| Label |
$n$ |
Polynomial |
$p$ |
$e$ |
$f$ |
$c$ |
Galois group |
$u$ |
$t$ |
Visible slopes |
Slope content |
Unram. Ext. |
Eisen. Poly. |
Ind. of Insep. |
Assoc. Inertia |
| 2.14.21.1 |
$14$ |
$x^{14} - 24 x^{13} + 310 x^{12} - 448 x^{11} + 31892 x^{10} - 21856 x^{9} + 718648 x^{8} - 960512 x^{7} + 7507504 x^{6} - 4420736 x^{5} + 55408160 x^{4} + 18013184 x^{3} + 137399744 x^{2} + 37318144 x + 94078592$ |
$2$ |
$2$ |
$7$ |
$21$ |
$C_2 \wr C_7$ (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) |
$7$ |
$1$ |
$[3]$ |
$[2, 2, 2, 2, 2, 2, 3]^{7}$ |
$t^{7} + t + 1$ |
$x^{2} + \left(4 t^{6} + 4\right) x + 12 t^{4} + 12 t^{3} + 12 t^{2} + 4 t + 6$ |
$[2, 0]$ |
$[1]$ |
| 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) |
$7$ |
$1$ |
$[3]$ |
$[2, 2, 2, 2, 2, 2, 3]^{7}$ |
$t^{7} + t + 1$ |
$x^{2} + \left(4 t^{3} + 4\right) x + 4 t^{6} + 4 t^{5} + 12 t^{4} + 12 t^{3} + 12 t^{2} + 14$ |
$[2, 0]$ |
$[1]$ |
| 2.14.21.21 |
$14$ |
$x^{14} - 24 x^{13} + 678 x^{12} - 8272 x^{11} + 62532 x^{10} - 233472 x^{9} + 428312 x^{8} + 879488 x^{7} + 149168 x^{6} + 3373696 x^{5} + 39634464 x^{4} + 53888768 x^{3} + 131006656 x^{2} + 137477120 x + 78949504$ |
$2$ |
$2$ |
$7$ |
$21$ |
$C_2\times F_8$ (as 14T9) |
$7$ |
$1$ |
$[3]$ |
$[2, 2, 2, 3]^{7}$ |
$t^{7} + t + 1$ |
$x^{2} + \left(4 t^{6} + 4 t^{4} + 4 t^{3} + 4 t^{2} + 4 t\right) x + 4 t^{5} + 12 t^{4} + 8 t^{3} + 4 t^{2} + 12 t + 10$ |
$[2, 0]$ |
$[1]$ |
| 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) |
$7$ |
$1$ |
$[3]$ |
$[2, 2, 2, 2, 2, 2, 3]^{7}$ |
$t^{7} + t + 1$ |
$x^{2} + \left(4 t^{3} + 4 t^{2} + 4 t\right) x + 12 t^{5} + 12 t^{4} + 4 t^{3} + 4 t^{2} + 4 t + 10$ |
$[2, 0]$ |
$[1]$ |
| 2.14.21.25 |
$14$ |
$x^{14} + 4 x^{13} + 390 x^{12} + 4112 x^{11} + 47956 x^{10} + 463280 x^{9} + 3361336 x^{8} + 16377216 x^{7} + 56539440 x^{6} + 135426496 x^{5} + 163386656 x^{4} - 35395328 x^{3} - 242580032 x^{2} - 42148608 x + 158410368$ |
$2$ |
$2$ |
$7$ |
$21$ |
$C_2\times F_8$ (as 14T9) |
$7$ |
$1$ |
$[3]$ |
$[2, 2, 2, 3]^{7}$ |
$t^{7} + t + 1$ |
$x^{2} + \left(4 t^{6} + 4 t^{5} + 4 t^{3} + 4 t^{2} + 4 t + 4\right) x + 8 t^{6} + 4 t^{5} + 12 t^{4} + 12 t^{3} + 8 t^{2} + 10$ |
$[2, 0]$ |
$[1]$ |
| 2.14.21.26 |
$14$ |
$x^{14} + 4 x^{13} + 158 x^{12} + 1552 x^{11} + 13300 x^{10} + 104368 x^{9} + 595480 x^{8} + 3074944 x^{7} + 14740016 x^{6} + 51153344 x^{5} + 110226848 x^{4} + 124621056 x^{3} + 45717440 x^{2} - 16065280 x + 50331776$ |
$2$ |
$2$ |
$7$ |
$21$ |
$C_2\times F_8$ (as 14T9) |
$7$ |
$1$ |
$[3]$ |
$[2, 2, 2, 3]^{7}$ |
$t^{7} + t + 1$ |
$x^{2} + \left(4 t^{6} + 4 t^{4} + 4 t + 4\right) x + 4 t^{6} + 8 t^{5} + 4 t^{4} + 8 t^{2} + 12 t + 10$ |
$[2, 0]$ |
$[1]$ |
| 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) |
$7$ |
$1$ |
$[3]$ |
$[2, 2, 2, 2, 2, 2, 3]^{7}$ |
$t^{7} + t + 1$ |
$x^{2} + \left(4 t^{6} + 4 t^{5} + 4 t^{4} + 4 t^{3}\right) x + 4 t^{6} + 4 t^{5} + 4 t^{4} + 12 t^{2} + 4 t + 6$ |
$[2, 0]$ |
$[1]$ |
| 2.14.21.33 |
$14$ |
$x^{14} + 4 x^{13} + 126 x^{12} + 144 x^{11} + 4644 x^{10} + 52656 x^{9} + 921976 x^{8} + 7067008 x^{7} + 34762928 x^{6} + 107908544 x^{5} + 244214944 x^{4} + 384102656 x^{3} + 616921792 x^{2} + 962137344 x + 1200756352$ |
$2$ |
$2$ |
$7$ |
$21$ |
$C_{14}$ (as 14T1) |
$7$ |
$1$ |
$[3]$ |
$[3]^{7}$ |
$t^{7} + t + 1$ |
$x^{2} + \left(4 t^{6} + 4 t^{3} + 4 t^{2} + 4 t + 4\right) x + 8 t^{6} + 12 t^{5} + 4 t^{4} + 12 t^{2} + 2$ |
$[2, 0]$ |
$[1]$ |
| 2.14.21.34 |
$14$ |
$x^{14} + 4 x^{13} + 14 x^{12} + 656 x^{11} + 1236 x^{10} - 43472 x^{9} - 244456 x^{8} + 434816 x^{7} + 8570160 x^{6} + 35893184 x^{5} + 77018272 x^{4} + 105671936 x^{3} + 121134528 x^{2} + 74194176 x - 52979584$ |
$2$ |
$2$ |
$7$ |
$21$ |
$C_{14}$ (as 14T1) |
$7$ |
$1$ |
$[3]$ |
$[3]^{7}$ |
$t^{7} + t + 1$ |
$x^{2} + \left(4 t^{6} + 4 t^{3} + 4 t^{2} + 4\right) x + 8 t^{6} + 12 t^{5} + 4 t^{4} + 8 t^{3} + 2$ |
$[2, 0]$ |
$[1]$ |
| 2.14.21.35 |
$14$ |
$x^{14} + 28 x^{13} + 362 x^{12} + 3344 x^{11} + 25284 x^{10} + 157968 x^{9} + 910056 x^{8} + 4673920 x^{7} + 20010928 x^{6} + 72133184 x^{5} + 214998240 x^{4} + 505239808 x^{3} + 963040448 x^{2} + 1210556160 x + 1086915456$ |
$2$ |
$2$ |
$7$ |
$21$ |
$C_2\times F_8$ (as 14T9) |
$7$ |
$1$ |
$[3]$ |
$[2, 2, 2, 3]^{7}$ |
$t^{7} + t + 1$ |
$x^{2} + \left(4 t^{4} + 4 t + 4\right) x + 12 t^{6} + 8 t^{5} + 4 t^{3} + 4 t^{2} + 12 t + 14$ |
$[2, 0]$ |
$[1]$ |
| 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) |
$7$ |
$1$ |
$[3]$ |
$[2, 2, 2, 2, 2, 2, 3]^{7}$ |
$t^{7} + t + 1$ |
$x^{2} + \left(4 t^{6} + 4 t^{4} + 4 t^{3} + 4 t^{2}\right) x + 12 t^{5} + 4 t^{3} + 12 t + 10$ |
$[2, 0]$ |
$[1]$ |
| 2.14.21.38 |
$14$ |
$x^{14} + 406 x^{12} + 1040 x^{11} - 684 x^{10} + 48928 x^{9} + 76088 x^{8} + 232064 x^{7} + 2009392 x^{6} - 844544 x^{5} + 13171232 x^{4} + 3040512 x^{3} + 20874688 x^{2} - 9766400 x + 108060288$ |
$2$ |
$2$ |
$7$ |
$21$ |
$C_2\times F_8$ (as 14T9) |
$7$ |
$1$ |
$[3]$ |
$[2, 2, 2, 3]^{7}$ |
$t^{7} + t + 1$ |
$x^{2} + \left(4 t^{5} + 4 t^{4} + 4 t^{3} + 4 t^{2} + 4 t\right) x + 12 t^{6} + 8 t^{5} + 4 t^{3} + 4 t^{2} + 2$ |
$[2, 0]$ |
$[1]$ |
| 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) |
$7$ |
$1$ |
$[3]$ |
$[2, 2, 2, 2, 2, 2, 3]^{7}$ |
$t^{7} + t + 1$ |
$x^{2} + \left(4 t^{5} + 4 t^{4} + 4\right) x + 4 t^{6} + 4 t^{5} + 12 t^{4} + 12 t + 10$ |
$[2, 0]$ |
$[1]$ |
| 2.14.21.40 |
$14$ |
$x^{14} + 28 x^{13} + 530 x^{12} + 6592 x^{11} + 70004 x^{10} + 568560 x^{9} + 3483880 x^{8} + 16019456 x^{7} + 59065136 x^{6} + 169683776 x^{5} + 367736672 x^{4} + 550228992 x^{3} + 585563072 x^{2} + 456203520 x + 295014272$ |
$2$ |
$2$ |
$7$ |
$21$ |
$C_{14}$ (as 14T1) |
$7$ |
$1$ |
$[3]$ |
$[3]^{7}$ |
$t^{7} + t + 1$ |
$x^{2} + \left(4 t^{5} + 4 t + 4\right) x + 12 t^{4} + 12 t^{3} + 12 t^{2} + 8 t + 14$ |
$[2, 0]$ |
$[1]$ |
| 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) |
$7$ |
$1$ |
$[3]$ |
$[2, 2, 2, 2, 2, 2, 3]^{7}$ |
$t^{7} + t + 1$ |
$x^{2} + \left(4 t^{5} + 4 t^{4}\right) x + 4 t^{6} + 12 t^{5} + 8 t^{4} + 12 t^{2} + 12 t + 2$ |
$[2, 0]$ |
$[1]$ |
| 2.14.21.6 |
$14$ |
$x^{14} + 158 x^{12} + 1568 x^{11} + 1332 x^{10} - 32384 x^{9} + 95128 x^{8} + 683008 x^{7} + 3694128 x^{6} + 18752000 x^{5} + 49924512 x^{4} + 51764736 x^{3} - 10775616 x^{2} + 27525120 x + 167639168$ |
$2$ |
$2$ |
$7$ |
$21$ |
$C_{14}$ (as 14T1) |
$7$ |
$1$ |
$[3]$ |
$[3]^{7}$ |
$t^{7} + t + 1$ |
$x^{2} + \left(4 t^{5} + 4 t^{3} + 4 t^{2}\right) x + 12 t^{6} + 8 t^{4} + 4 t^{3} + 8 t^{2} + 8 t + 10$ |
$[2, 0]$ |
$[1]$ |
| 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) |
$7$ |
$1$ |
$[3]$ |
$[2, 2, 2, 2, 2, 2, 3]^{7}$ |
$t^{7} + t + 1$ |
$x^{2} + \left(4 t^{5} + 4 t^{2}\right) x + 8 t^{6} + 12 t^{5} + 4 t^{4} + 4 t^{2} + 12 t + 6$ |
$[2, 0]$ |
$[1]$ |
