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Degree Residue characteristic Galois group Galois unramified degree Assoc. Inertia
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Residue field degree Top slope Wild Visible Wild inertia subgroup
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Results (31 matches)

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Label Polynomial $p$ $e$ $f$ $c$ Galois group Visible slopes Slope content Unram. Ext. Eisen. Poly.
7.14.15.10 $x^{14} + 21 x^{3} + 35 x^{2} + 21$ $7$ $14$ $1$ $15$ $F_7$ (as 14T4) $[7/6]$ $[7/6]_{6}$ $t + 4$ $x^{14} + 21 x^{3} + 35 x^{2} + 21$
7.14.15.5 $x^{14} + 7 x^{3} + 7 x^{2} + 7$ $7$ $14$ $1$ $15$ $F_7$ (as 14T4) $[7/6]$ $[7/6]_{6}$ $t + 4$ $x^{14} + 7 x^{3} + 7 x^{2} + 7$
7.14.15.6 $x^{14} + 7 x^{3} + 21 x^{2} + 21$ $7$ $14$ $1$ $15$ $F_7$ (as 14T4) $[7/6]$ $[7/6]_{6}$ $t + 4$ $x^{14} + 7 x^{3} + 21 x^{2} + 21$
7.14.15.7 $x^{14} + 21 x^{3} + 28 x^{2} + 7$ $7$ $14$ $1$ $15$ $F_7$ (as 14T4) $[7/6]$ $[7/6]_{6}$ $t + 4$ $x^{14} + 21 x^{3} + 28 x^{2} + 7$
7.14.15.8 $x^{14} + 14 x^{3} + 42 x^{2} + 21$ $7$ $14$ $1$ $15$ $F_7$ (as 14T4) $[7/6]$ $[7/6]_{6}$ $t + 4$ $x^{14} + 14 x^{3} + 42 x^{2} + 21$
7.14.15.9 $x^{14} + 21 x^{3} + 14 x^{2} + 7$ $7$ $14$ $1$ $15$ $F_7$ (as 14T4) $[7/6]$ $[7/6]_{6}$ $t + 4$ $x^{14} + 21 x^{3} + 14 x^{2} + 7$
7.14.16.11 $x^{14} - 70 x^{10} + 84 x^{9} + 14 x^{7} - 1421 x^{6} - 2940 x^{5} + 1764 x^{4} - 490 x^{3} + 588 x^{2} + 49$ $7$ $7$ $2$ $16$ $F_7$ (as 14T4) $[4/3]$ $[4/3]_{3}^{2}$ $t^{2} + 6 t + 3$ $x^{7} + \left(21 t + 28\right) x^{3} + 42 x^{2} + 7$
7.14.16.23 $x^{14} - 140 x^{10} + 42 x^{9} + 14 x^{7} - 2450 x^{6} - 2940 x^{5} + 441 x^{4} - 980 x^{3} + 294 x^{2} + 49$ $7$ $7$ $2$ $16$ $F_7$ (as 14T4) $[4/3]$ $[4/3]_{3}^{2}$ $t^{2} + 6 t + 3$ $x^{7} + \left(35 t + 35\right) x^{3} + 21 x^{2} + 7$
7.14.16.25 $x^{14} + 42 x^{13} + 777 x^{12} + 8316 x^{11} + 56945 x^{10} + 261436 x^{9} + 829395 x^{8} + 1922318 x^{7} + 3820201 x^{6} + 8117116 x^{5} + 17134810 x^{4} + 27153266 x^{3} + 26418889 x^{2} + 13670286 x + 3306187$ $7$ $7$ $2$ $16$ $F_7$ (as 14T4) $[4/3]$ $[4/3]_{3}^{2}$ $t^{2} + 6 t + 3$ $x^{7} + 28 x^{3} + 35 x^{2} + 7$
7.14.19.1 $x^{14} + 21 x^{7} + 14 x^{6} + 21$ $7$ $14$ $1$ $19$ $F_7$ (as 14T4) $[3/2]$ $[3/2]_{2}^{3}$ $t + 4$ $x^{14} + 21 x^{7} + 14 x^{6} + 21$
7.14.19.12 $x^{14} + 7 x^{7} + 21 x^{6} + 7$ $7$ $14$ $1$ $19$ $F_7$ (as 14T4) $[3/2]$ $[3/2]_{2}^{3}$ $t + 4$ $x^{14} + 7 x^{7} + 21 x^{6} + 7$
7.14.19.6 $x^{14} + 14 x^{7} + 28 x^{6} + 21$ $7$ $14$ $1$ $19$ $F_7$ (as 14T4) $[3/2]$ $[3/2]_{2}^{3}$ $t + 4$ $x^{14} + 14 x^{7} + 28 x^{6} + 21$
7.14.19.7 $x^{14} + 21 x^{7} + 42 x^{6} + 7$ $7$ $14$ $1$ $19$ $F_7$ (as 14T4) $[3/2]$ $[3/2]_{2}^{3}$ $t + 4$ $x^{14} + 21 x^{7} + 42 x^{6} + 7$
7.14.20.21 $x^{14} + 42 x^{13} + 819 x^{12} + 9898 x^{11} + 83580 x^{10} + 527856 x^{9} + 2593927 x^{8} + 9990938 x^{7} + 29248947 x^{6} + 61272834 x^{5} + 85460683 x^{4} + 74405856 x^{3} + 38886624 x^{2} + 12484584 x + 3099820$ $7$ $7$ $2$ $20$ $F_7$ (as 14T4) $[5/3]$ $[5/3]_{3}^{2}$ $t^{2} + 6 t + 3$ $x^{7} + 21 x^{5} + 35 x^{4} + 7$
7.14.20.5 $x^{14} - 168 x^{12} + 42 x^{11} + 2352 x^{10} - 3528 x^{9} + 441 x^{8} + 14 x^{7} - 1176 x^{5} + 294 x^{4} + 49$ $7$ $7$ $2$ $20$ $F_7$ (as 14T4) $[5/3]$ $[5/3]_{3}^{2}$ $t^{2} + 6 t + 3$ $x^{7} + 28 t x^{5} + 21 x^{4} + 7$
7.14.20.8 $x^{14} + 28 x^{12} + 84 x^{11} - 98 x^{10} + 1176 x^{9} + 1764 x^{8} + 14 x^{7} + 196 x^{5} + 588 x^{4} + 49$ $7$ $7$ $2$ $20$ $F_7$ (as 14T4) $[5/3]$ $[5/3]_{3}^{2}$ $t^{2} + 6 t + 3$ $x^{7} + \left(7 t + 35\right) x^{5} + 42 x^{4} + 7$
7.14.23.12 $x^{14} + 7 x^{12} + 35 x^{10} + 7$ $7$ $14$ $1$ $23$ $F_7$ (as 14T4) $[11/6]$ $[11/6]_{6}$ $t + 4$ $x^{14} + 7 x^{12} + 35 x^{10} + 7$
7.14.23.25 $x^{14} + 21 x^{12} + 28 x^{10} + 21$ $7$ $14$ $1$ $23$ $F_7$ (as 14T4) $[11/6]$ $[11/6]_{6}$ $t + 4$ $x^{14} + 21 x^{12} + 28 x^{10} + 21$
7.14.23.26 $x^{14} + 35 x^{11} + 14 x^{10} + 14 x^{7} + 21$ $7$ $14$ $1$ $23$ $F_7$ (as 14T4) $[11/6]$ $[11/6]_{6}$ $t + 4$ $x^{14} + 35 x^{11} + 14 x^{10} + 14 x^{7} + 21$
7.14.23.27 $x^{14} + 14 x^{12} + 21 x^{11} + 42 x^{10} + 14 x^{7} + 7$ $7$ $14$ $1$ $23$ $F_7$ (as 14T4) $[11/6]$ $[11/6]_{6}$ $t + 4$ $x^{14} + 14 x^{12} + 21 x^{11} + 42 x^{10} + 14 x^{7} + 7$
7.14.23.33 $x^{14} + 42 x^{11} + 21 x^{10} + 7 x^{7} + 7$ $7$ $14$ $1$ $23$ $F_7$ (as 14T4) $[11/6]$ $[11/6]_{6}$ $t + 4$ $x^{14} + 42 x^{11} + 21 x^{10} + 7 x^{7} + 7$
7.14.23.40 $x^{14} + 7 x^{10} + 21$ $7$ $14$ $1$ $23$ $F_7$ (as 14T4) $[11/6]$ $[11/6]_{6}$ $t + 4$ $x^{14} + 7 x^{10} + 21$
7.14.24.11 $x^{14} + 56 x^{13} + 784 x^{12} - 1554 x^{7} - 43512 x^{6} + 85113$ $7$ $7$ $2$ $24$ $F_7$ (as 14T4) $[2]$ $[2]^{6}$ $t^{2} + 6 t + 3$ $x^{7} + 28 x^{6} + 294 t + 105$
7.14.24.36 $x^{14} + 28 x^{13} + 196 x^{12} - 1260 x^{7} - 17640 x^{6} - 121716$ $7$ $7$ $2$ $24$ $F_7$ (as 14T4) $[2]$ $[2]^{6}$ $t^{2} + 6 t + 3$ $x^{7} + 14 x^{6} + 294 t + 252$
7.14.27.40 $x^{14} + 42 x^{7} + 196 x^{2} + 294 x + 105$ $7$ $14$ $1$ $27$ $F_7$ (as 14T4) $[13/6]$ $[13/6]_{6}$ $t + 4$ $x^{14} + 42 x^{7} + 196 x^{2} + 294 x + 105$
7.14.27.42 $x^{14} + 14 x^{7} + 147 x^{3} + 294 x^{2} + 98 x + 252$ $7$ $14$ $1$ $27$ $F_7$ (as 14T4) $[13/6]$ $[13/6]_{6}$ $t + 4$ $x^{14} + 14 x^{7} + 147 x^{3} + 294 x^{2} + 98 x + 252$
7.14.27.45 $x^{14} + 294 x^{2} + 105$ $7$ $14$ $1$ $27$ $F_7$ (as 14T4) $[13/6]$ $[13/6]_{6}$ $t + 4$ $x^{14} + 294 x^{2} + 105$
7.14.27.51 $x^{14} + 294 x^{3} + 245 x^{2} + 7$ $7$ $14$ $1$ $27$ $F_7$ (as 14T4) $[13/6]$ $[13/6]_{6}$ $t + 4$ $x^{14} + 294 x^{3} + 245 x^{2} + 7$
7.14.27.53 $x^{14} + 14 x^{7} + 98 x + 7$ $7$ $14$ $1$ $27$ $F_7$ (as 14T4) $[13/6]$ $[13/6]_{6}$ $t + 4$ $x^{14} + 14 x^{7} + 98 x + 7$
7.14.27.54 $x^{14} + 49 x^{2} + 301$ $7$ $14$ $1$ $27$ $F_7$ (as 14T4) $[13/6]$ $[13/6]_{6}$ $t + 4$ $x^{14} + 49 x^{2} + 301$
7.14.27.56 $x^{14} + 7 x^{7} + 245 x^{3} + 196 x^{2} + 49 x + 154$ $7$ $14$ $1$ $27$ $F_7$ (as 14T4) $[13/6]$ $[13/6]_{6}$ $t + 4$ $x^{14} + 7 x^{7} + 245 x^{3} + 196 x^{2} + 49 x + 154$
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