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Label Polynomial $p$ $e$ $f$ $c$ Galois group Visible slopes Slope content Unram. Ext. Eisen. Poly.
2.14.14.39 $x^{14} + 2 x + 2$ $2$ $14$ $1$ $14$ $F_8:C_6$ (as 14T18) $[8/7]$ $[8/7, 8/7, 8/7]_{7}^{6}$ $t + 1$ $x^{14} + 2 x + 2$
2.14.14.40 $x^{14} + 2 x^{2} + 2 x + 2$ $2$ $14$ $1$ $14$ $F_8:C_3$ (as 14T11) $[8/7]$ $[8/7, 8/7, 8/7]_{7}^{3}$ $t + 1$ $x^{14} + 2 x^{2} + 2 x + 2$
2.14.16.1 $x^{14} + 2 x^{6} + 2 x^{3} + 2$ $2$ $14$ $1$ $16$ $F_8:C_6$ (as 14T18) $[10/7]$ $[10/7, 10/7, 10/7]_{7}^{6}$ $t + 1$ $x^{14} + 2 x^{6} + 2 x^{3} + 2$
2.14.16.2 $x^{14} + 2 x^{6} + 2 x^{4} + 2 x^{3} + 2$ $2$ $14$ $1$ $16$ $C_2\wr C_7:C_3$ (as 14T44) $[10/7]$ $[8/7, 8/7, 8/7, 10/7, 10/7, 10/7]_{7}^{6}$ $t + 1$ $x^{14} + 2 x^{6} + 2 x^{4} + 2 x^{3} + 2$
2.14.16.3 $x^{14} + 2 x^{4} + 2 x^{3} + 2$ $2$ $14$ $1$ $16$ $C_2^3:F_8:C_3$ (as 14T35) $[10/7]$ $[8/7, 8/7, 8/7, 10/7, 10/7, 10/7]_{7}^{3}$ $t + 1$ $x^{14} + 2 x^{4} + 2 x^{3} + 2$
2.14.16.4 $x^{14} + 2 x^{3} + 2$ $2$ $14$ $1$ $16$ $F_8:C_3$ (as 14T11) $[10/7]$ $[10/7, 10/7, 10/7]_{7}^{3}$ $t + 1$ $x^{14} + 2 x^{3} + 2$
2.14.18.1 $x^{14} + 2 x^{10} + 2 x^{5} + 2$ $2$ $14$ $1$ $18$ $F_8:C_3$ (as 14T11) $[12/7]$ $[12/7, 12/7, 12/7]_{7}^{3}$ $t + 1$ $x^{14} + 2 x^{10} + 2 x^{5} + 2$
2.14.18.2 $x^{14} + 2 x^{10} + 2 x^{9} + 2 x^{7} + 2 x^{5} + 2$ $2$ $14$ $1$ $18$ $F_8:C_3$ (as 14T11) $[12/7]$ $[12/7, 12/7, 12/7]_{7}^{3}$ $t + 1$ $x^{14} + 2 x^{10} + 2 x^{9} + 2 x^{7} + 2 x^{5} + 2$
2.14.18.3 $x^{14} + 2 x^{10} + 2 x^{9} + 2 x^{5} + 2$ $2$ $14$ $1$ $18$ $C_2^3:F_8:C_3$ (as 14T35) $[12/7]$ $[8/7, 8/7, 8/7, 12/7, 12/7, 12/7]_{7}^{3}$ $t + 1$ $x^{14} + 2 x^{10} + 2 x^{9} + 2 x^{5} + 2$
2.14.18.4 $x^{14} + 2 x^{10} + 2 x^{9} + 2 x^{7} + 2 x^{6} + 2 x^{5} + 2$ $2$ $14$ $1$ $18$ $C_2\wr C_7:C_3$ (as 14T44) $[12/7]$ $[8/7, 8/7, 8/7, 12/7, 12/7, 12/7]_{7}^{6}$ $t + 1$ $x^{14} + 2 x^{10} + 2 x^{9} + 2 x^{7} + 2 x^{6} + 2 x^{5} + 2$
2.14.18.5 $x^{14} + 2 x^{9} + 2 x^{6} + 2 x^{5} + 2$ $2$ $14$ $1$ $18$ $F_8:C_6$ (as 14T18) $[12/7]$ $[12/7, 12/7, 12/7]_{7}^{6}$ $t + 1$ $x^{14} + 2 x^{9} + 2 x^{6} + 2 x^{5} + 2$
2.14.18.6 $x^{14} + 2 x^{10} + 2 x^{7} + 2 x^{5} + 2$ $2$ $14$ $1$ $18$ $C_2^3:F_8:C_3$ (as 14T35) $[12/7]$ $[8/7, 8/7, 8/7, 12/7, 12/7, 12/7]_{7}^{3}$ $t + 1$ $x^{14} + 2 x^{10} + 2 x^{7} + 2 x^{5} + 2$
2.14.18.7 $x^{14} + 2 x^{8} + 2 x^{7} + 2 x^{5} + 2$ $2$ $14$ $1$ $18$ $F_8:C_6$ (as 14T18) $[12/7]$ $[12/7, 12/7, 12/7]_{7}^{6}$ $t + 1$ $x^{14} + 2 x^{8} + 2 x^{7} + 2 x^{5} + 2$
2.14.18.8 $x^{14} + 2 x^{6} + 2 x^{5} + 2$ $2$ $14$ $1$ $18$ $C_2\wr C_7:C_3$ (as 14T44) $[12/7]$ $[8/7, 8/7, 8/7, 12/7, 12/7, 12/7]_{7}^{6}$ $t + 1$ $x^{14} + 2 x^{6} + 2 x^{5} + 2$
2.14.20.1 $x^{14} + 2 x^{11} + 2 x^{10} + 2 x^{9} + 2 x^{8} + 2 x^{7} + 2$ $2$ $14$ $1$ $20$ $C_2\wr C_7:C_3$ (as 14T44) $[2]$ $[8/7, 8/7, 8/7, 12/7, 12/7, 12/7, 2]_{7}^{3}$ $t + 1$ $x^{14} + 2 x^{11} + 2 x^{10} + 2 x^{9} + 2 x^{8} + 2 x^{7} + 2$
2.14.20.10 $x^{14} + 2 x^{13} + 2 x^{10} + 2 x^{7} + 6$ $2$ $14$ $1$ $20$ $(C_7:C_3) \times C_2$ (as 14T5) $[2]$ $[2]_{7}^{3}$ $t + 1$ $x^{14} + 2 x^{13} + 2 x^{10} + 2 x^{7} + 6$
2.14.20.11 $x^{14} + 2 x^{12} + 2 x^{11} + 2 x^{10} + 2 x^{7} + 2 x^{6} + 6$ $2$ $14$ $1$ $20$ $C_2\wr C_7:C_3$ (as 14T44) $[2]$ $[8/7, 8/7, 8/7, 10/7, 10/7, 10/7, 2]_{7}^{3}$ $t + 1$ $x^{14} + 2 x^{12} + 2 x^{11} + 2 x^{10} + 2 x^{7} + 2 x^{6} + 6$
2.14.20.12 $x^{14} + 2 x^{7} + 2 x^{6} + 6$ $2$ $14$ $1$ $20$ $F_8:C_6$ (as 14T18) $[2]$ $[8/7, 8/7, 8/7, 2]_{7}^{3}$ $t + 1$ $x^{14} + 2 x^{7} + 2 x^{6} + 6$
2.14.20.13 $x^{14} + 2 x^{13} + 2 x^{11} + 2 x^{10} + 2 x^{9} + 2 x^{7} + 2 x^{6} + 2$ $2$ $14$ $1$ $20$ $C_2\wr C_7:C_3$ (as 14T44) $[2]$ $[8/7, 8/7, 8/7, 12/7, 12/7, 12/7, 2]_{7}^{3}$ $t + 1$ $x^{14} + 2 x^{13} + 2 x^{11} + 2 x^{10} + 2 x^{9} + 2 x^{7} + 2 x^{6} + 2$
2.14.20.14 $x^{14} + 2 x^{11} + 2 x^{7} + 2 x^{6} + 2$ $2$ $14$ $1$ $20$ $C_2\wr C_7:C_3$ (as 14T44) $[2]$ $[8/7, 8/7, 8/7, 10/7, 10/7, 10/7, 2]_{7}^{3}$ $t + 1$ $x^{14} + 2 x^{11} + 2 x^{7} + 2 x^{6} + 2$
2.14.20.15 $x^{14} + 2 x^{12} + 2 x^{11} + 2 x^{10} + 2 x^{9} + 2 x^{7} + 6$ $2$ $14$ $1$ $20$ $C_2\wr C_7:C_3$ (as 14T44) $[2]$ $[8/7, 8/7, 8/7, 12/7, 12/7, 12/7, 2]_{7}^{3}$ $t + 1$ $x^{14} + 2 x^{12} + 2 x^{11} + 2 x^{10} + 2 x^{9} + 2 x^{7} + 6$
2.14.20.16 $x^{14} + 2 x^{13} + 2 x^{12} + 2 x^{10} + 2 x^{9} + 2 x^{7} + 6$ $2$ $14$ $1$ $20$ $F_8:C_6$ (as 14T18) $[2]$ $[12/7, 12/7, 12/7, 2]_{7}^{3}$ $t + 1$ $x^{14} + 2 x^{13} + 2 x^{12} + 2 x^{10} + 2 x^{9} + 2 x^{7} + 6$
2.14.20.2 $x^{14} + 2 x^{12} + 2 x^{10} + 2 x^{9} + 2 x^{8} + 2 x^{7} + 6$ $2$ $14$ $1$ $20$ $F_8:C_6$ (as 14T18) $[2]$ $[12/7, 12/7, 12/7, 2]_{7}^{3}$ $t + 1$ $x^{14} + 2 x^{12} + 2 x^{10} + 2 x^{9} + 2 x^{8} + 2 x^{7} + 6$
2.14.20.3 $x^{14} + 2 x^{11} + 2 x^{10} + 2 x^{9} + 2 x^{8} + 2 x^{7} + 6$ $2$ $14$ $1$ $20$ $C_2\wr C_7:C_3$ (as 14T44) $[2]$ $[8/7, 8/7, 8/7, 12/7, 12/7, 12/7, 2]_{7}^{3}$ $t + 1$ $x^{14} + 2 x^{11} + 2 x^{10} + 2 x^{9} + 2 x^{8} + 2 x^{7} + 6$
2.14.20.4 $x^{14} + 2 x^{13} + 2 x^{11} + 2 x^{9} + 2 x^{7} + 6$ $2$ $14$ $1$ $20$ $F_8:C_6$ (as 14T18) $[2]$ $[12/7, 12/7, 12/7, 2]_{7}^{3}$ $t + 1$ $x^{14} + 2 x^{13} + 2 x^{11} + 2 x^{9} + 2 x^{7} + 6$
2.14.20.5 $x^{14} + 2 x^{12} + 2 x^{10} + 2 x^{7} + 2 x^{6} + 2$ $2$ $14$ $1$ $20$ $F_8:C_6$ (as 14T18) $[2]$ $[8/7, 8/7, 8/7, 2]_{7}^{3}$ $t + 1$ $x^{14} + 2 x^{12} + 2 x^{10} + 2 x^{7} + 2 x^{6} + 2$
2.14.20.6 $x^{14} + 2 x^{13} + 2 x^{12} + 2 x^{8} + 2 x^{7} + 6$ $2$ $14$ $1$ $20$ $F_8:C_6$ (as 14T18) $[2]$ $[10/7, 10/7, 10/7, 2]_{7}^{3}$ $t + 1$ $x^{14} + 2 x^{13} + 2 x^{12} + 2 x^{8} + 2 x^{7} + 6$
2.14.20.7 $x^{14} + 2 x^{13} + 2 x^{12} + 2 x^{11} + 2 x^{9} + 2 x^{8} + 2 x^{7} + 6$ $2$ $14$ $1$ $20$ $F_8:C_6$ (as 14T18) $[2]$ $[12/7, 12/7, 12/7, 2]_{7}^{3}$ $t + 1$ $x^{14} + 2 x^{13} + 2 x^{12} + 2 x^{11} + 2 x^{9} + 2 x^{8} + 2 x^{7} + 6$
2.14.20.8 $x^{14} + 2 x^{13} + 2 x^{10} + 2 x^{7} + 2$ $2$ $14$ $1$ $20$ $(C_7:C_3) \times C_2$ (as 14T5) $[2]$ $[2]_{7}^{3}$ $t + 1$ $x^{14} + 2 x^{13} + 2 x^{10} + 2 x^{7} + 2$
2.14.20.9 $x^{14} + 2 x^{13} + 2 x^{12} + 2 x^{11} + 2 x^{7} + 2$ $2$ $14$ $1$ $20$ $F_8:C_6$ (as 14T18) $[2]$ $[10/7, 10/7, 10/7, 2]_{7}^{3}$ $t + 1$ $x^{14} + 2 x^{13} + 2 x^{12} + 2 x^{11} + 2 x^{7} + 2$
2.14.22.1 $x^{14} + 2 x^{12} + 2 x^{9} + 2 x^{8} + 2 x^{6} + 4 x^{4} + 4 x^{3} + 2$ $2$ $14$ $1$ $22$ $C_2\wr C_7:C_3$ (as 14T44) $[16/7]$ $[12/7, 12/7, 12/7, 16/7, 16/7, 16/7]_{7}^{6}$ $t + 1$ $x^{14} + 2 x^{12} + 2 x^{9} + 2 x^{8} + 2 x^{6} + 4 x^{4} + 4 x^{3} + 2$
2.14.22.10 $x^{14} + 2 x^{11} + 2 x^{9} + 2 x^{8} + 2 x^{6} + 4 x^{4} + 4 x^{3} + 4 x^{2} + 4 x + 6$ $2$ $14$ $1$ $22$ $C_2\wr C_7:C_3$ (as 14T44) $[16/7]$ $[10/7, 10/7, 10/7, 2, 16/7, 16/7, 16/7]_{7}^{3}$ $t + 1$ $x^{14} + 2 x^{11} + 2 x^{9} + 2 x^{8} + 2 x^{6} + 4 x^{4} + 4 x^{3} + 4 x^{2} + 4 x + 6$
2.14.22.11 $x^{14} + 2 x^{13} + 2 x^{11} + 2 x^{9} + 4 x^{4} + 4 x^{3} + 4 x^{2} + 4 x + 2$ $2$ $14$ $1$ $22$ $F_8:C_6$ (as 14T18) $[16/7]$ $[2, 16/7, 16/7, 16/7]_{7}^{3}$ $t + 1$ $x^{14} + 2 x^{13} + 2 x^{11} + 2 x^{9} + 4 x^{4} + 4 x^{3} + 4 x^{2} + 4 x + 2$
2.14.22.12 $x^{14} + 2 x^{9} + 2 x^{8} + 2 x^{6} + 4 x^{3} + 4 x^{2} + 2$ $2$ $14$ $1$ $22$ $C_2\wr C_7:C_3$ (as 14T44) $[16/7]$ $[12/7, 12/7, 12/7, 16/7, 16/7, 16/7]_{7}^{6}$ $t + 1$ $x^{14} + 2 x^{9} + 2 x^{8} + 2 x^{6} + 4 x^{3} + 4 x^{2} + 2$
2.14.22.13 $x^{14} + 2 x^{13} + 2 x^{12} + 2 x^{9} + 4 x^{4} + 4 x^{3} + 4 x^{2} + 4 x + 2$ $2$ $14$ $1$ $22$ $C_2^3:F_8:C_3$ (as 14T35) $[16/7]$ $[12/7, 12/7, 12/7, 16/7, 16/7, 16/7]_{7}^{3}$ $t + 1$ $x^{14} + 2 x^{13} + 2 x^{12} + 2 x^{9} + 4 x^{4} + 4 x^{3} + 4 x^{2} + 4 x + 2$
2.14.22.14 $x^{14} + 2 x^{13} + 2 x^{11} + 2 x^{9} + 2 x^{8} + 2 x^{6} + 4 x^{3} + 4 x^{2} + 4 x + 2$ $2$ $14$ $1$ $22$ $C_2\wr C_7:C_3$ (as 14T44) $[16/7]$ $[12/7, 12/7, 12/7, 2, 16/7, 16/7, 16/7]_{7}^{3}$ $t + 1$ $x^{14} + 2 x^{13} + 2 x^{11} + 2 x^{9} + 2 x^{8} + 2 x^{6} + 4 x^{3} + 4 x^{2} + 4 x + 2$
2.14.22.15 $x^{14} + 2 x^{11} + 2 x^{9} + 2 x^{8} + 2 x^{6} + 4 x^{4} + 4 x^{3} + 4 x + 6$ $2$ $14$ $1$ $22$ $C_2\wr C_7:C_3$ (as 14T44) $[16/7]$ $[10/7, 10/7, 10/7, 2, 16/7, 16/7, 16/7]_{7}^{3}$ $t + 1$ $x^{14} + 2 x^{11} + 2 x^{9} + 2 x^{8} + 2 x^{6} + 4 x^{4} + 4 x^{3} + 4 x + 6$
2.14.22.16 $x^{14} + 2 x^{12} + 2 x^{9} + 4 x^{3} + 4 x^{2} + 2$ $2$ $14$ $1$ $22$ $C_2\wr C_7:C_3$ (as 14T44) $[16/7]$ $[10/7, 10/7, 10/7, 16/7, 16/7, 16/7]_{7}^{6}$ $t + 1$ $x^{14} + 2 x^{12} + 2 x^{9} + 4 x^{3} + 4 x^{2} + 2$
2.14.22.17 $x^{14} + 2 x^{13} + 2 x^{11} + 2 x^{9} + 4 x^{2} + 2$ $2$ $14$ $1$ $22$ $C_2\wr C_7:C_3$ (as 14T44) $[16/7]$ $[10/7, 10/7, 10/7, 2, 16/7, 16/7, 16/7]_{7}^{3}$ $t + 1$ $x^{14} + 2 x^{13} + 2 x^{11} + 2 x^{9} + 4 x^{2} + 2$
2.14.22.18 $x^{14} + 2 x^{13} + 2 x^{12} + 2 x^{9} + 2 x^{8} + 2 x^{6} + 4 x^{4} + 4 x^{3} + 2$ $2$ $14$ $1$ $22$ $C_2\wr C_7:C_3$ (as 14T44) $[16/7]$ $[10/7, 10/7, 10/7, 16/7, 16/7, 16/7]_{7}^{6}$ $t + 1$ $x^{14} + 2 x^{13} + 2 x^{12} + 2 x^{9} + 2 x^{8} + 2 x^{6} + 4 x^{4} + 4 x^{3} + 2$
2.14.22.19 $x^{14} + 2 x^{13} + 2 x^{12} + 2 x^{9} + 4 x^{4} + 4 x^{3} + 6$ $2$ $14$ $1$ $22$ $C_2^3:F_8:C_3$ (as 14T35) $[16/7]$ $[12/7, 12/7, 12/7, 16/7, 16/7, 16/7]_{7}^{3}$ $t + 1$ $x^{14} + 2 x^{13} + 2 x^{12} + 2 x^{9} + 4 x^{4} + 4 x^{3} + 6$
2.14.22.2 $x^{14} + 2 x^{12} + 2 x^{10} + 2 x^{9} + 4 x^{4} + 6$ $2$ $14$ $1$ $22$ $C_2^3:F_8:C_3$ (as 14T35) $[16/7]$ $[10/7, 10/7, 10/7, 16/7, 16/7, 16/7]_{7}^{3}$ $t + 1$ $x^{14} + 2 x^{12} + 2 x^{10} + 2 x^{9} + 4 x^{4} + 6$
2.14.22.20 $x^{14} + 2 x^{13} + 2 x^{9} + 4 x^{3} + 4 x^{2} + 4 x + 2$ $2$ $14$ $1$ $22$ $C_2\wr C_7:C_3$ (as 14T44) $[16/7]$ $[12/7, 12/7, 12/7, 16/7, 16/7, 16/7]_{7}^{6}$ $t + 1$ $x^{14} + 2 x^{13} + 2 x^{9} + 4 x^{3} + 4 x^{2} + 4 x + 2$
2.14.22.21 $x^{14} + 2 x^{12} + 2 x^{9} + 4 x^{3} + 4 x^{2} + 4 x + 6$ $2$ $14$ $1$ $22$ $F_8:C_6$ (as 14T18) $[16/7]$ $[16/7, 16/7, 16/7]_{7}^{6}$ $t + 1$ $x^{14} + 2 x^{12} + 2 x^{9} + 4 x^{3} + 4 x^{2} + 4 x + 6$
2.14.22.22 $x^{14} + 2 x^{9} + 4 x^{2} + 6$ $2$ $14$ $1$ $22$ $F_8:C_6$ (as 14T18) $[16/7]$ $[16/7, 16/7, 16/7]_{7}^{6}$ $t + 1$ $x^{14} + 2 x^{9} + 4 x^{2} + 6$
2.14.22.23 $x^{14} + 2 x^{9} + 2 x^{8} + 2 x^{6} + 4 x^{2} + 2$ $2$ $14$ $1$ $22$ $C_2\wr C_7:C_3$ (as 14T44) $[16/7]$ $[12/7, 12/7, 12/7, 16/7, 16/7, 16/7]_{7}^{6}$ $t + 1$ $x^{14} + 2 x^{9} + 2 x^{8} + 2 x^{6} + 4 x^{2} + 2$
2.14.22.24 $x^{14} + 2 x^{13} + 2 x^{12} + 2 x^{11} + 2 x^{9} + 4 x^{3} + 2$ $2$ $14$ $1$ $22$ $F_8:C_6$ (as 14T18) $[16/7]$ $[2, 16/7, 16/7, 16/7]_{7}^{3}$ $t + 1$ $x^{14} + 2 x^{13} + 2 x^{12} + 2 x^{11} + 2 x^{9} + 4 x^{3} + 2$
2.14.22.25 $x^{14} + 2 x^{11} + 2 x^{9} + 4 x^{4} + 4 x^{3} + 4 x^{2} + 4 x + 2$ $2$ $14$ $1$ $22$ $C_2\wr C_7:C_3$ (as 14T44) $[16/7]$ $[12/7, 12/7, 12/7, 2, 16/7, 16/7, 16/7]_{7}^{3}$ $t + 1$ $x^{14} + 2 x^{11} + 2 x^{9} + 4 x^{4} + 4 x^{3} + 4 x^{2} + 4 x + 2$
2.14.22.26 $x^{14} + 2 x^{13} + 2 x^{11} + 2 x^{9} + 4 x^{4} + 4 x^{2} + 6$ $2$ $14$ $1$ $22$ $C_2\wr C_7:C_3$ (as 14T44) $[16/7]$ $[10/7, 10/7, 10/7, 2, 16/7, 16/7, 16/7]_{7}^{3}$ $t + 1$ $x^{14} + 2 x^{13} + 2 x^{11} + 2 x^{9} + 4 x^{4} + 4 x^{2} + 6$
2.14.22.27 $x^{14} + 2 x^{12} + 2 x^{10} + 2 x^{9} + 2 x^{8} + 2 x^{6} + 4 x^{3} + 4 x + 6$ $2$ $14$ $1$ $22$ $C_2^3:F_8:C_3$ (as 14T35) $[16/7]$ $[12/7, 12/7, 12/7, 16/7, 16/7, 16/7]_{7}^{3}$ $t + 1$ $x^{14} + 2 x^{12} + 2 x^{10} + 2 x^{9} + 2 x^{8} + 2 x^{6} + 4 x^{3} + 4 x + 6$
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