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Label Polynomial $p$ $e$ $f$ $c$ Galois group Visible slopes Slope content Unram. Ext. Eisen. Poly.
7.14.14.1 $x^{14} + 14 x^{9} - 28 x^{8} + 14 x^{7} - 245 x^{4} - 1372 x^{3} - 882 x^{2} - 196 x + 49$ $7$ $7$ $2$ $14$ $D_7:F_7$ (as 14T24) $[7/6]$ $[7/6, 7/6]_{6}^{2}$ $t^{2} + 6 t + 3$ $x^{7} + \left(7 t + 28\right) x^{2} + \left(14 t + 28\right) x + 7$
7.14.14.11 $x^{14} - 238 x^{9} - 14 x^{8} + 14 x^{7} + 3577 x^{4} - 1862 x^{3} - 1911 x^{2} - 98 x + 49$ $7$ $7$ $2$ $14$ $D_7:F_7$ (as 14T24) $[7/6]$ $[7/6, 7/6]_{6}^{2}$ $t^{2} + 6 t + 3$ $x^{7} + \left(42 t + 7\right) x^{2} + \left(7 t + 14\right) x + 7$
7.14.14.14 $x^{14} - 14 x^{9} - 140 x^{8} + 14 x^{7} - 245 x^{4} - 1372 x^{3} + 98 x^{2} - 980 x + 49$ $7$ $7$ $2$ $14$ $D_7:F_7$ (as 14T24) $[7/6]$ $[7/6, 7/6]_{6}^{2}$ $t^{2} + 6 t + 3$ $x^{7} + \left(7 t + 14\right) x^{2} + \left(28 t + 14\right) x + 7$
7.14.14.15 $x^{14} - 168 x^{9} + 14 x^{7} - 3528 x^{4} - 7056 x^{3} - 2352 x^{2} + 49$ $7$ $7$ $2$ $14$ $D_7:F_7$ (as 14T24) $[7/6]$ $[7/6, 7/6]_{6}^{2}$ $t^{2} + 6 t + 3$ $x^{7} + \left(42 t + 42\right) x^{2} + \left(14 t + 42\right) x + 7$
7.14.14.20 $x^{14} - 210 x^{9} - 168 x^{8} + 14 x^{7} + 3675 x^{4} + 2940 x^{3} - 1764 x^{2} - 1176 x + 49$ $7$ $7$ $2$ $14$ $D_7:F_7$ (as 14T24) $[7/6]$ $[7/6, 7/6]_{6}^{2}$ $t^{2} + 6 t + 3$ $x^{7} + 35 t x^{2} + \left(35 t + 21\right) x + 7$
7.14.14.22 $x^{14} + 14 x^{9} - 182 x^{8} + 14 x^{7} + 49 x^{4} - 1274 x^{3} - 2205 x^{2} - 1274 x + 49$ $7$ $7$ $2$ $14$ $D_7:F_7$ (as 14T24) $[7/6]$ $[7/6, 7/6]_{6}^{2}$ $t^{2} + 6 t + 3$ $x^{7} + 7 x^{2} + \left(42 t + 35\right) x + 7$
7.14.14.27 $x^{14} - 70 x^{9} - 98 x^{8} + 14 x^{7} + 49 x^{4} - 1274 x^{3} - 2793 x^{2} - 686 x + 49$ $7$ $7$ $2$ $14$ $D_7:F_7$ (as 14T24) $[7/6]$ $[7/6, 7/6]_{6}^{2}$ $t^{2} + 6 t + 3$ $x^{7} + \left(14 t + 7\right) x^{2} + \left(28 t + 35\right) x + 7$
7.14.14.7 $x^{14} - 238 x^{9} - 196 x^{8} + 14 x^{7} + 3577 x^{4} + 2156 x^{3} - 2646 x^{2} - 1372 x + 49$ $7$ $7$ $2$ $14$ $D_7:F_7$ (as 14T24) $[7/6]$ $[7/6, 7/6]_{6}^{2}$ $t^{2} + 6 t + 3$ $x^{7} + \left(42 t + 7\right) x^{2} + \left(42 t + 28\right) x + 7$
7.14.14.9 $x^{14} + 14 x^{9} - 56 x^{8} + 14 x^{7} + 49 x^{4} - 392 x^{3} - 1764 x^{2} - 392 x + 49$ $7$ $7$ $2$ $14$ $D_7:F_7$ (as 14T24) $[7/6]$ $[7/6, 7/6]_{6}^{2}$ $t^{2} + 6 t + 3$ $x^{7} + 7 x^{2} + \left(21 t + 35\right) x + 7$
7.14.18.15 $x^{14} - 154 x^{11} - 1421 x^{8} - 2926 x^{7} - 294 x^{6} - 1078 x^{4} + 49$ $7$ $7$ $2$ $18$ $D_7:F_7$ (as 14T24) $[3/2]$ $[3/2, 3/2]_{2}^{6}$ $t^{2} + 6 t + 3$ $x^{7} + \left(35 t + 28\right) x^{4} + \left(7 t + 21\right) x^{3} + 7$
7.14.18.17 $x^{14} - 126 x^{11} - 28 x^{10} - 3381 x^{8} - 4102 x^{7} - 980 x^{6} - 882 x^{4} - 196 x^{3} + 49$ $7$ $7$ $2$ $18$ $D_7:F_7$ (as 14T24) $[3/2]$ $[3/2, 3/2]_{2}^{6}$ $t^{2} + 6 t + 3$ $x^{7} + \left(35 t + 42\right) x^{4} + \left(14 t + 28\right) x^{3} + 7$
7.14.18.2 $x^{14} - 42 x^{11} - 70 x^{10} - 735 x^{8} - 868 x^{7} + 49 x^{6} - 294 x^{4} - 490 x^{3} + 49$ $7$ $7$ $2$ $18$ $D_7:F_7$ (as 14T24) $[3/2]$ $[3/2, 3/2]_{2}^{6}$ $t^{2} + 6 t + 3$ $x^{7} + \left(14 t + 21\right) x^{4} + \left(14 t + 7\right) x^{3} + 7$
7.14.18.24 $x^{14} - 42 x^{11} - 182 x^{10} + 147 x^{8} + 308 x^{7} - 2303 x^{6} - 294 x^{4} - 1274 x^{3} + 49$ $7$ $7$ $2$ $18$ $D_7:F_7$ (as 14T24) $[3/2]$ $[3/2, 3/2]_{2}^{6}$ $t^{2} + 6 t + 3$ $x^{7} + 7 t x^{4} + \left(42 t + 35\right) x^{3} + 7$
7.14.18.3 $x^{14} - 98 x^{11} - 210 x^{10} - 2303 x^{8} - 3808 x^{7} + 441 x^{6} - 686 x^{4} - 1470 x^{3} + 49$ $7$ $7$ $2$ $18$ $D_7:F_7$ (as 14T24) $[3/2]$ $[3/2, 3/2]_{2}^{6}$ $t^{2} + 6 t + 3$ $x^{7} + \left(28 t + 35\right) x^{4} + \left(42 t + 21\right) x^{3} + 7$
7.14.18.9 $x^{14} - 70 x^{11} - 98 x^{10} - 1421 x^{8} - 3612 x^{7} - 2303 x^{6} - 490 x^{4} - 686 x^{3} + 49$ $7$ $7$ $2$ $18$ $D_7:F_7$ (as 14T24) $[3/2]$ $[3/2, 3/2]_{2}^{6}$ $t^{2} + 6 t + 3$ $x^{7} + \left(21 t + 28\right) x^{4} + \left(28 t + 35\right) x^{3} + 7$
7.14.21.10 $x^{14} + 28 x^{10} + 14 x^{9} + 42 x^{8} + 14 x^{7} + 7$ $7$ $14$ $1$ $21$ $D_7:F_7$ (as 14T24) $[5/3]$ $[7/6, 5/3]_{6}^{2}$ $t + 4$ $x^{14} + 28 x^{10} + 14 x^{9} + 42 x^{8} + 14 x^{7} + 7$
7.14.21.11 $x^{14} + 42 x^{10} + 21 x^{9} + 21 x^{8} + 7$ $7$ $14$ $1$ $21$ $D_7:F_7$ (as 14T24) $[5/3]$ $[7/6, 5/3]_{6}^{2}$ $t + 4$ $x^{14} + 42 x^{10} + 21 x^{9} + 21 x^{8} + 7$
7.14.21.15 $x^{14} + 14 x^{10} + 7 x^{9} + 14 x^{8} + 21$ $7$ $14$ $1$ $21$ $D_7:F_7$ (as 14T24) $[5/3]$ $[7/6, 5/3]_{6}^{2}$ $t + 4$ $x^{14} + 14 x^{10} + 7 x^{9} + 14 x^{8} + 21$
7.14.21.2 $x^{14} + 14 x^{10} + 42 x^{9} + 35 x^{8} + 14 x^{7} + 7$ $7$ $14$ $1$ $21$ $D_7:F_7$ (as 14T24) $[5/3]$ $[7/6, 5/3]_{6}^{2}$ $t + 4$ $x^{14} + 14 x^{10} + 42 x^{9} + 35 x^{8} + 14 x^{7} + 7$
7.14.21.24 $x^{14} + 14 x^{10} + 28 x^{9} + 28 x^{8} + 28 x^{7} + 21$ $7$ $14$ $1$ $21$ $D_7:F_7$ (as 14T24) $[5/3]$ $[7/6, 5/3]_{6}^{2}$ $t + 4$ $x^{14} + 14 x^{10} + 28 x^{9} + 28 x^{8} + 28 x^{7} + 21$
7.14.21.25 $x^{14} + 35 x^{10} + 7 x^{9} + 28 x^{8} + 21$ $7$ $14$ $1$ $21$ $D_7:F_7$ (as 14T24) $[5/3]$ $[7/6, 5/3]_{6}^{2}$ $t + 4$ $x^{14} + 35 x^{10} + 7 x^{9} + 28 x^{8} + 21$
7.14.21.26 $x^{14} + 7 x^{9} + 35 x^{8} + 14 x^{7} + 7$ $7$ $14$ $1$ $21$ $D_7:F_7$ (as 14T24) $[5/3]$ $[7/6, 5/3]_{6}^{2}$ $t + 4$ $x^{14} + 7 x^{9} + 35 x^{8} + 14 x^{7} + 7$
7.14.21.27 $x^{14} + 14 x^{9} + 7 x^{8} + 21$ $7$ $14$ $1$ $21$ $D_7:F_7$ (as 14T24) $[5/3]$ $[7/6, 5/3]_{6}^{2}$ $t + 4$ $x^{14} + 14 x^{9} + 7 x^{8} + 21$
7.14.21.31 $x^{14} + 7 x^{10} + 21 x^{9} + 42 x^{8} + 7$ $7$ $14$ $1$ $21$ $D_7:F_7$ (as 14T24) $[5/3]$ $[7/6, 5/3]_{6}^{2}$ $t + 4$ $x^{14} + 7 x^{10} + 21 x^{9} + 42 x^{8} + 7$
7.14.21.32 $x^{14} + 14 x^{10} + 7 x^{9} + 7 x^{8} + 21$ $7$ $14$ $1$ $21$ $D_7:F_7$ (as 14T24) $[5/3]$ $[7/6, 5/3]_{6}^{2}$ $t + 4$ $x^{14} + 14 x^{10} + 7 x^{9} + 7 x^{8} + 21$
7.14.21.34 $x^{14} + 21 x^{9} + 14 x^{8} + 28 x^{7} + 21$ $7$ $14$ $1$ $21$ $D_7:F_7$ (as 14T24) $[5/3]$ $[7/6, 5/3]_{6}^{2}$ $t + 4$ $x^{14} + 21 x^{9} + 14 x^{8} + 28 x^{7} + 21$
7.14.21.38 $x^{14} + 28 x^{10} + 35 x^{9} + 21 x^{8} + 7$ $7$ $14$ $1$ $21$ $D_7:F_7$ (as 14T24) $[5/3]$ $[7/6, 5/3]_{6}^{2}$ $t + 4$ $x^{14} + 28 x^{10} + 35 x^{9} + 21 x^{8} + 7$
7.14.21.39 $x^{14} + 7 x^{10} + 7 x^{9} + 21 x^{8} + 7$ $7$ $14$ $1$ $21$ $D_7:F_7$ (as 14T24) $[5/3]$ $[7/6, 5/3]_{6}^{2}$ $t + 4$ $x^{14} + 7 x^{10} + 7 x^{9} + 21 x^{8} + 7$
7.14.21.4 $x^{14} + 21 x^{10} + 35 x^{8} + 35 x^{7} + 7$ $7$ $14$ $1$ $21$ $D_7:F_7$ (as 14T24) $[5/3]$ $[7/6, 5/3]_{6}^{2}$ $t + 4$ $x^{14} + 21 x^{10} + 35 x^{8} + 35 x^{7} + 7$
7.14.21.45 $x^{14} + 28 x^{10} + 28 x^{8} + 7 x^{7} + 21$ $7$ $14$ $1$ $21$ $D_7:F_7$ (as 14T24) $[5/3]$ $[7/6, 5/3]_{6}^{2}$ $t + 4$ $x^{14} + 28 x^{10} + 28 x^{8} + 7 x^{7} + 21$
7.14.21.46 $x^{14} + 35 x^{10} + 7 x^{8} + 21 x^{7} + 21$ $7$ $14$ $1$ $21$ $D_7:F_7$ (as 14T24) $[5/3]$ $[7/6, 5/3]_{6}^{2}$ $t + 4$ $x^{14} + 35 x^{10} + 7 x^{8} + 21 x^{7} + 21$
7.14.21.5 $x^{14} + 42 x^{10} + 14 x^{9} + 42 x^{8} + 7$ $7$ $14$ $1$ $21$ $D_7:F_7$ (as 14T24) $[5/3]$ $[7/6, 5/3]_{6}^{2}$ $t + 4$ $x^{14} + 42 x^{10} + 14 x^{9} + 42 x^{8} + 7$
7.14.21.9 $x^{14} + 7 x^{10} + 42 x^{9} + 14 x^{8} + 35 x^{7} + 21$ $7$ $14$ $1$ $21$ $D_7:F_7$ (as 14T24) $[5/3]$ $[7/6, 5/3]_{6}^{2}$ $t + 4$ $x^{14} + 7 x^{10} + 42 x^{9} + 14 x^{8} + 35 x^{7} + 21$
7.14.22.16 $x^{14} - 238 x^{13} + 3591 x^{12} - 5194 x^{11} - 245 x^{10} + 14 x^{7} - 1666 x^{6} + 98 x^{5} + 49$ $7$ $7$ $2$ $22$ $D_7:F_7$ (as 14T24) $[11/6]$ $[11/6, 11/6]_{6}^{2}$ $t^{2} + 6 t + 3$ $x^{7} + \left(42 t + 7\right) x^{6} + \left(7 t + 28\right) x^{5} + 7$
7.14.22.17 $x^{14} - 182 x^{13} - 2499 x^{12} + 196 x^{11} + 2254 x^{10} + 14 x^{7} - 1274 x^{6} - 1372 x^{5} + 49$ $7$ $7$ $2$ $22$ $D_7:F_7$ (as 14T24) $[11/6]$ $[11/6, 11/6]_{6}^{2}$ $t^{2} + 6 t + 3$ $x^{7} + \left(42 t + 35\right) x^{6} + \left(35 t + 7\right) x^{5} + 7$
7.14.22.19 $x^{14} - 14 x^{13} - 1253 x^{12} - 4998 x^{11} - 3381 x^{10} + 14 x^{7} - 98 x^{6} - 882 x^{5} + 49$ $7$ $7$ $2$ $22$ $D_7:F_7$ (as 14T24) $[11/6]$ $[11/6, 11/6]_{6}^{2}$ $t^{2} + 6 t + 3$ $x^{7} + \left(14 t + 35\right) x^{6} + \left(35 t + 42\right) x^{5} + 7$
7.14.22.2 $x^{14} - 98 x^{13} - 2373 x^{12} - 1274 x^{11} + 49 x^{10} + 14 x^{7} - 686 x^{6} - 490 x^{5} + 49$ $7$ $7$ $2$ $22$ $D_7:F_7$ (as 14T24) $[11/6]$ $[11/6, 11/6]_{6}^{2}$ $t^{2} + 6 t + 3$ $x^{7} + \left(28 t + 35\right) x^{6} + \left(14 t + 7\right) x^{5} + 7$
7.14.22.21 $x^{14} + 28 x^{13} - 196 x^{12} - 3724 x^{11} - 2303 x^{10} + 14 x^{7} + 196 x^{6} - 686 x^{5} + 49$ $7$ $7$ $2$ $22$ $D_7:F_7$ (as 14T24) $[11/6]$ $[11/6, 11/6]_{6}^{2}$ $t^{2} + 6 t + 3$ $x^{7} + \left(7 t + 35\right) x^{6} + \left(28 t + 35\right) x^{5} + 7$
7.14.22.22 $x^{14} - 210 x^{13} + 231 x^{12} + 882 x^{11} + 441 x^{10} + 14 x^{7} - 1470 x^{6} - 1470 x^{5} + 49$ $7$ $7$ $2$ $22$ $D_7:F_7$ (as 14T24) $[11/6]$ $[11/6, 11/6]_{6}^{2}$ $t^{2} + 6 t + 3$ $x^{7} + \left(42 t + 21\right) x^{6} + \left(42 t + 21\right) x^{5} + 7$
7.14.22.23 $x^{14} - 196 x^{13} - 1036 x^{12} - 5096 x^{11} - 1862 x^{10} + 14 x^{7} - 1372 x^{6} - 392 x^{5} + 49$ $7$ $7$ $2$ $22$ $D_7:F_7$ (as 14T24) $[11/6]$ $[11/6, 11/6]_{6}^{2}$ $t^{2} + 6 t + 3$ $x^{7} + \left(42 t + 28\right) x^{6} + \left(21 t + 35\right) x^{5} + 7$
7.14.22.26 $x^{14} - 112 x^{13} + 294 x^{12} + 392 x^{11} - 980 x^{10} + 14 x^{7} - 784 x^{6} - 1372 x^{5} + 49$ $7$ $7$ $2$ $22$ $D_7:F_7$ (as 14T24) $[11/6]$ $[11/6, 11/6]_{6}^{2}$ $t^{2} + 6 t + 3$ $x^{7} + \left(21 t + 7\right) x^{6} + \left(42 t + 28\right) x^{5} + 7$
7.14.22.9 $x^{14} - 14 x^{13} - 1169 x^{12} - 3234 x^{11} - 2205 x^{10} + 14 x^{7} - 98 x^{6} - 294 x^{5} + 49$ $7$ $7$ $2$ $22$ $D_7:F_7$ (as 14T24) $[11/6]$ $[11/6, 11/6]_{6}^{2}$ $t^{2} + 6 t + 3$ $x^{7} + \left(14 t + 35\right) x^{6} + \left(21 t + 42\right) x^{5} + 7$
7.14.23.1 $x^{14} + 7 x^{12} + 7 x^{11} + 42 x^{10} + 7 x^{7} + 21$ $7$ $14$ $1$ $23$ $D_7:F_7$ (as 14T24) $[11/6]$ $[4/3, 11/6]_{6}^{2}$ $t + 4$ $x^{14} + 7 x^{12} + 7 x^{11} + 42 x^{10} + 7 x^{7} + 21$
7.14.23.11 $x^{14} + 14 x^{12} + 28 x^{11} + 14 x^{10} + 21 x^{7} + 7$ $7$ $14$ $1$ $23$ $D_7:F_7$ (as 14T24) $[11/6]$ $[4/3, 11/6]_{6}^{2}$ $t + 4$ $x^{14} + 14 x^{12} + 28 x^{11} + 14 x^{10} + 21 x^{7} + 7$
7.14.23.13 $x^{14} + 28 x^{11} + 14 x^{10} + 28 x^{7} + 7$ $7$ $14$ $1$ $23$ $D_7:F_7$ (as 14T24) $[11/6]$ $[4/3, 11/6]_{6}^{2}$ $t + 4$ $x^{14} + 28 x^{11} + 14 x^{10} + 28 x^{7} + 7$
7.14.23.14 $x^{14} + 7 x^{11} + 28 x^{10} + 28 x^{7} + 7$ $7$ $14$ $1$ $23$ $D_7:F_7$ (as 14T24) $[11/6]$ $[4/3, 11/6]_{6}^{2}$ $t + 4$ $x^{14} + 7 x^{11} + 28 x^{10} + 28 x^{7} + 7$
7.14.23.2 $x^{14} + 14 x^{12} + 28 x^{11} + 21 x^{10} + 35 x^{7} + 21$ $7$ $14$ $1$ $23$ $D_7:F_7$ (as 14T24) $[11/6]$ $[4/3, 11/6]_{6}^{2}$ $t + 4$ $x^{14} + 14 x^{12} + 28 x^{11} + 21 x^{10} + 35 x^{7} + 21$
7.14.23.20 $x^{14} + 7 x^{12} + 14 x^{11} + 7 x^{10} + 28 x^{7} + 7$ $7$ $14$ $1$ $23$ $D_7:F_7$ (as 14T24) $[11/6]$ $[4/3, 11/6]_{6}^{2}$ $t + 4$ $x^{14} + 7 x^{12} + 14 x^{11} + 7 x^{10} + 28 x^{7} + 7$
7.14.23.21 $x^{14} + 7 x^{12} + 14 x^{11} + 28 x^{10} + 28 x^{7} + 7$ $7$ $14$ $1$ $23$ $D_7:F_7$ (as 14T24) $[11/6]$ $[4/3, 11/6]_{6}^{2}$ $t + 4$ $x^{14} + 7 x^{12} + 14 x^{11} + 28 x^{10} + 28 x^{7} + 7$
7.14.23.22 $x^{14} + 42 x^{12} + 14 x^{11} + 42 x^{10} + 21$ $7$ $14$ $1$ $23$ $D_7:F_7$ (as 14T24) $[11/6]$ $[4/3, 11/6]_{6}^{2}$ $t + 4$ $x^{14} + 42 x^{12} + 14 x^{11} + 42 x^{10} + 21$
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