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Label Polynomial $p$ $e$ $f$ $c$ Galois group Visible slopes Slope content Unram. Ext. Eisen. Poly.
2.14.14.14 $x^{14} + 2 x^{12} + 56 x^{11} + 12 x^{10} + 192 x^{9} + 1336 x^{8} + 768 x^{7} + 1712 x^{6} - 512 x^{5} + 18528 x^{4} + 39552 x^{3} - 204224 x^{2} - 195584 x + 259712$ $2$ $2$ $7$ $14$ $C_2\times F_8$ (as 14T9) $[2]$ $[2, 2, 2, 2]^{7}$ $t^{7} + t + 1$ $x^{2} + \left(2 t^{3} + 2 t\right) x + 4 t^{6} + 4 t^{4} + 4 t + 2$
2.14.14.2 $x^{14} + 14 x^{13} + 102 x^{12} + 576 x^{11} + 3140 x^{10} + 14392 x^{9} + 49912 x^{8} + 153536 x^{7} + 453296 x^{6} + 957216 x^{5} + 952608 x^{4} + 59648 x^{3} + 31936 x^{2} + 608384 x - 370048$ $2$ $2$ $7$ $14$ $C_2\times F_8$ (as 14T9) $[2]$ $[2, 2, 2]^{14}$ $t^{7} + t + 1$ $x^{2} + \left(2 t^{5} + 2 t^{2} + 2\right) x + 4 t^{6} + 4 t^{5} + 4 t + 2$
2.14.14.24 $x^{14} + 54 x^{12} + 64 x^{11} + 1396 x^{10} + 192 x^{9} + 12440 x^{8} - 2496 x^{7} + 52592 x^{6} + 38144 x^{5} + 19360 x^{4} + 147712 x^{3} - 46912 x^{2} - 86016 x + 382592$ $2$ $2$ $7$ $14$ $C_2\times F_8$ (as 14T9) $[2]$ $[2, 2, 2, 2]^{7}$ $t^{7} + t + 1$ $x^{2} + \left(2 t^{4} + 2 t^{3}\right) x + 4 t^{5} + 4 t^{2} + 2$
2.14.14.26 $x^{14} + 54 x^{12} + 472 x^{11} + 100 x^{10} - 320 x^{9} + 18968 x^{8} - 22912 x^{7} + 7600 x^{6} + 72576 x^{5} - 237792 x^{4} - 117632 x^{3} + 112320 x^{2} - 91648 x + 62592$ $2$ $2$ $7$ $14$ $C_2\times F_8$ (as 14T9) $[2]$ $[2, 2, 2]^{14}$ $t^{7} + t + 1$ $x^{2} + \left(2 t^{5} + 2 t^{4} + 2 t^{3} + 2 t\right) x + 4 t^{6} + 4 t^{5} + 4 t^{2} + 4 t + 2$
2.14.14.6 $x^{14} - 12 x^{13} + 130 x^{12} - 136 x^{11} + 3012 x^{10} + 8480 x^{9} + 51432 x^{8} + 193984 x^{7} + 470000 x^{6} + 1112768 x^{5} + 2842336 x^{4} + 5511552 x^{3} + 6262208 x^{2} + 3639808 x + 686464$ $2$ $2$ $7$ $14$ $C_2\times F_8$ (as 14T9) $[2]$ $[2, 2, 2, 2]^{7}$ $t^{7} + t + 1$ $x^{2} + \left(2 t^{6} + 2 t^{5} + 2 t^{4} + 2 t^{2}\right) x + 4 t^{6} + 4 t^{5} + 4 t^{3} + 4 t + 6$
2.14.14.8 $x^{14} + 78 x^{12} + 192 x^{11} + 2268 x^{10} + 6096 x^{9} + 22024 x^{8} + 23936 x^{7} - 49104 x^{6} - 507904 x^{5} - 1496672 x^{4} - 3429888 x^{3} - 3524800 x^{2} - 2472192 x + 1761664$ $2$ $2$ $7$ $14$ $C_2\times F_8$ (as 14T9) $[2]$ $[2, 2, 2, 2]^{7}$ $t^{7} + t + 1$ $x^{2} + \left(2 t^{5} + 2 t^{3} + 2 t\right) x + 4 t^{5} + 4 t^{4} + 4 t^{3} + 4 t + 6$
2.14.21.10 $x^{14} - 24 x^{13} + 514 x^{12} - 3712 x^{11} + 8436 x^{10} - 19808 x^{9} + 82344 x^{8} - 38144 x^{7} + 781104 x^{6} + 735616 x^{5} + 1508448 x^{4} + 3283968 x^{3} + 4817856 x^{2} + 3159552 x + 7312256$ $2$ $2$ $7$ $21$ $C_2\times F_8$ (as 14T9) $[3]$ $[2, 2, 2, 3]^{7}$ $t^{7} + t + 1$ $x^{2} + \left(4 t^{6} + 4 t^{4} + 4 t^{3} + 4 t^{2}\right) x + 4 t^{6} + 4 t^{5} + 4 t^{4} + 4 t^{3} + 8 t^{2} + 4 t + 6$
2.14.21.17 $x^{14} + 28 x^{13} + 410 x^{12} + 4112 x^{11} + 30036 x^{10} + 164432 x^{9} + 681928 x^{8} + 2051712 x^{7} + 4403248 x^{6} + 9311808 x^{5} + 24241888 x^{4} + 43488512 x^{3} + 115665344 x^{2} + 466148096 x + 695222656$ $2$ $2$ $7$ $21$ $C_2\times F_8$ (as 14T9) $[3]$ $[2, 2, 2, 3]^{7}$ $t^{7} + t + 1$ $x^{2} + \left(4 t^{3} + 4 t + 4\right) x + 12 t^{6} + 4 t^{4} + 12 t^{3} + 8 t^{2} + 12 t + 14$
2.14.21.19 $x^{14} + 28 x^{13} + 350 x^{12} + 2736 x^{11} + 14612 x^{10} + 45264 x^{9} + 53720 x^{8} - 162944 x^{7} - 706000 x^{6} + 153152 x^{5} + 3920288 x^{4} + 1750784 x^{3} - 10328640 x^{2} - 6376704 x + 24757376$ $2$ $2$ $7$ $21$ $C_2\times F_8$ (as 14T9) $[3]$ $[2, 2, 2, 3]^{7}$ $t^{7} + t + 1$ $x^{2} + \left(4 t^{2} + 4 t + 4\right) x + 12 t^{4} + 8 t^{3} + 8 t^{2} + 4 t + 2$
2.14.21.21 $x^{14} - 24 x^{13} + 678 x^{12} - 8272 x^{11} + 62532 x^{10} - 233472 x^{9} + 428312 x^{8} + 879488 x^{7} + 149168 x^{6} + 3373696 x^{5} + 39634464 x^{4} + 53888768 x^{3} + 131006656 x^{2} + 137477120 x + 78949504$ $2$ $2$ $7$ $21$ $C_2\times F_8$ (as 14T9) $[3]$ $[2, 2, 2, 3]^{7}$ $t^{7} + t + 1$ $x^{2} + \left(4 t^{6} + 4 t^{4} + 4 t^{3} + 4 t^{2} + 4 t\right) x + 4 t^{5} + 12 t^{4} + 8 t^{3} + 4 t^{2} + 12 t + 10$
2.14.21.25 $x^{14} + 4 x^{13} + 390 x^{12} + 4112 x^{11} + 47956 x^{10} + 463280 x^{9} + 3361336 x^{8} + 16377216 x^{7} + 56539440 x^{6} + 135426496 x^{5} + 163386656 x^{4} - 35395328 x^{3} - 242580032 x^{2} - 42148608 x + 158410368$ $2$ $2$ $7$ $21$ $C_2\times F_8$ (as 14T9) $[3]$ $[2, 2, 2, 3]^{7}$ $t^{7} + t + 1$ $x^{2} + \left(4 t^{6} + 4 t^{5} + 4 t^{3} + 4 t^{2} + 4 t + 4\right) x + 8 t^{6} + 4 t^{5} + 12 t^{4} + 12 t^{3} + 8 t^{2} + 10$
2.14.21.26 $x^{14} + 4 x^{13} + 158 x^{12} + 1552 x^{11} + 13300 x^{10} + 104368 x^{9} + 595480 x^{8} + 3074944 x^{7} + 14740016 x^{6} + 51153344 x^{5} + 110226848 x^{4} + 124621056 x^{3} + 45717440 x^{2} - 16065280 x + 50331776$ $2$ $2$ $7$ $21$ $C_2\times F_8$ (as 14T9) $[3]$ $[2, 2, 2, 3]^{7}$ $t^{7} + t + 1$ $x^{2} + \left(4 t^{6} + 4 t^{4} + 4 t + 4\right) x + 4 t^{6} + 8 t^{5} + 4 t^{4} + 8 t^{2} + 12 t + 10$
2.14.21.35 $x^{14} + 28 x^{13} + 362 x^{12} + 3344 x^{11} + 25284 x^{10} + 157968 x^{9} + 910056 x^{8} + 4673920 x^{7} + 20010928 x^{6} + 72133184 x^{5} + 214998240 x^{4} + 505239808 x^{3} + 963040448 x^{2} + 1210556160 x + 1086915456$ $2$ $2$ $7$ $21$ $C_2\times F_8$ (as 14T9) $[3]$ $[2, 2, 2, 3]^{7}$ $t^{7} + t + 1$ $x^{2} + \left(4 t^{4} + 4 t + 4\right) x + 12 t^{6} + 8 t^{5} + 4 t^{3} + 4 t^{2} + 12 t + 14$
2.14.21.38 $x^{14} + 406 x^{12} + 1040 x^{11} - 684 x^{10} + 48928 x^{9} + 76088 x^{8} + 232064 x^{7} + 2009392 x^{6} - 844544 x^{5} + 13171232 x^{4} + 3040512 x^{3} + 20874688 x^{2} - 9766400 x + 108060288$ $2$ $2$ $7$ $21$ $C_2\times F_8$ (as 14T9) $[3]$ $[2, 2, 2, 3]^{7}$ $t^{7} + t + 1$ $x^{2} + \left(4 t^{5} + 4 t^{4} + 4 t^{3} + 4 t^{2} + 4 t\right) x + 12 t^{6} + 8 t^{5} + 4 t^{3} + 4 t^{2} + 2$
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