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Label Polynomial $p$ $e$ $f$ $c$ Galois group Visible slopes Slope content Unram. Ext. Eisen. Poly.
7.14.19.10 $x^{14} + 21 x^{7} + 7 x^{6} + 21$ $7$ $14$ $1$ $19$ $C_7 \wr C_2$ (as 14T8) $[3/2]$ $[3/2]_{2}^{7}$ $t + 4$ $x^{14} + 21 x^{7} + 7 x^{6} + 21$
7.14.19.14 $x^{14} + 14 x^{7} + 35 x^{6} + 7$ $7$ $14$ $1$ $19$ $C_7 \wr C_2$ (as 14T8) $[3/2]$ $[3/2]_{2}^{7}$ $t + 4$ $x^{14} + 14 x^{7} + 35 x^{6} + 7$
7.14.19.15 $x^{14} + 7 x^{7} + 35 x^{6} + 7$ $7$ $14$ $1$ $19$ $C_7 \wr C_2$ (as 14T8) $[3/2]$ $[3/2]_{2}^{7}$ $t + 4$ $x^{14} + 7 x^{7} + 35 x^{6} + 7$
7.14.19.16 $x^{14} + 14 x^{7} + 7 x^{6} + 21$ $7$ $14$ $1$ $19$ $C_7 \wr C_2$ (as 14T8) $[3/2]$ $[3/2]_{2}^{7}$ $t + 4$ $x^{14} + 14 x^{7} + 7 x^{6} + 21$
7.14.19.17 $x^{14} + 7 x^{7} + 7 x^{6} + 21$ $7$ $14$ $1$ $19$ $C_7 \wr C_2$ (as 14T8) $[3/2]$ $[3/2]_{2}^{7}$ $t + 4$ $x^{14} + 7 x^{7} + 7 x^{6} + 21$
7.14.19.8 $x^{14} + 21 x^{7} + 35 x^{6} + 7$ $7$ $14$ $1$ $19$ $C_7 \wr C_2$ (as 14T8) $[3/2]$ $[3/2]_{2}^{7}$ $t + 4$ $x^{14} + 21 x^{7} + 35 x^{6} + 7$
7.14.24.1 $x^{14} - 168 x^{13} - 294 x^{12} - 182 x^{7} - 25872 x^{6} - 49343$ $7$ $7$ $2$ $24$ $C_7 \wr C_2$ (as 14T8) $[2]$ $[2, 2]^{2}$ $t^{2} + 6 t + 3$ $x^{7} + \left(35 t + 21\right) x^{6} + 98 t + 203$
7.14.24.12 $x^{14} - 168 x^{13} - 294 x^{12} - 84 x^{7} - 34104 x^{6} - 55860$ $7$ $7$ $2$ $24$ $C_7 \wr C_2$ (as 14T8) $[2]$ $[2, 2]^{2}$ $t^{2} + 6 t + 3$ $x^{7} + \left(35 t + 21\right) x^{6} + 98 t + 252$
7.14.24.18 $x^{14} - 28 x^{13} - 980 x^{12} - 1064 x^{7} - 26264 x^{6} - 77126$ $7$ $7$ $2$ $24$ $C_7 \wr C_2$ (as 14T8) $[2]$ $[2, 2]^{2}$ $t^{2} + 6 t + 3$ $x^{7} + \left(14 t + 28\right) x^{6} + 245 t + 203$
7.14.24.19 $x^{14} - 126 x^{13} - 3381 x^{12} - 1456 x^{7} - 31752 x^{6} + 11368$ $7$ $7$ $2$ $24$ $C_7 \wr C_2$ (as 14T8) $[2]$ $[2, 2]^{2}$ $t^{2} + 6 t + 3$ $x^{7} + \left(35 t + 42\right) x^{6} + 294 t + 154$
7.14.24.20 $x^{14} - 28 x^{13} - 980 x^{12} - 476 x^{7} - 18032 x^{6} - 73010$ $7$ $7$ $2$ $24$ $C_7 \wr C_2$ (as 14T8) $[2]$ $[2, 2]^{2}$ $t^{2} + 6 t + 3$ $x^{7} + \left(14 t + 28\right) x^{6} + 147 t + 203$
7.14.24.21 $x^{14} - 126 x^{13} - 3381 x^{12} - 1064 x^{7} - 15288 x^{6} + 52528$ $7$ $7$ $2$ $24$ $C_7 \wr C_2$ (as 14T8) $[2]$ $[2, 2]^{2}$ $t^{2} + 6 t + 3$ $x^{7} + \left(35 t + 42\right) x^{6} + 196 t + 56$
7.14.24.28 $x^{14} - 294 x^{12} - 1750 x^{7} - 24696 x^{6} + 247009$ $7$ $7$ $2$ $24$ $C_7 \wr C_2$ (as 14T8) $[2]$ $[2, 2]^{2}$ $t^{2} + 6 t + 3$ $x^{7} + \left(7 t + 21\right) x^{6} + 294 t + 7$
7.14.24.3 $x^{14} - 294 x^{12} - 672 x^{7} - 16464 x^{6} - 117600$ $7$ $7$ $2$ $24$ $C_7 \wr C_2$ (as 14T8) $[2]$ $[2, 2]^{2}$ $t^{2} + 6 t + 3$ $x^{7} + \left(7 t + 21\right) x^{6} + 196 t + 252$
7.14.24.31 $x^{14} - 196 x^{13} - 980 x^{12} - 1358 x^{7} - 15092 x^{6} - 57575$ $7$ $7$ $2$ $24$ $C_7 \wr C_2$ (as 14T8) $[2]$ $[2, 2]^{2}$ $t^{2} + 6 t + 3$ $x^{7} + \left(42 t + 28\right) x^{6} + 294 t + 203$
7.14.24.32 $x^{14} + 14 x^{13} + 49 x^{12} - 770 x^{7} - 5390 x^{6} + 18571$ $7$ $7$ $2$ $24$ $C_7 \wr C_2$ (as 14T8) $[2]$ $[2]^{14}$ $t^{2} + 6 t + 3$ $x^{7} + 7 x^{6} + 147 t + 56$
7.14.24.33 $x^{14} - 126 x^{13} - 3381 x^{12} + 112 x^{7} - 27636 x^{6} - 11270$ $7$ $7$ $2$ $24$ $C_7 \wr C_2$ (as 14T8) $[2]$ $[2, 2]^{2}$ $t^{2} + 6 t + 3$ $x^{7} + \left(35 t + 42\right) x^{6} + 49 t + 203$
7.14.24.35 $x^{14} - 70 x^{13} + 49 x^{12} - 1162 x^{7} + 7742 x^{6} + 107065$ $7$ $7$ $2$ $24$ $C_7 \wr C_2$ (as 14T8) $[2]$ $[2, 2]^{2}$ $t^{2} + 6 t + 3$ $x^{7} + \left(14 t + 7\right) x^{6} + 196 t + 7$
7.14.24.38 $x^{14} - 126 x^{13} - 3381 x^{12} + 308 x^{7} - 39984 x^{6} + 9310$ $7$ $7$ $2$ $24$ $C_7 \wr C_2$ (as 14T8) $[2]$ $[2, 2]^{2}$ $t^{2} + 6 t + 3$ $x^{7} + \left(35 t + 42\right) x^{6} + 49 t + 301$
7.14.24.39 $x^{14} - 294 x^{12} - 1064 x^{7} - 20580 x^{6} - 77126$ $7$ $7$ $2$ $24$ $C_7 \wr C_2$ (as 14T8) $[2]$ $[2, 2]^{2}$ $t^{2} + 6 t + 3$ $x^{7} + \left(7 t + 21\right) x^{6} + 245 t + 203$
7.14.24.4 $x^{14} - 126 x^{13} - 3381 x^{12} - 84 x^{7} - 35868 x^{6} - 55860$ $7$ $7$ $2$ $24$ $C_7 \wr C_2$ (as 14T8) $[2]$ $[2, 2]^{2}$ $t^{2} + 6 t + 3$ $x^{7} + \left(35 t + 42\right) x^{6} + 98 t + 252$
7.14.24.40 $x^{14} - 294 x^{12} - 966 x^{7} - 16464 x^{6} + 2793$ $7$ $7$ $2$ $24$ $C_7 \wr C_2$ (as 14T8) $[2]$ $[2, 2]^{2}$ $t^{2} + 6 t + 3$ $x^{7} + \left(7 t + 21\right) x^{6} + 196 t + 105$
7.14.24.41 $x^{14} - 168 x^{13} - 294 x^{12} - 672 x^{7} - 25872 x^{6} - 117600$ $7$ $7$ $2$ $24$ $C_7 \wr C_2$ (as 14T8) $[2]$ $[2, 2]^{2}$ $t^{2} + 6 t + 3$ $x^{7} + \left(35 t + 21\right) x^{6} + 196 t + 252$
7.14.24.42 $x^{14} - 196 x^{13} - 980 x^{12} - 1064 x^{7} - 19208 x^{6} - 77126$ $7$ $7$ $2$ $24$ $C_7 \wr C_2$ (as 14T8) $[2]$ $[2, 2]^{2}$ $t^{2} + 6 t + 3$ $x^{7} + \left(42 t + 28\right) x^{6} + 245 t + 203$
7.14.24.43 $x^{14} - 168 x^{13} - 294 x^{12} + 504 x^{7} - 42336 x^{6} + 63504$ $7$ $7$ $2$ $24$ $C_7 \wr C_2$ (as 14T8) $[2]$ $[2, 2]^{2}$ $t^{2} + 6 t + 3$ $x^{7} + \left(35 t + 21\right) x^{6} + 252$
7.14.24.47 $x^{14} - 168 x^{13} - 294 x^{12} - 280 x^{7} - 17640 x^{6} - 38024$ $7$ $7$ $2$ $24$ $C_7 \wr C_2$ (as 14T8) $[2]$ $[2, 2]^{2}$ $t^{2} + 6 t + 3$ $x^{7} + \left(35 t + 21\right) x^{6} + 98 t + 154$
7.14.24.48 $x^{14} - 70 x^{13} + 49 x^{12} - 1064 x^{7} + 4312 x^{6} + 52528$ $7$ $7$ $2$ $24$ $C_7 \wr C_2$ (as 14T8) $[2]$ $[2, 2]^{2}$ $t^{2} + 6 t + 3$ $x^{7} + \left(14 t + 7\right) x^{6} + 196 t + 56$
7.14.24.49 $x^{14} - 294 x^{12} - 868 x^{7} - 12348 x^{6} + 58702$ $7$ $7$ $2$ $24$ $C_7 \wr C_2$ (as 14T8) $[2]$ $[2, 2]^{2}$ $t^{2} + 6 t + 3$ $x^{7} + \left(7 t + 21\right) x^{6} + 147 t + 7$
7.14.24.5 $x^{14} + 14 x^{13} + 49 x^{12} + 14 x^{7} + 98 x^{6} - 14357$ $7$ $7$ $2$ $24$ $C_7 \wr C_2$ (as 14T8) $[2]$ $[2]^{14}$ $t^{2} + 6 t + 3$ $x^{7} + 7 x^{6} + 49 t + 154$
7.14.24.50 $x^{14} + 14 x^{13} + 49 x^{12} - 1162 x^{7} - 8134 x^{6} - 22589$ $7$ $7$ $2$ $24$ $C_7 \wr C_2$ (as 14T8) $[2]$ $[2]^{14}$ $t^{2} + 6 t + 3$ $x^{7} + 7 x^{6} + 245 t + 154$
7.14.25.10 $x^{14} + 14 x^{13} + 28 x^{12} + 21$ $7$ $14$ $1$ $25$ $C_7 \wr C_2$ (as 14T8) $[2]$ $[3/2, 2]_{2}$ $t + 4$ $x^{14} + 14 x^{13} + 28 x^{12} + 21$
7.14.25.11 $x^{14} + 28 x^{12} + 21 x^{7} + 315$ $7$ $14$ $1$ $25$ $C_7 \wr C_2$ (as 14T8) $[2]$ $[3/2, 2]_{2}$ $t + 4$ $x^{14} + 28 x^{12} + 21 x^{7} + 315$
7.14.25.17 $x^{14} + 7 x^{13} + 42 x^{12} + 35 x^{7} + 7$ $7$ $14$ $1$ $25$ $C_7 \wr C_2$ (as 14T8) $[2]$ $[3/2, 2]_{2}$ $t + 4$ $x^{14} + 7 x^{13} + 42 x^{12} + 35 x^{7} + 7$
7.14.25.2 $x^{14} + 28 x^{12} + 7 x^{7} + 119$ $7$ $14$ $1$ $25$ $C_7 \wr C_2$ (as 14T8) $[2]$ $[3/2, 2]_{2}$ $t + 4$ $x^{14} + 28 x^{12} + 7 x^{7} + 119$
7.14.25.23 $x^{14} + 42 x^{12} + 21 x^{7} + 105$ $7$ $14$ $1$ $25$ $C_7 \wr C_2$ (as 14T8) $[2]$ $[3/2, 2]_{2}$ $t + 4$ $x^{14} + 42 x^{12} + 21 x^{7} + 105$
7.14.25.26 $x^{14} + 7 x^{13} + 42 x^{12} + 301$ $7$ $14$ $1$ $25$ $C_7 \wr C_2$ (as 14T8) $[2]$ $[3/2, 2]_{2}$ $t + 4$ $x^{14} + 7 x^{13} + 42 x^{12} + 301$
7.14.25.29 $x^{14} + 7 x^{13} + 28 x^{12} + 28 x^{7} + 315$ $7$ $14$ $1$ $25$ $C_7 \wr C_2$ (as 14T8) $[2]$ $[3/2, 2]_{2}$ $t + 4$ $x^{14} + 7 x^{13} + 28 x^{12} + 28 x^{7} + 315$
7.14.25.4 $x^{14} + 14 x^{13} + 28 x^{12} + 168$ $7$ $14$ $1$ $25$ $C_7 \wr C_2$ (as 14T8) $[2]$ $[3/2, 2]_{2}$ $t + 4$ $x^{14} + 14 x^{13} + 28 x^{12} + 168$
7.14.25.41 $x^{14} + 42 x^{12} + 21 x^{7} + 301$ $7$ $14$ $1$ $25$ $C_7 \wr C_2$ (as 14T8) $[2]$ $[3/2, 2]_{2}$ $t + 4$ $x^{14} + 42 x^{12} + 21 x^{7} + 301$
7.14.25.43 $x^{14} + 21 x^{13} + 28 x^{12} + 70$ $7$ $14$ $1$ $25$ $C_7 \wr C_2$ (as 14T8) $[2]$ $[3/2, 2]_{2}$ $t + 4$ $x^{14} + 21 x^{13} + 28 x^{12} + 70$
7.14.25.44 $x^{14} + 28 x^{13} + 28 x^{12} + 7 x^{7} + 315$ $7$ $14$ $1$ $25$ $C_7 \wr C_2$ (as 14T8) $[2]$ $[3/2, 2]_{2}$ $t + 4$ $x^{14} + 28 x^{13} + 28 x^{12} + 7 x^{7} + 315$
7.14.25.46 $x^{14} + 21 x^{13} + 42 x^{12} + 252$ $7$ $14$ $1$ $25$ $C_7 \wr C_2$ (as 14T8) $[2]$ $[3/2, 2]_{2}$ $t + 4$ $x^{14} + 21 x^{13} + 42 x^{12} + 252$
7.14.25.48 $x^{14} + 28 x^{12} + 7 x^{7} + 168$ $7$ $14$ $1$ $25$ $C_7 \wr C_2$ (as 14T8) $[2]$ $[3/2, 2]_{2}$ $t + 4$ $x^{14} + 28 x^{12} + 7 x^{7} + 168$
7.14.25.51 $x^{14} + 42 x^{12} + 28 x^{7} + 56$ $7$ $14$ $1$ $25$ $C_7 \wr C_2$ (as 14T8) $[2]$ $[3/2, 2]_{2}$ $t + 4$ $x^{14} + 42 x^{12} + 28 x^{7} + 56$
7.14.25.55 $x^{14} + 42 x^{13} + 42 x^{12} + 154$ $7$ $14$ $1$ $25$ $C_7 \wr C_2$ (as 14T8) $[2]$ $[3/2, 2]_{2}$ $t + 4$ $x^{14} + 42 x^{13} + 42 x^{12} + 154$
7.14.25.57 $x^{14} + 7 x^{13} + 28 x^{12} + 35 x^{7} + 70$ $7$ $14$ $1$ $25$ $C_7 \wr C_2$ (as 14T8) $[2]$ $[3/2, 2]_{2}$ $t + 4$ $x^{14} + 7 x^{13} + 28 x^{12} + 35 x^{7} + 70$
7.14.25.58 $x^{14} + 28 x^{12} + 7 x^{7} + 70$ $7$ $14$ $1$ $25$ $C_7 \wr C_2$ (as 14T8) $[2]$ $[3/2, 2]_{2}$ $t + 4$ $x^{14} + 28 x^{12} + 7 x^{7} + 70$
7.14.25.61 $x^{14} + 14 x^{13} + 42 x^{12} + 252$ $7$ $14$ $1$ $25$ $C_7 \wr C_2$ (as 14T8) $[2]$ $[3/2, 2]_{2}$ $t + 4$ $x^{14} + 14 x^{13} + 42 x^{12} + 252$
7.14.25.64 $x^{14} + 14 x^{13} + 28 x^{12} + 28 x^{7} + 315$ $7$ $14$ $1$ $25$ $C_7 \wr C_2$ (as 14T8) $[2]$ $[3/2, 2]_{2}$ $t + 4$ $x^{14} + 14 x^{13} + 28 x^{12} + 28 x^{7} + 315$
7.14.25.65 $x^{14} + 42 x^{12} + 7 x^{7} + 154$ $7$ $14$ $1$ $25$ $C_7 \wr C_2$ (as 14T8) $[2]$ $[3/2, 2]_{2}$ $t + 4$ $x^{14} + 42 x^{12} + 7 x^{7} + 154$
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