} + 4791856 x^{6} + 51322240 x^{5} + 204417760 x^{4} + 462090752 x^{3} + 689997248 x^{2} + 615309824 x + 301016448$ |
$2$ |
$2$ |
$7$ |
$21$ |
$C_2 \wr C_7$ (as 14T29) |
$7$ |
$1$ |
$[3]$ |
$[2, 2, 2, 2, 2, 2, 3]^{7}$ |
$t^{7} + t + 1$ |
$x^{2} + \left(4 t^{6} + 4 t^{5} + 4 t^{4} + 4 t^{2} + 4 t\right) x + 8 t^{5} + 12 t^{4} + 8 t^{2} + 8 t + 6$ |
$[2, 0]$ |
$[1]$ |
| 2.14.21.8 |
$14$ |
$x^{14} + 28 x^{13} + 514 x^{12} + 6496 x^{11} + 66548 x^{10} + 443120 x^{9} + 1856232 x^{8} + 4701440 x^{7} + 6244912 x^{6} + 10711872 x^{5} + 55838816 x^{4} + 147228160 x^{3} + 232757184 x^{2} + 259431680 x - 65736832$ |
$2$ |
$2$ |
$7$ |
$21$ |
$C_2 \wr C_7$ (as 14T29) |
$7$ |
$1$ |
$[3]$ |
$[2, 2, 2, 2, 2, 2, 3]^{7}$ |
$t^{7} + t + 1$ |
$x^{2} + \left(4 t^{4} + 4 t^{3} + 4\right) x + 4 t^{6} + 12 t^{5} + 4 t^{3} + 12 t^{2} + 12 t + 6$ |
$[2, 0]$ |
$[1]$ |
| 2.14.21.9 |
$14$ |
$x^{14} + 106 x^{12} + 1088 x^{11} + 10884 x^{10} + 77568 x^{9} + 675880 x^{8} + 5133824 x^{7} + 23392432 x^{6} + 54729728 x^{5} + 38550752 x^{4} - 56208384 x^{3} - 30083904 x^{2} + 68354048 x - 30937216$ |
$2$ |
$2$ |
$7$ |
$21$ |
$C_2 \wr C_7$ (as 14T29) |
$7$ |
$1$ |
$[3]$ |
$[2, 2, 2, 2, 2, 2, 3]^{7}$ |
$t^{7} + t + 1$ |
$x^{2} + \left(4 t^{5} + 4 t^{2}\right) x + 8 t^{6} + 12 t^{5} + 4 t^{4} + 4 t^{2} + 12 t + 6$ |
$[2, 0]$ |
$[1]$ |
