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Label Polynomial $p$ $e$ $f$ $c$ Galois group Visible slopes Slope content Unram. Ext. Eisen. Poly.
7.14.16.1 $x^{14} - 182 x^{10} - 210 x^{9} + 14 x^{7} - 2303 x^{6} - 2058 x^{5} + 441 x^{4} - 1274 x^{3} - 1470 x^{2} + 49$ $7$ $7$ $2$ $16$ $C_7:F_7$ (as 14T14) $[4/3]$ $[4/3, 4/3]_{3}^{2}$ $t^{2} + 6 t + 3$ $x^{7} + \left(42 t + 35\right) x^{3} + \left(42 t + 21\right) x^{2} + 7$
7.14.16.12 $x^{14} - 168 x^{10} - 56 x^{9} + 14 x^{7} - 3528 x^{6} - 5880 x^{5} - 1862 x^{4} - 1176 x^{3} - 392 x^{2} + 49$ $7$ $7$ $2$ $16$ $C_7:F_7$ (as 14T14) $[4/3]$ $[4/3, 4/3]_{3}^{2}$ $t^{2} + 6 t + 3$ $x^{7} + \left(42 t + 42\right) x^{3} + \left(21 t + 35\right) x^{2} + 7$
7.14.16.14 $x^{14} - 98 x^{10} + 14 x^{7} - 2303 x^{6} - 4704 x^{5} - 1176 x^{4} - 686 x^{3} + 49$ $7$ $7$ $2$ $16$ $C_7:F_7$ (as 14T14) $[4/3]$ $[4/3, 4/3]_{3}^{2}$ $t^{2} + 6 t + 3$ $x^{7} + \left(28 t + 35\right) x^{3} + \left(14 t + 42\right) x^{2} + 7$
7.14.16.15 $x^{14} - 168 x^{10} + 14 x^{9} + 14 x^{7} - 294 x^{6} - 4116 x^{5} - 245 x^{4} - 1176 x^{3} + 98 x^{2} + 49$ $7$ $7$ $2$ $16$ $C_7:F_7$ (as 14T14) $[4/3]$ $[4/3, 4/3]_{3}^{2}$ $t^{2} + 6 t + 3$ $x^{7} + \left(35 t + 21\right) x^{3} + \left(7 t + 28\right) x^{2} + 7$
7.14.16.20 $x^{14} + 28 x^{10} - 98 x^{9} + 14 x^{7} - 98 x^{6} - 3136 x^{5} - 245 x^{4} + 196 x^{3} - 686 x^{2} + 49$ $7$ $7$ $2$ $16$ $C_7:F_7$ (as 14T14) $[4/3]$ $[4/3, 4/3]_{3}^{2}$ $t^{2} + 6 t + 3$ $x^{7} + \left(7 t + 35\right) x^{3} + \left(21 t + 14\right) x^{2} + 7$
7.14.16.24 $x^{14} - 14 x^{10} - 70 x^{9} + 14 x^{7} - 1127 x^{6} - 1862 x^{5} + 49 x^{4} - 98 x^{3} - 490 x^{2} + 49$ $7$ $7$ $2$ $16$ $C_7:F_7$ (as 14T14) $[4/3]$ $[4/3, 4/3]_{3}^{2}$ $t^{2} + 6 t + 3$ $x^{7} + \left(14 t + 35\right) x^{3} + \left(14 t + 7\right) x^{2} + 7$
7.14.16.3 $x^{14} - 168 x^{10} - 140 x^{9} + 14 x^{7} - 3528 x^{6} - 2352 x^{5} + 196 x^{4} - 1176 x^{3} - 980 x^{2} + 49$ $7$ $7$ $2$ $16$ $C_7:F_7$ (as 14T14) $[4/3]$ $[4/3, 4/3]_{3}^{2}$ $t^{2} + 6 t + 3$ $x^{7} + \left(42 t + 42\right) x^{3} + \left(28 t + 14\right) x^{2} + 7$
7.14.16.5 $x^{14} - 252 x^{10} - 126 x^{9} + 14 x^{7} + 5292 x^{6} - 1764 x^{5} - 3381 x^{4} - 1764 x^{3} - 882 x^{2} + 49$ $7$ $7$ $2$ $16$ $C_7:F_7$ (as 14T14) $[4/3]$ $[4/3, 4/3]_{3}^{2}$ $t^{2} + 6 t + 3$ $x^{7} + 42 t x^{3} + \left(35 t + 42\right) x^{2} + 7$
7.14.16.6 $x^{14} - 238 x^{10} + 14 x^{7} + 3577 x^{6} - 3528 x^{5} - 294 x^{4} - 1666 x^{3} + 49$ $7$ $7$ $2$ $16$ $C_7:F_7$ (as 14T14) $[4/3]$ $[4/3, 4/3]_{3}^{2}$ $t^{2} + 6 t + 3$ $x^{7} + \left(42 t + 7\right) x^{3} + \left(7 t + 21\right) x^{2} + 7$
7.14.20.10 $x^{14} - 28 x^{12} - 126 x^{11} - 98 x^{10} - 1176 x^{9} - 3381 x^{8} + 14 x^{7} - 196 x^{5} - 882 x^{4} + 49$ $7$ $7$ $2$ $20$ $C_7:F_7$ (as 14T14) $[5/3]$ $[5/3, 5/3]_{3}^{2}$ $t^{2} + 6 t + 3$ $x^{7} + \left(7 t + 7\right) x^{5} + \left(35 t + 42\right) x^{4} + 7$
7.14.20.13 $x^{14} - 238 x^{12} - 140 x^{11} + 3577 x^{10} + 2548 x^{9} + 196 x^{8} + 14 x^{7} - 1666 x^{5} - 980 x^{4} + 49$ $7$ $7$ $2$ $20$ $C_7:F_7$ (as 14T14) $[5/3]$ $[5/3, 5/3]_{3}^{2}$ $t^{2} + 6 t + 3$ $x^{7} + \left(42 t + 7\right) x^{5} + \left(28 t + 14\right) x^{4} + 7$
7.14.20.19 $x^{14} - 196 x^{12} - 154 x^{11} - 980 x^{10} + 980 x^{9} + 1225 x^{8} + 14 x^{7} - 1372 x^{5} - 1078 x^{4} + 49$ $7$ $7$ $2$ $20$ $C_7:F_7$ (as 14T14) $[5/3]$ $[5/3, 5/3]_{3}^{2}$ $t^{2} + 6 t + 3$ $x^{7} + \left(42 t + 28\right) x^{5} + \left(28 t + 7\right) x^{4} + 7$
7.14.20.2 $x^{14} - 84 x^{12} - 196 x^{11} - 882 x^{10} - 588 x^{9} + 2254 x^{8} + 14 x^{7} - 588 x^{5} - 1372 x^{4} + 49$ $7$ $7$ $2$ $20$ $C_7:F_7$ (as 14T14) $[5/3]$ $[5/3, 5/3]_{3}^{2}$ $t^{2} + 6 t + 3$ $x^{7} + \left(21 t + 21\right) x^{5} + \left(35 t + 7\right) x^{4} + 7$
7.14.20.24 $x^{14} - 42 x^{12} - 196 x^{11} - 2205 x^{10} - 6468 x^{9} - 980 x^{8} + 14 x^{7} - 294 x^{5} - 1372 x^{4} + 49$ $7$ $7$ $2$ $20$ $C_7:F_7$ (as 14T14) $[5/3]$ $[5/3, 5/3]_{3}^{2}$ $t^{2} + 6 t + 3$ $x^{7} + \left(21 t + 42\right) x^{5} + \left(42 t + 28\right) x^{4} + 7$
7.14.20.25 $x^{14} - 140 x^{12} - 182 x^{11} - 2450 x^{10} - 4900 x^{9} - 2303 x^{8} + 14 x^{7} - 980 x^{5} - 1274 x^{4} + 49$ $7$ $7$ $2$ $20$ $C_7:F_7$ (as 14T14) $[5/3]$ $[5/3, 5/3]_{3}^{2}$ $t^{2} + 6 t + 3$ $x^{7} + \left(35 t + 35\right) x^{5} + \left(42 t + 35\right) x^{4} + 7$
7.14.20.3 $x^{14} + 14 x^{12} - 70 x^{11} - 245 x^{10} - 1666 x^{9} + 49 x^{8} + 14 x^{7} + 98 x^{5} - 490 x^{4} + 49$ $7$ $7$ $2$ $20$ $C_7:F_7$ (as 14T14) $[5/3]$ $[5/3, 5/3]_{3}^{2}$ $t^{2} + 6 t + 3$ $x^{7} + \left(7 t + 28\right) x^{5} + \left(14 t + 7\right) x^{4} + 7$
7.14.20.6 $x^{14} - 56 x^{12} - 98 x^{11} - 1862 x^{10} - 4312 x^{9} - 2303 x^{8} + 14 x^{7} - 392 x^{5} - 686 x^{4} + 49$ $7$ $7$ $2$ $20$ $C_7:F_7$ (as 14T14) $[5/3]$ $[5/3, 5/3]_{3}^{2}$ $t^{2} + 6 t + 3$ $x^{7} + \left(21 t + 35\right) x^{5} + \left(28 t + 35\right) x^{4} + 7$
7.14.20.7 $x^{14} - 196 x^{12} - 14 x^{11} - 980 x^{10} - 2156 x^{9} - 245 x^{8} + 14 x^{7} - 1372 x^{5} - 98 x^{4} + 49$ $7$ $7$ $2$ $20$ $C_7:F_7$ (as 14T14) $[5/3]$ $[5/3, 5/3]_{3}^{2}$ $t^{2} + 6 t + 3$ $x^{7} + \left(42 t + 28\right) x^{5} + \left(7 t + 14\right) x^{4} + 7$
7.14.21.1 $x^{14} + 14 x^{10} + 21 x^{9} + 14 x^{8} + 35 x^{7} + 7$ $7$ $14$ $1$ $21$ $C_7:F_7$ (as 14T14) $[5/3]$ $[7/6, 5/3]_{6}$ $t + 4$ $x^{14} + 14 x^{10} + 21 x^{9} + 14 x^{8} + 35 x^{7} + 7$
7.14.21.12 $x^{14} + 21 x^{10} + 21 x^{9} + 7 x^{8} + 21 x^{7} + 7$ $7$ $14$ $1$ $21$ $C_7:F_7$ (as 14T14) $[5/3]$ $[7/6, 5/3]_{6}$ $t + 4$ $x^{14} + 21 x^{10} + 21 x^{9} + 7 x^{8} + 21 x^{7} + 7$
7.14.21.13 $x^{14} + 35 x^{10} + 28 x^{9} + 42 x^{8} + 21$ $7$ $14$ $1$ $21$ $C_7:F_7$ (as 14T14) $[5/3]$ $[7/6, 5/3]_{6}$ $t + 4$ $x^{14} + 35 x^{10} + 28 x^{9} + 42 x^{8} + 21$
7.14.21.16 $x^{14} + 7 x^{9} + 35 x^{8} + 21$ $7$ $14$ $1$ $21$ $C_7:F_7$ (as 14T14) $[5/3]$ $[7/6, 5/3]_{6}$ $t + 4$ $x^{14} + 7 x^{9} + 35 x^{8} + 21$
7.14.21.18 $x^{14} + 21 x^{10} + 35 x^{9} + 7 x^{8} + 7$ $7$ $14$ $1$ $21$ $C_7:F_7$ (as 14T14) $[5/3]$ $[7/6, 5/3]_{6}$ $t + 4$ $x^{14} + 21 x^{10} + 35 x^{9} + 7 x^{8} + 7$
7.14.21.19 $x^{14} + 7 x^{10} + 42 x^{9} + 21 x^{8} + 21$ $7$ $14$ $1$ $21$ $C_7:F_7$ (as 14T14) $[5/3]$ $[7/6, 5/3]_{6}$ $t + 4$ $x^{14} + 7 x^{10} + 42 x^{9} + 21 x^{8} + 21$
7.14.21.21 $x^{14} + 42 x^{8} + 35 x^{7} + 21$ $7$ $14$ $1$ $21$ $C_7:F_7$ (as 14T14) $[5/3]$ $[7/6, 5/3]_{6}$ $t + 4$ $x^{14} + 42 x^{8} + 35 x^{7} + 21$
7.14.21.22 $x^{14} + 7 x^{9} + 21 x^{8} + 42 x^{7} + 21$ $7$ $14$ $1$ $21$ $C_7:F_7$ (as 14T14) $[5/3]$ $[7/6, 5/3]_{6}$ $t + 4$ $x^{14} + 7 x^{9} + 21 x^{8} + 42 x^{7} + 21$
7.14.21.23 $x^{14} + 7 x^{10} + 28 x^{9} + 28 x^{8} + 7 x^{7} + 7$ $7$ $14$ $1$ $21$ $C_7:F_7$ (as 14T14) $[5/3]$ $[7/6, 5/3]_{6}$ $t + 4$ $x^{14} + 7 x^{10} + 28 x^{9} + 28 x^{8} + 7 x^{7} + 7$
7.14.21.28 $x^{14} + 35 x^{8} + 42 x^{7} + 21$ $7$ $14$ $1$ $21$ $C_7:F_7$ (as 14T14) $[5/3]$ $[7/6, 5/3]_{6}$ $t + 4$ $x^{14} + 35 x^{8} + 42 x^{7} + 21$
7.14.21.3 $x^{14} + 42 x^{10} + 7 x^{9} + 42 x^{8} + 21$ $7$ $14$ $1$ $21$ $C_7:F_7$ (as 14T14) $[5/3]$ $[7/6, 5/3]_{6}$ $t + 4$ $x^{14} + 42 x^{10} + 7 x^{9} + 42 x^{8} + 21$
7.14.21.33 $x^{14} + 28 x^{10} + 21 x^{9} + 28 x^{8} + 7$ $7$ $14$ $1$ $21$ $C_7:F_7$ (as 14T14) $[5/3]$ $[7/6, 5/3]_{6}$ $t + 4$ $x^{14} + 28 x^{10} + 21 x^{9} + 28 x^{8} + 7$
7.14.21.41 $x^{14} + 42 x^{10} + 14 x^{8} + 21 x^{7} + 7$ $7$ $14$ $1$ $21$ $C_7:F_7$ (as 14T14) $[5/3]$ $[7/6, 5/3]_{6}$ $t + 4$ $x^{14} + 42 x^{10} + 14 x^{8} + 21 x^{7} + 7$
7.14.21.42 $x^{14} + 42 x^{10} + 14 x^{9} + 21 x^{8} + 21$ $7$ $14$ $1$ $21$ $C_7:F_7$ (as 14T14) $[5/3]$ $[7/6, 5/3]_{6}$ $t + 4$ $x^{14} + 42 x^{10} + 14 x^{9} + 21 x^{8} + 21$
7.14.21.48 $x^{14} + 14 x^{10} + 14 x^{9} + 7 x^{8} + 14 x^{7} + 7$ $7$ $14$ $1$ $21$ $C_7:F_7$ (as 14T14) $[5/3]$ $[7/6, 5/3]_{6}$ $t + 4$ $x^{14} + 14 x^{10} + 14 x^{9} + 7 x^{8} + 14 x^{7} + 7$
7.14.21.6 $x^{14} + 35 x^{9} + 28 x^{8} + 14 x^{7} + 7$ $7$ $14$ $1$ $21$ $C_7:F_7$ (as 14T14) $[5/3]$ $[7/6, 5/3]_{6}$ $t + 4$ $x^{14} + 35 x^{9} + 28 x^{8} + 14 x^{7} + 7$
7.14.21.7 $x^{14} + 14 x^{10} + 21 x^{9} + 35 x^{8} + 21$ $7$ $14$ $1$ $21$ $C_7:F_7$ (as 14T14) $[5/3]$ $[7/6, 5/3]_{6}$ $t + 4$ $x^{14} + 14 x^{10} + 21 x^{9} + 35 x^{8} + 21$
7.14.21.8 $x^{14} + 35 x^{10} + 14 x^{9} + 14 x^{8} + 7$ $7$ $14$ $1$ $21$ $C_7:F_7$ (as 14T14) $[5/3]$ $[7/6, 5/3]_{6}$ $t + 4$ $x^{14} + 35 x^{10} + 14 x^{9} + 14 x^{8} + 7$
7.14.23.10 $x^{14} + 14 x^{12} + 28 x^{11} + 14 x^{10} + 21$ $7$ $14$ $1$ $23$ $C_7:F_7$ (as 14T14) $[11/6]$ $[4/3, 11/6]_{6}$ $t + 4$ $x^{14} + 14 x^{12} + 28 x^{11} + 14 x^{10} + 21$
7.14.23.15 $x^{14} + 28 x^{12} + 14 x^{11} + 14 x^{10} + 21$ $7$ $14$ $1$ $23$ $C_7:F_7$ (as 14T14) $[11/6]$ $[4/3, 11/6]_{6}$ $t + 4$ $x^{14} + 28 x^{12} + 14 x^{11} + 14 x^{10} + 21$
7.14.23.17 $x^{14} + 35 x^{12} + 21 x^{11} + 42 x^{10} + 28 x^{7} + 7$ $7$ $14$ $1$ $23$ $C_7:F_7$ (as 14T14) $[11/6]$ $[4/3, 11/6]_{6}$ $t + 4$ $x^{14} + 35 x^{12} + 21 x^{11} + 42 x^{10} + 28 x^{7} + 7$
7.14.23.18 $x^{14} + 7 x^{12} + 28 x^{10} + 35 x^{7} + 21$ $7$ $14$ $1$ $23$ $C_7:F_7$ (as 14T14) $[11/6]$ $[4/3, 11/6]_{6}$ $t + 4$ $x^{14} + 7 x^{12} + 28 x^{10} + 35 x^{7} + 21$
7.14.23.19 $x^{14} + 7 x^{11} + 21 x^{10} + 7$ $7$ $14$ $1$ $23$ $C_7:F_7$ (as 14T14) $[11/6]$ $[4/3, 11/6]_{6}$ $t + 4$ $x^{14} + 7 x^{11} + 21 x^{10} + 7$
7.14.23.24 $x^{14} + 35 x^{12} + 35 x^{11} + 42 x^{10} + 7$ $7$ $14$ $1$ $23$ $C_7:F_7$ (as 14T14) $[11/6]$ $[4/3, 11/6]_{6}$ $t + 4$ $x^{14} + 35 x^{12} + 35 x^{11} + 42 x^{10} + 7$
7.14.23.3 $x^{14} + 7 x^{12} + 7 x^{11} + 28 x^{10} + 21$ $7$ $14$ $1$ $23$ $C_7:F_7$ (as 14T14) $[11/6]$ $[4/3, 11/6]_{6}$ $t + 4$ $x^{14} + 7 x^{12} + 7 x^{11} + 28 x^{10} + 21$
7.14.23.30 $x^{14} + 28 x^{12} + 28 x^{11} + 35 x^{10} + 7$ $7$ $14$ $1$ $23$ $C_7:F_7$ (as 14T14) $[11/6]$ $[4/3, 11/6]_{6}$ $t + 4$ $x^{14} + 28 x^{12} + 28 x^{11} + 35 x^{10} + 7$
7.14.23.32 $x^{14} + 21 x^{12} + 42 x^{11} + 7 x^{10} + 21$ $7$ $14$ $1$ $23$ $C_7:F_7$ (as 14T14) $[11/6]$ $[4/3, 11/6]_{6}$ $t + 4$ $x^{14} + 21 x^{12} + 42 x^{11} + 7 x^{10} + 21$
7.14.23.34 $x^{14} + 21 x^{12} + 7 x^{11} + 14 x^{10} + 21$ $7$ $14$ $1$ $23$ $C_7:F_7$ (as 14T14) $[11/6]$ $[4/3, 11/6]_{6}$ $t + 4$ $x^{14} + 21 x^{12} + 7 x^{11} + 14 x^{10} + 21$
7.14.23.35 $x^{14} + 7 x^{12} + 7 x^{11} + 35 x^{10} + 21 x^{7} + 7$ $7$ $14$ $1$ $23$ $C_7:F_7$ (as 14T14) $[11/6]$ $[4/3, 11/6]_{6}$ $t + 4$ $x^{14} + 7 x^{12} + 7 x^{11} + 35 x^{10} + 21 x^{7} + 7$
7.14.23.37 $x^{14} + 42 x^{12} + 14 x^{11} + 21 x^{10} + 7$ $7$ $14$ $1$ $23$ $C_7:F_7$ (as 14T14) $[11/6]$ $[4/3, 11/6]_{6}$ $t + 4$ $x^{14} + 42 x^{12} + 14 x^{11} + 21 x^{10} + 7$
7.14.23.4 $x^{14} + 7 x^{12} + 7 x^{11} + 21 x^{10} + 21 x^{7} + 7$ $7$ $14$ $1$ $23$ $C_7:F_7$ (as 14T14) $[11/6]$ $[4/3, 11/6]_{6}$ $t + 4$ $x^{14} + 7 x^{12} + 7 x^{11} + 21 x^{10} + 21 x^{7} + 7$
7.14.23.41 $x^{14} + 14 x^{12} + 42 x^{11} + 28 x^{10} + 21 x^{7} + 21$ $7$ $14$ $1$ $23$ $C_7:F_7$ (as 14T14) $[11/6]$ $[4/3, 11/6]_{6}$ $t + 4$ $x^{14} + 14 x^{12} + 42 x^{11} + 28 x^{10} + 21 x^{7} + 21$
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