| 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) |
$7$ |
$1$ |
$[2]$ |
$[2, 2, 2, 2, 2, 2, 2]^{7}$ |
$t^{7} + t + 1$ |
$x^{2} + \left(2 t^{5} + 2 t^{4} + 2 t^{3} + 2 t^{2}\right) x + 4 t^{6} + 4 t^{4} + 4 t^{2} + 4 t + 6$ |
$[1, 0]$ |
$[1]$ |
| 2.14.14.14 |
$14$ |
$x^{14} + 2 x^{12} + 56 x^{11} + 12 x^{10} + 192 x^{9} + 1336 x^{8} + 768 x^{7} + 1712 x^{6} - 512 x^{5} + 18528 x^{4} + 39552 x^{3} - 204224 x^{2} - 195584 x + 259712$ |
$2$ |
$2$ |
$7$ |
$14$ |
$C_2\times F_8$ (as 14T9) |
$7$ |
$1$ |
$[2]$ |
$[2, 2, 2, 2]^{7}$ |
$t^{7} + t + 1$ |
$x^{2} + \left(2 t^{3} + 2 t\right) x + 4 t^{6} + 4 t^{4} + 4 t + 2$ |
$[1, 0]$ |
$[1]$ |
| 2.14.14.15 |
$14$ |
$x^{14} + 14 x^{13} + 126 x^{12} + 784 x^{11} + 4300 x^{10} + 19592 x^{9} + 80680 x^{8} + 276608 x^{7} + 822832 x^{6} + 1982880 x^{5} + 3998112 x^{4} + 6222080 x^{3} + 7679040 x^{2} + 6275456 x + 3453824$ |
$2$ |
$2$ |
$7$ |
$14$ |
$C_{14}$ (as 14T1) |
$7$ |
$1$ |
$[2]$ |
$[2]^{7}$ |
$t^{7} + t + 1$ |
$x^{2} + 2 x + 4 t^{5} + 4 t^{4} + 4 t^{3} + 4 t^{2} + 4 t + 6$ |
$[1, 0]$ |
$[1]$ |
| 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) |
$7$ |
$1$ |
$[2]$ |
$[2, 2, 2, 2, 2, 2, 2]^{7}$ |
$t^{7} + t + 1$ |
$x^{2} + \left(2 t^{6} + 2 t^{4} + 2\right) x + 4 t^{6} + 4 t + 6$ |
$[1, 0]$ |
$[1]$ |
| 2.14.14.19 |
$14$ |
$x^{14} + 14 x^{13} + 98 x^{12} + 400 x^{11} + 956 x^{10} + 1160 x^{9} + 152 x^{8} - 320 x^{7} + 5296 x^{6} + 6432 x^{5} - 11936 x^{4} + 21504 x^{3} + 2368 x^{2} - 13440 x + 16512$ |
$2$ |
$2$ |
$7$ |
$14$ |
$C_2^3:F_8$ (as 14T21) |
$7$ |
$1$ |
$[2]$ |
$[2, 2, 2, 2, 2, 2]^{7}$ |
$t^{7} + t + 1$ |
$x^{2} + \left(2 t^{4} + 2 t^{2} + 2\right) x + 4 t^{6} + 2$ |
$[1, 0]$ |
$[1]$ |
| 2.14.14.2 |
$14$ |
$x^{14} + 14 x^{13} + 102 x^{12} + 576 x^{11} + 3140 x^{10} + 14392 x^{9} + 49912 x^{8} + 153536 x^{7} + 453296 x^{6} + 957216 x^{5} + 952608 x^{4} + 59648 x^{3} + 31936 x^{2} + 608384 x - 370048$ |
$2$ |
$2$ |
$7$ |
$14$ |
$C_2\times F_8$ (as 14T9) |
$14$ |
$1$ |
$[2]$ |
$[2, 2, 2]^{14}$ |
$t^{7} + t + 1$ |
$x^{2} + \left(2 t^{5} + 2 t^{2} + 2\right) x + 4 t^{6} + 4 t^{5} + 4 t + 2$ |
$[1, 0]$ |
$[1]$ |
| 2.14.14.20 |
$14$ |
$x^{14} + 14 x^{13} + 126 x^{12} + 1168 x^{11} + 9868 x^{10} + 64520 x^{9} + 317384 x^{8} + 1190080 x^{7} + 3447536 x^{6} + 7751584 x^{5} + 13448736 x^{4} + 17658368 x^{3} + 16807744 x^{2} + 10589568 x + 3453824$ |
$2$ |
$2$ |
$7$ |
$14$ |
$C_2^3:F_8$ (as 14T21) |
$7$ |
$1$ |
$[2]$ |
$[2, 2, 2, 2, 2, 2]^{7}$ |
$t^{7} + t + 1$ |
$x^{2} + \left(2 t^{5} + 2 t^{4} + 2\right) x + 4 t^{5} + 4 t^{4} + 4 t^{3} + 4 t^{2} + 4 t + 6$ |
$[1, 0]$ |
$[1]$ |
| 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) |
$7$ |
$1$ |
$[2]$ |
$[2, 2, 2, 2, 2, 2, 2]^{7}$ |
$t^{7} + t + 1$ |
$x^{2} + \left(2 t^{4} + 2 t^{2} + 2 t\right) x + 4 t^{5} + 4 t^{4} + 2$ |
$[1, 0]$ |
$[1]$ |
| 2.14.14.23 |
$14$ |
$x^{14} - 12 x^{13} + 142 x^{12} - 640 x^{11} + 2548 x^{10} - 3904 x^{9} + 12280 x^{8} - 34048 x^{7} + 159536 x^{6} - 121792 x^{5} - 109152 x^{4} - 121344 x^{3} + 389056 x^{2} - 197120 x + 9856$ |
$2$ |
$2$ |
$7$ |
$14$ |
$F_8$ (as 14T6) |
$7$ |
$1$ |
$[2]$ |
$[2, 2, 2]^{7}$ |
$t^{7} + t + 1$ |
$x^{2} + \left(2 t^{6} + 2 t^{4} + 2 t^{3} + 2 t\right) x + 4 t^{5} + 4 t^{2} + 4 t + 2$ |
$[1, 0]$ |
$[1]$ |
| 2.14.14.24 |
$14$ |
$x^{14} + 54 x^{12} + 64 x^{11} + 1396 x^{10} + 192 x^{9} + 12440 x^{8} - 2496 x^{7} + 52592 x^{6} + 38144 x^{5} + 19360 x^{4} + 147712 x^{3} - 46912 x^{2} - 86016 x + 382592$ |
$2$ |
$2$ |
$7$ |
$14$ |
$C_2\times F_8$ (as 14T9) |
$7$ |
$1$ |
$[2]$ |
$[2, 2, 2, 2]^{7}$ |
$t^{7} + t + 1$ |
$x^{2} + \left(2 t^{4} + 2 t^{3}\right) x + 4 t^{5} + 4 t^{2} + 2$ |
$[1, 0]$ |
$[1]$ |
| 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) |
$14$ |
$1$ |
$[2]$ |
$[2, 2, 2, 2, 2, 2]^{14}$ |
$t^{7} + t + 1$ |
$x^{2} + \left(2 t^{5} + 2 t^{4} + 2 t^{3} + 2\right) x + 4 t^{6} + 4 t^{5} + 4 t^{4} + 4 t^{3} + 4 t^{2} + 2$ |
$[1, 0]$ |
$[1]$ |
| 2.14.14.26 |
$14$ |
$x^{14} + 54 x^{12} + 472 x^{11} + 100 x^{10} - 320 x^{9} + 18968 x^{8} - 22912 x^{7} + 7600 x^{6} + 72576 x^{5} - 237792 x^{4} - 117632 x^{3} + 112320 x^{2} - 91648 x + 62592$ |
$2$ |
$2$ |
$7$ |
$14$ |
$C_2\times F_8$ (as 14T9) |
$14$ |
$1$ |
$[2]$ |
$[2, 2, 2]^{14}$ |
$t^{7} + t + 1$ |
$x^{2} + \left(2 t^{5} + 2 t^{4} + 2 t^{3} + 2 t\right) x + 4 t^{6} + 4 t^{5} + 4 t^{2} + 4 t + 2$ |
$[1, 0]$ |
$[1]$ |
| 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) |
$14$ |
$1$ |
$[2]$ |
$[2, 2, 2, 2, 2, 2]^{14}$ |
$t^{7} + t + 1$ |
$x^{2} + \left(2 t^{5} + 2 t^{4} + 2 t\right) x + 4 t^{6} + 4 t^{4} + 4 t^{3} + 4 t^{2} + 4 t + 6$ |
$[1, 0]$ |
$[1]$ |
| 2.14.14.3 |
$14$ |
$x^{14} + 2 x^{13} + 30 x^{12} + 904 x^{11} + 7764 x^{10} + 37432 x^{9} + 112280 x^{8} + 199872 x^{7} + 219312 x^{6} + 231392 x^{5} + 682912 x^{4} + 1931904 x^{3} + 3165120 x^{2} + 2978944 x + 1331328$ |
$2$ |
$2$ |
$7$ |
$14$ |
$F_8$ (as 14T6) |
$7$ |
$1$ |
$[2]$ |
$[2, 2, 2]^{7}$ |
$t^{7} + t + 1$ |
$x^{2} + \left(2 t^{6} + 2 t^{5} + 2 t^{4} + 2 t^{3} + 2\right) x + 4 t^{6} + 4 t^{5} + 4 t^{3} + 4 t^{2} + 2$ |
$[1, 0]$ |
$[1]$ |
| 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) |
$7$ |
$1$ |
$[2]$ |
$[2, 2, 2, 2, 2, 2, 2]^{7}$ |
$t^{7} + t + 1$ |
$x^{2} + \left(2 t^{5} + 2 t^{4} + 2 t^{3} + 2 t + 2\right) x + 4 t^{3} + 4 t^{2} + 6$ |
$[1, 0]$ |
$[1]$ |
| 2.14.14.31 |
$14$ |
$x^{14} - 12 x^{13} + 50 x^{12} + 120 x^{11} - 820 x^{10} - 144 x^{9} + 8472 x^{8} + 9920 x^{7} - 30672 x^{6} - 59456 x^{5} + 106336 x^{4} + 342912 x^{3} + 180800 x^{2} - 207616 x - 301952$ |
$2$ |
$2$ |
$7$ |
$14$ |
$C_2^3:F_8$ (as 14T21) |
$7$ |
$1$ |
$[2]$ |
$[2, 2, 2, 2, 2, 2]^{7}$ |
$t^{7} + t + 1$ |
$x^{2} + \left(2 t^{6} + 2 t^{4}\right) x + 4 t^{6} + 4 t^{3} + 4 t + 2$ |
$[1, 0]$ |
$[1]$ |
| 2.14.14.32 |
$14$ |
$x^{14} + 54 x^{12} + 120 x^{11} + 820 x^{10} + 2720 x^{9} + 6776 x^{8} + 25024 x^{7} + 26992 x^{6} + 10880 x^{5} - 106848 x^{4} - 260736 x^{3} + 163520 x^{2} - 376832 x + 67712$ |
$2$ |
$2$ |
$7$ |
$14$ |
$C_2^3:F_8$ (as 14T21) |
$7$ |
$1$ |
$[2]$ |
$[2, 2, 2, 2, 2, 2]^{7}$ |
$t^{7} + t + 1$ |
$x^{2} + \left(2 t^{4} + 2 t^{3} + 2 t\right) x + 4 t^{5} + 4 t^{4} + 4 t^{3} + 2$ |
$[1, 0]$ |
$[1]$ |
| 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) |
$7$ |
$1$ |
$[2]$ |
$[2, 2, 2, 2, 2, 2, 2]^{7}$ |
$t^{7} + t + 1$ |
$x^{2} + 2 t^{3} x + 4 t^{5} + 4 t^{3} + 6$ |
$[1, 0]$ |
$[1]$ |
| 2.14.14.34 |
$14$ |
$x^{14} + 14 x^{13} + 98 x^{12} + 680 x^{11} + 4124 x^{10} + 16872 x^{9} + 59992 x^{8} + 168192 x^{7} + 397680 x^{6} + 807456 x^{5} + 1341920 x^{4} + 1886592 x^{3} + 2248768 x^{2} + 1722752 x + 1571456$ |
$2$ |
$2$ |
$7$ |
$14$ |
$C_2^3:F_8$ (as 14T21) |
$7$ |
$1$ |
$[2]$ |
$[2, 2, 2, 2, 2, 2]^{7}$ |
$t^{7} + t + 1$ |
$x^{2} + \left(2 t^{5} + 2 t^{4} + 2 t + 2\right) x + 4 t^{6} + 4 t^{5} + 4 t^{2} + 2$ |
$[1, 0]$ |
$[1]$ |
| 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) |
$7$ |
$1$ |
$[2]$ |
$[2, 2, 2, 2, 2, 2, 2]^{7}$ |
$t^{7} + t + 1$ |
$x^{2} + \left(2 t^{4} + 2 t^{2} + 2 t\right) x + 4 t^{6} + 4 t^{5} + 4 t^{2} + 4 t + 2$ |
$[1, 0]$ |
$[1]$ |
| 2.14.14.36 |
$14$ |
$x^{14} + 14 x^{13} + 178 x^{12} + 1408 x^{11} + 9124 x^{10} + 39752 x^{9} + 139912 x^{8} + 354816 x^{7} + 759216 x^{6} + 1347488 x^{5} + 2155616 x^{4} + 3190784 x^{3} + 3149504 x^{2} + 1996160 x + 1327488$ |
$2$ |
$2$ |
$7$ |
$14$ |
$C_2^3:F_8$ (as 14T21) |
$7$ |
$1$ |
$[2]$ |
$[2, 2, 2, 2, 2, 2]^{7}$ |
$t^{7} + t + 1$ |
$x^{2} + \left(2 t^{5} + 2 t^{4} + 2 t^{2} + 2 t + 2\right) x + 4 t^{6} + 4 t^{4} + 4 t^{3} + 6$ |
$[1, 0]$ |
$[1]$ |
| 2.14.14.37 |
$14$ |
$x^{14} + 78 x^{12} + 80 x^{11} + 532 x^{10} + 192 x^{9} - 1160 x^{8} + 640 x^{7} + 496 x^{6} - 13824 x^{5} - 11744 x^{4} + 30464 x^{3} + 65216 x^{2} + 35840 x + 119936$ |
$2$ |
$2$ |
$7$ |
$14$ |
$C_2^3:F_8$ (as 14T21) |
$7$ |
$1$ |
$[2]$ |
$[2, 2, 2, 2, 2, 2]^{7}$ |
$t^{7} + t + 1$ |
$x^{2} + \left(2 t^{5} + 2 t^{3} + 2 t^{2} + 2 t\right) x + 4 t^{4} + 4 t^{3} + 4 t^{2} + 2$ |
$[1, 0]$ |
$[1]$ |
| 2.14.14.38 |
$14$ |
$x^{14} + 14 x^{13} + 98 x^{12} + 448 x^{11} + 1948 x^{10} + 8392 x^{9} + 30520 x^{8} + 84992 x^{7} + 178608 x^{6} + 284064 x^{5} + 325984 x^{4} + 242688 x^{3} + 97600 x^{2} + 11648 x - 5504$ |
$2$ |
$2$ |
$7$ |
$14$ |
$C_{14}$ (as 14T1) |
$7$ |
$1$ |
$[2]$ |
$[2]^{7}$ |
$t^{7} + t + 1$ |
$x^{2} + 2 x + 4 t^{5} + 4 t^{4} + 4 t^{3} + 4 t^{2} + 4 t + 2$ |
$[1, 0]$ |
$[1]$ |
| 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) |
$7$ |
$1$ |
$[2]$ |
$[2, 2, 2, 2, 2, 2, 2]^{7}$ |
$t^{7} + t + 1$ |
$x^{2} + \left(2 t^{6} + 2 t^{5} + 2 t^{4} + 2 t^{2} + 2\right) x + 4 t^{6} + 4 t^{5} + 4 t^{4} + 4 t^{3} + 4 t^{2} + 6$ |
$[1, 0]$ |
$[1]$ |
| 2.14.14.6 |
$14$ |
$x^{14} - 12 x^{13} + 130 x^{12} - 136 x^{11} + 3012 x^{10} + 8480 x^{9} + 51432 x^{8} + 193984 x^{7} + 470000 x^{6} + 1112768 x^{5} + 2842336 x^{4} + 5511552 x^{3} + 6262208 x^{2} + 3639808 x + 686464$ |
$2$ |
$2$ |
$7$ |
$14$ |
$C_2\times F_8$ (as 14T9) |
$7$ |
$1$ |
$[2]$ |
$[2, 2, 2, 2]^{7}$ |
$t^{7} + t + 1$ |
$x^{2} + \left(2 t^{6} + 2 t^{5} + 2 t^{4} + 2 t^{2}\right) x + 4 t^{6} + 4 t^{5} + 4 t^{3} + 4 t + 6$ |
$[1, 0]$ |
$[1]$ |
| 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) |
$7$ |
$1$ |
$[2]$ |
$[2, 2, 2, 2, 2, 2, 2]^{7}$ |
$t^{7} + t + 1$ |
$x^{2} + \left(2 t^{6} + 2 t^{5} + 2 t^{4} + 2 t^{2} + 2\right) x + 4 t^{6} + 4 t^{2} + 4 t + 2$ |
$[1, 0]$ |
$[1]$ |
| 2.14.14.8 |
$14$ |
$x^{14} + 78 x^{12} + 192 x^{11} + 2268 x^{10} + 6096 x^{9} + 22024 x^{8} + 23936 x^{7} - 49104 x^{6} - 507904 x^{5} - 1496672 x^{4} - 3429888 x^{3} - 3524800 x^{2} - 2472192 x + 1761664$ |
$2$ |
$2$ |
$7$ |
$14$ |
$C_2\times F_8$ (as 14T9) |
$7$ |
$1$ |
$[2]$ |
$[2, 2, 2, 2]^{7}$ |
$t^{7} + t + 1$ |
$x^{2} + \left(2 t^{5} + 2 t^{3} + 2 t\right) x + 4 t^{5} + 4 t^{4} + 4 t^{3} + 4 t + 6$ |
$[1, 0]$ |
$[1]$ |
| 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) |
$7$ |
$1$ |
$[3]$ |
$[2, 2, 2, 2, 2, 2, 3]^{7}$ |
$t^{7} + t + 1$ |
$x^{2} + \left(4 t^{6} + 4 t^{5} + 4 t^{4}\right) x + 8 t^{4} + 8 t^{2} + 10$ |
$[2, 0]$ |
$[1]$ |
| 2.14.21.10 |
$14$ |
$x^{14} - 24 x^{13} + 514 x^{12} - 3712 x^{11} + 8436 x^{10} - 19808 x^{9} + 82344 x^{8} - 38144 x^{7} + 781104 x^{6} + 735616 x^{5} + 1508448 x^{4} + 3283968 x^{3} + 4817856 x^{2} + 3159552 x + 7312256$ |
$2$ |
$2$ |
$7$ |
$21$ |
$C_2\times F_8$ (as 14T9) |
$7$ |
$1$ |
$[3]$ |
$[2, 2, 2, 3]^{7}$ |
$t^{7} + t + 1$ |
$x^{2} + \left(4 t^{6} + 4 t^{4} + 4 t^{3} + 4 t^{2}\right) x + 4 t^{6} + 4 t^{5} + 4 t^{4} + 4 t^{3} + 8 t^{2} + 4 t + 6$ |
$[2, 0]$ |
$[1]$ |
| 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) |
$7$ |
$1$ |
$[3]$ |
$[2, 2, 2, 2, 2, 2, 3]^{7}$ |
$t^{7} + t + 1$ |
$x^{2} + 4 t^{2} x + 12 t^{6} + 8 t^{5} + 12 t^{3} + 4 t + 2$ |
$[2, 0]$ |
$[1]$ |
| 2.14.21.17 |
$14$ |
$x^{14} + 28 x^{13} + 410 x^{12} + 4112 x^{11} + 30036 x^{10} + 164432 x^{9} + 681928 x^{8} + 2051712 x^{7} + 4403248 x^{6} + 9311808 x^{5} + 24241888 x^{4} + 43488512 x^{3} + 115665344 x^{2} + 466148096 x + 695222656$ |
$2$ |
$2$ |
$7$ |
$21$ |
$C_2\times F_8$ (as 14T9) |
$7$ |
$1$ |
$[3]$ |
$[2, 2, 2, 3]^{7}$ |
$t^{7} + t + 1$ |
$x^{2} + \left(4 t^{3} + 4 t + 4\right) x + 12 t^{6} + 4 t^{4} + 12 t^{3} + 8 t^{2} + 12 t + 14$ |
$[2, 0]$ |
$[1]$ |
| 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) |
$7$ |
$1$ |
$[3]$ |
$[2, 2, 2, 2, 2, 2, 3]^{7}$ |
$t^{7} + t + 1$ |
$x^{2} + \left(4 t^{6} + 4 t^{5} + 4 t^{3} + 4 t^{2}\right) x + 12 t^{6} + 8 t^{4} + 12 t^{3} + 2$ |
$[2, 0]$ |
$[1]$ |
| 2.14.21.19 |
$14$ |
$x^{14} + 28 x^{13} + 350 x^{12} + 2736 x^{11} + 14612 x^{10} + 45264 x^{9} + 53720 x^{8} - 162944 x^{7} - 706000 x^{6} + 153152 x^{5} + 3920288 x^{4} + 1750784 x^{3} - 10328640 x^{2} - 6376704 x + 24757376$ |
$2$ |
$2$ |
$7$ |
$21$ |
$C_2\times F_8$ (as 14T9) |
$7$ |
$1$ |
$[3]$ |
$[2, 2, 2, 3]^{7}$ |
$t^{7} + t + 1$ |
$x^{2} + \left(4 t^{2} + 4 t + 4\right) x + 12 t^{4} + 8 t^{3} + 8 t^{2} + 4 t + 2$ |
$[2, 0]$ |
$[1]$ |
| 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) |
$7$ |
$1$ |
$[3]$ |
$[2, 2, 2, 2, 2, 2, 3]^{7}$ |
$t^{7} + t + 1$ |
$x^{2} + \left(4 t^{6} + 4\right) x + 12 t^{4} + 12 t^{3} + 12 t^{2} + 4 t + 6$ |
$[2, 0]$ |
$[1]$ |
