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Degree $n$ Residue characteristic $p$ Discriminant exponent $c$ Galois group
Ramification index $e$ Residue field degree $f$ Galois tame degree $t$ Galois unram. degree $u$
Num. automorphisms Inertia subgroup Indices Assoc. Inertia Jump Set
Top Artin slope Galois Artin Visible Artin Wild inertia subgroup
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Results (1-50 of 95 matches)

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Label Polynomial $p$ $f$ $e$ $c$ Galois group $u$ $t$ Visible Artin slopes Visible Swan slopes Artin slope content Swan slope content Hidden Artin slopes Hidden Swan slopes Unram. Ext. Eisen. Poly. Ind. of Insep. Assoc. Inertia Resid. Poly Jump Set
2.7.1.0a1.1 $x^{7} + x + 1$ $2$ $7$ $1$ $0$ $C_7$ (as 7T1) $7$ $1$ $[\ ]$ $[\ ]$ $[\ ]^{7}$ $[\ ]^{7}$ $[\ ]$ $[\ ]$ $t^{7} + t + 1$ $x - 2$ $[0]$ $[\ ]$ $[1]$
3.7.1.0a1.1 $x^{7} + 2 x^{2} + 1$ $3$ $7$ $1$ $0$ $C_7$ (as 7T1) $7$ $1$ $[\ ]$ $[\ ]$ $[\ ]^{7}$ $[\ ]^{7}$ $[\ ]$ $[\ ]$ $t^{7} + 2 t^{2} + 1$ $x - 3$ $[0]$ $[\ ]$ undefined
5.7.1.0a1.1 $x^{7} + 3 x + 3$ $5$ $7$ $1$ $0$ $C_7$ (as 7T1) $7$ $1$ $[\ ]$ $[\ ]$ $[\ ]^{7}$ $[\ ]^{7}$ $[\ ]$ $[\ ]$ $t^{7} + 3 t + 3$ $x - 5$ $[0]$ $[\ ]$ undefined
7.7.1.0a1.1 $x^{7} + 6 x + 4$ $7$ $7$ $1$ $0$ $C_7$ (as 7T1) $7$ $1$ $[\ ]$ $[\ ]$ $[\ ]^{7}$ $[\ ]^{7}$ $[\ ]$ $[\ ]$ $t^{7} + 6 t + 4$ $x - 7$ $[0]$ $[\ ]$ undefined
7.1.7.12a6.1 $x^{7} + 42 x^{6} + 7$ $7$ $1$ $7$ $12$ $C_7$ (as 7T1) $1$ $1$ $[2]$ $[1]$ $[2]$ $[1]$ $[\ ]$ $[\ ]$ $t + 4$ $x^{7} + 42 x^{6} + 7$ $[6, 0]$ $[1]$ $z^6 + 6$ undefined
7.1.7.12a6.2 $x^{7} + 42 x^{6} + 56$ $7$ $1$ $7$ $12$ $C_7$ (as 7T1) $1$ $1$ $[2]$ $[1]$ $[2]$ $[1]$ $[\ ]$ $[\ ]$ $t + 4$ $x^{7} + 42 x^{6} + 56$ $[6, 0]$ $[1]$ $z^6 + 6$ undefined
7.1.7.12a6.3 $x^{7} + 42 x^{6} + 105$ $7$ $1$ $7$ $12$ $C_7$ (as 7T1) $1$ $1$ $[2]$ $[1]$ $[2]$ $[1]$ $[\ ]$ $[\ ]$ $t + 4$ $x^{7} + 42 x^{6} + 105$ $[6, 0]$ $[1]$ $z^6 + 6$ undefined
7.1.7.12a6.4 $x^{7} + 42 x^{6} + 154$ $7$ $1$ $7$ $12$ $C_7$ (as 7T1) $1$ $1$ $[2]$ $[1]$ $[2]$ $[1]$ $[\ ]$ $[\ ]$ $t + 4$ $x^{7} + 42 x^{6} + 154$ $[6, 0]$ $[1]$ $z^6 + 6$ undefined
7.1.7.12a6.5 $x^{7} + 42 x^{6} + 203$ $7$ $1$ $7$ $12$ $C_7$ (as 7T1) $1$ $1$ $[2]$ $[1]$ $[2]$ $[1]$ $[\ ]$ $[\ ]$ $t + 4$ $x^{7} + 42 x^{6} + 203$ $[6, 0]$ $[1]$ $z^6 + 6$ undefined
7.1.7.12a6.6 $x^{7} + 42 x^{6} + 252$ $7$ $1$ $7$ $12$ $C_7$ (as 7T1) $1$ $1$ $[2]$ $[1]$ $[2]$ $[1]$ $[\ ]$ $[\ ]$ $t + 4$ $x^{7} + 42 x^{6} + 252$ $[6, 0]$ $[1]$ $z^6 + 6$ undefined
7.1.7.12a6.7 $x^{7} + 42 x^{6} + 301$ $7$ $1$ $7$ $12$ $C_7$ (as 7T1) $1$ $1$ $[2]$ $[1]$ $[2]$ $[1]$ $[\ ]$ $[\ ]$ $t + 4$ $x^{7} + 42 x^{6} + 301$ $[6, 0]$ $[1]$ $z^6 + 6$ undefined
11.7.1.0a1.1 $x^{7} + 4 x + 9$ $11$ $7$ $1$ $0$ $C_7$ (as 7T1) $7$ $1$ $[\ ]$ $[\ ]$ $[\ ]^{7}$ $[\ ]^{7}$ $[\ ]$ $[\ ]$ $t^{7} + 4 t + 9$ $x - 11$ $[0]$ $[\ ]$ undefined
13.7.1.0a1.1 $x^{7} + 3 x + 11$ $13$ $7$ $1$ $0$ $C_7$ (as 7T1) $7$ $1$ $[\ ]$ $[\ ]$ $[\ ]^{7}$ $[\ ]^{7}$ $[\ ]$ $[\ ]$ $t^{7} + 3 t + 11$ $x - 13$ $[0]$ $[\ ]$ undefined
17.7.1.0a1.1 $x^{7} + 12 x + 14$ $17$ $7$ $1$ $0$ $C_7$ (as 7T1) $7$ $1$ $[\ ]$ $[\ ]$ $[\ ]^{7}$ $[\ ]^{7}$ $[\ ]$ $[\ ]$ $t^{7} + 12 t + 14$ $x - 17$ $[0]$ $[\ ]$ undefined
19.7.1.0a1.1 $x^{7} + 6 x + 17$ $19$ $7$ $1$ $0$ $C_7$ (as 7T1) $7$ $1$ $[\ ]$ $[\ ]$ $[\ ]^{7}$ $[\ ]^{7}$ $[\ ]$ $[\ ]$ $t^{7} + 6 t + 17$ $x - 19$ $[0]$ $[\ ]$ undefined
23.7.1.0a1.1 $x^{7} + 21 x + 18$ $23$ $7$ $1$ $0$ $C_7$ (as 7T1) $7$ $1$ $[\ ]$ $[\ ]$ $[\ ]^{7}$ $[\ ]^{7}$ $[\ ]$ $[\ ]$ $t^{7} + 21 t + 18$ $x - 23$ $[0]$ $[\ ]$ undefined
29.7.1.0a1.1 $x^{7} + 2 x + 27$ $29$ $7$ $1$ $0$ $C_7$ (as 7T1) $7$ $1$ $[\ ]$ $[\ ]$ $[\ ]^{7}$ $[\ ]^{7}$ $[\ ]$ $[\ ]$ $t^{7} + 2 t + 27$ $x - 29$ $[0]$ $[\ ]$ undefined
29.1.7.6a1.1 $x^{7} + 29$ $29$ $1$ $7$ $6$ $C_7$ (as 7T1) $1$ $7$ $[\ ]$ $[\ ]$ $[\ ]_{7}$ $[\ ]_{7}$ $[\ ]$ $[\ ]$ $t + 27$ $x^{7} + 29$ $[0]$ $[1]$ $z^6 + 7 z^5 + 21 z^4 + 6 z^3 + 6 z^2 + 21 z + 7$ undefined
29.1.7.6a1.2 $x^{7} + 58$ $29$ $1$ $7$ $6$ $C_7$ (as 7T1) $1$ $7$ $[\ ]$ $[\ ]$ $[\ ]_{7}$ $[\ ]_{7}$ $[\ ]$ $[\ ]$ $t + 27$ $x^{7} + 58$ $[0]$ $[1]$ $z^6 + 7 z^5 + 21 z^4 + 6 z^3 + 6 z^2 + 21 z + 7$ undefined
29.1.7.6a1.3 $x^{7} + 87$ $29$ $1$ $7$ $6$ $C_7$ (as 7T1) $1$ $7$ $[\ ]$ $[\ ]$ $[\ ]_{7}$ $[\ ]_{7}$ $[\ ]$ $[\ ]$ $t + 27$ $x^{7} + 87$ $[0]$ $[1]$ $z^6 + 7 z^5 + 21 z^4 + 6 z^3 + 6 z^2 + 21 z + 7$ undefined
29.1.7.6a1.4 $x^{7} + 116$ $29$ $1$ $7$ $6$ $C_7$ (as 7T1) $1$ $7$ $[\ ]$ $[\ ]$ $[\ ]_{7}$ $[\ ]_{7}$ $[\ ]$ $[\ ]$ $t + 27$ $x^{7} + 116$ $[0]$ $[1]$ $z^6 + 7 z^5 + 21 z^4 + 6 z^3 + 6 z^2 + 21 z + 7$ undefined
29.1.7.6a1.5 $x^{7} + 174$ $29$ $1$ $7$ $6$ $C_7$ (as 7T1) $1$ $7$ $[\ ]$ $[\ ]$ $[\ ]_{7}$ $[\ ]_{7}$ $[\ ]$ $[\ ]$ $t + 27$ $x^{7} + 174$ $[0]$ $[1]$ $z^6 + 7 z^5 + 21 z^4 + 6 z^3 + 6 z^2 + 21 z + 7$ undefined
29.1.7.6a1.6 $x^{7} + 232$ $29$ $1$ $7$ $6$ $C_7$ (as 7T1) $1$ $7$ $[\ ]$ $[\ ]$ $[\ ]_{7}$ $[\ ]_{7}$ $[\ ]$ $[\ ]$ $t + 27$ $x^{7} + 232$ $[0]$ $[1]$ $z^6 + 7 z^5 + 21 z^4 + 6 z^3 + 6 z^2 + 21 z + 7$ undefined
29.1.7.6a1.7 $x^{7} + 464$ $29$ $1$ $7$ $6$ $C_7$ (as 7T1) $1$ $7$ $[\ ]$ $[\ ]$ $[\ ]_{7}$ $[\ ]_{7}$ $[\ ]$ $[\ ]$ $t + 27$ $x^{7} + 464$ $[0]$ $[1]$ $z^6 + 7 z^5 + 21 z^4 + 6 z^3 + 6 z^2 + 21 z + 7$ undefined
31.7.1.0a1.1 $x^{7} + x + 28$ $31$ $7$ $1$ $0$ $C_7$ (as 7T1) $7$ $1$ $[\ ]$ $[\ ]$ $[\ ]^{7}$ $[\ ]^{7}$ $[\ ]$ $[\ ]$ $t^{7} + t + 28$ $x - 31$ $[0]$ $[\ ]$ undefined
37.7.1.0a1.1 $x^{7} + 7 x + 35$ $37$ $7$ $1$ $0$ $C_7$ (as 7T1) $7$ $1$ $[\ ]$ $[\ ]$ $[\ ]^{7}$ $[\ ]^{7}$ $[\ ]$ $[\ ]$ $t^{7} + 7 t + 35$ $x - 37$ $[0]$ $[\ ]$ undefined
41.7.1.0a1.1 $x^{7} + 6 x + 35$ $41$ $7$ $1$ $0$ $C_7$ (as 7T1) $7$ $1$ $[\ ]$ $[\ ]$ $[\ ]^{7}$ $[\ ]^{7}$ $[\ ]$ $[\ ]$ $t^{7} + 6 t + 35$ $x - 41$ $[0]$ $[\ ]$ undefined
43.7.1.0a1.1 $x^{7} + 42 x^{2} + 7 x + 40$ $43$ $7$ $1$ $0$ $C_7$ (as 7T1) $7$ $1$ $[\ ]$ $[\ ]$ $[\ ]^{7}$ $[\ ]^{7}$ $[\ ]$ $[\ ]$ $t^{7} + 42 t^{2} + 7 t + 40$ $x - 43$ $[0]$ $[\ ]$ undefined
43.1.7.6a1.1 $x^{7} + 43$ $43$ $1$ $7$ $6$ $C_7$ (as 7T1) $1$ $7$ $[\ ]$ $[\ ]$ $[\ ]_{7}$ $[\ ]_{7}$ $[\ ]$ $[\ ]$ $t + 40$ $x^{7} + 43$ $[0]$ $[1]$ $z^6 + 7 z^5 + 21 z^4 + 35 z^3 + 35 z^2 + 21 z + 7$ undefined
43.1.7.6a1.2 $x^{7} + 129$ $43$ $1$ $7$ $6$ $C_7$ (as 7T1) $1$ $7$ $[\ ]$ $[\ ]$ $[\ ]_{7}$ $[\ ]_{7}$ $[\ ]$ $[\ ]$ $t + 40$ $x^{7} + 129$ $[0]$ $[1]$ $z^6 + 7 z^5 + 21 z^4 + 35 z^3 + 35 z^2 + 21 z + 7$ undefined
43.1.7.6a1.3 $x^{7} + 387$ $43$ $1$ $7$ $6$ $C_7$ (as 7T1) $1$ $7$ $[\ ]$ $[\ ]$ $[\ ]_{7}$ $[\ ]_{7}$ $[\ ]$ $[\ ]$ $t + 40$ $x^{7} + 387$ $[0]$ $[1]$ $z^6 + 7 z^5 + 21 z^4 + 35 z^3 + 35 z^2 + 21 z + 7$ undefined
43.1.7.6a1.4 $x^{7} + 1161$ $43$ $1$ $7$ $6$ $C_7$ (as 7T1) $1$ $7$ $[\ ]$ $[\ ]$ $[\ ]_{7}$ $[\ ]_{7}$ $[\ ]$ $[\ ]$ $t + 40$ $x^{7} + 1161$ $[0]$ $[1]$ $z^6 + 7 z^5 + 21 z^4 + 35 z^3 + 35 z^2 + 21 z + 7$ undefined
43.1.7.6a1.5 $x^{7} + 1204$ $43$ $1$ $7$ $6$ $C_7$ (as 7T1) $1$ $7$ $[\ ]$ $[\ ]$ $[\ ]_{7}$ $[\ ]_{7}$ $[\ ]$ $[\ ]$ $t + 40$ $x^{7} + 1204$ $[0]$ $[1]$ $z^6 + 7 z^5 + 21 z^4 + 35 z^3 + 35 z^2 + 21 z + 7$ undefined
43.1.7.6a1.6 $x^{7} + 1634$ $43$ $1$ $7$ $6$ $C_7$ (as 7T1) $1$ $7$ $[\ ]$ $[\ ]$ $[\ ]_{7}$ $[\ ]_{7}$ $[\ ]$ $[\ ]$ $t + 40$ $x^{7} + 1634$ $[0]$ $[1]$ $z^6 + 7 z^5 + 21 z^4 + 35 z^3 + 35 z^2 + 21 z + 7$ undefined
43.1.7.6a1.7 $x^{7} + 1763$ $43$ $1$ $7$ $6$ $C_7$ (as 7T1) $1$ $7$ $[\ ]$ $[\ ]$ $[\ ]_{7}$ $[\ ]_{7}$ $[\ ]$ $[\ ]$ $t + 40$ $x^{7} + 1763$ $[0]$ $[1]$ $z^6 + 7 z^5 + 21 z^4 + 35 z^3 + 35 z^2 + 21 z + 7$ undefined
47.7.1.0a1.1 $x^{7} + 12 x + 42$ $47$ $7$ $1$ $0$ $C_7$ (as 7T1) $7$ $1$ $[\ ]$ $[\ ]$ $[\ ]^{7}$ $[\ ]^{7}$ $[\ ]$ $[\ ]$ $t^{7} + 12 t + 42$ $x - 47$ $[0]$ $[\ ]$ undefined
53.7.1.0a1.1 $x^{7} + 9 x + 51$ $53$ $7$ $1$ $0$ $C_7$ (as 7T1) $7$ $1$ $[\ ]$ $[\ ]$ $[\ ]^{7}$ $[\ ]^{7}$ $[\ ]$ $[\ ]$ $t^{7} + 9 t + 51$ $x - 53$ $[0]$ $[\ ]$ undefined
59.7.1.0a1.1 $x^{7} + 10 x + 57$ $59$ $7$ $1$ $0$ $C_7$ (as 7T1) $7$ $1$ $[\ ]$ $[\ ]$ $[\ ]^{7}$ $[\ ]^{7}$ $[\ ]$ $[\ ]$ $t^{7} + 10 t + 57$ $x - 59$ $[0]$ $[\ ]$ undefined
61.7.1.0a1.1 $x^{7} + 2 x + 59$ $61$ $7$ $1$ $0$ $C_7$ (as 7T1) $7$ $1$ $[\ ]$ $[\ ]$ $[\ ]^{7}$ $[\ ]^{7}$ $[\ ]$ $[\ ]$ $t^{7} + 2 t + 59$ $x - 61$ $[0]$ $[\ ]$ undefined
67.7.1.0a1.1 $x^{7} + 7 x + 65$ $67$ $7$ $1$ $0$ $C_7$ (as 7T1) $7$ $1$ $[\ ]$ $[\ ]$ $[\ ]^{7}$ $[\ ]^{7}$ $[\ ]$ $[\ ]$ $t^{7} + 7 t + 65$ $x - 67$ $[0]$ $[\ ]$ undefined
71.7.1.0a1.1 $x^{7} + 2 x + 64$ $71$ $7$ $1$ $0$ $C_7$ (as 7T1) $7$ $1$ $[\ ]$ $[\ ]$ $[\ ]^{7}$ $[\ ]^{7}$ $[\ ]$ $[\ ]$ $t^{7} + 2 t + 64$ $x - 71$ $[0]$ $[\ ]$ undefined
71.1.7.6a1.1 $x^{7} + 71$ $71$ $1$ $7$ $6$ $C_7$ (as 7T1) $1$ $7$ $[\ ]$ $[\ ]$ $[\ ]_{7}$ $[\ ]_{7}$ $[\ ]$ $[\ ]$ $t + 64$ $x^{7} + 71$ $[0]$ $[1]$ $z^6 + 7 z^5 + 21 z^4 + 35 z^3 + 35 z^2 + 21 z + 7$ undefined
71.1.7.6a1.2 $x^{7} + 142$ $71$ $1$ $7$ $6$ $C_7$ (as 7T1) $1$ $7$ $[\ ]$ $[\ ]$ $[\ ]_{7}$ $[\ ]_{7}$ $[\ ]$ $[\ ]$ $t + 64$ $x^{7} + 142$ $[0]$ $[1]$ $z^6 + 7 z^5 + 21 z^4 + 35 z^3 + 35 z^2 + 21 z + 7$ undefined
71.1.7.6a1.3 $x^{7} + 497$ $71$ $1$ $7$ $6$ $C_7$ (as 7T1) $1$ $7$ $[\ ]$ $[\ ]$ $[\ ]_{7}$ $[\ ]_{7}$ $[\ ]$ $[\ ]$ $t + 64$ $x^{7} + 497$ $[0]$ $[1]$ $z^6 + 7 z^5 + 21 z^4 + 35 z^3 + 35 z^2 + 21 z + 7$ undefined
71.1.7.6a1.4 $x^{7} + 3479$ $71$ $1$ $7$ $6$ $C_7$ (as 7T1) $1$ $7$ $[\ ]$ $[\ ]$ $[\ ]_{7}$ $[\ ]_{7}$ $[\ ]$ $[\ ]$ $t + 64$ $x^{7} + 3479$ $[0]$ $[1]$ $z^6 + 7 z^5 + 21 z^4 + 35 z^3 + 35 z^2 + 21 z + 7$ undefined
71.1.7.6a1.5 $x^{7} + 3621$ $71$ $1$ $7$ $6$ $C_7$ (as 7T1) $1$ $7$ $[\ ]$ $[\ ]$ $[\ ]_{7}$ $[\ ]_{7}$ $[\ ]$ $[\ ]$ $t + 64$ $x^{7} + 3621$ $[0]$ $[1]$ $z^6 + 7 z^5 + 21 z^4 + 35 z^3 + 35 z^2 + 21 z + 7$ undefined
71.1.7.6a1.6 $x^{7} + 4118$ $71$ $1$ $7$ $6$ $C_7$ (as 7T1) $1$ $7$ $[\ ]$ $[\ ]$ $[\ ]_{7}$ $[\ ]_{7}$ $[\ ]$ $[\ ]$ $t + 64$ $x^{7} + 4118$ $[0]$ $[1]$ $z^6 + 7 z^5 + 21 z^4 + 35 z^3 + 35 z^2 + 21 z + 7$ undefined
71.1.7.6a1.7 $x^{7} + 4189$ $71$ $1$ $7$ $6$ $C_7$ (as 7T1) $1$ $7$ $[\ ]$ $[\ ]$ $[\ ]_{7}$ $[\ ]_{7}$ $[\ ]$ $[\ ]$ $t + 64$ $x^{7} + 4189$ $[0]$ $[1]$ $z^6 + 7 z^5 + 21 z^4 + 35 z^3 + 35 z^2 + 21 z + 7$ undefined
73.7.1.0a1.1 $x^{7} + 10 x + 68$ $73$ $7$ $1$ $0$ $C_7$ (as 7T1) $7$ $1$ $[\ ]$ $[\ ]$ $[\ ]^{7}$ $[\ ]^{7}$ $[\ ]$ $[\ ]$ $t^{7} + 10 t + 68$ $x - 73$ $[0]$ $[\ ]$ undefined
79.7.1.0a1.1 $x^{7} + 4 x + 76$ $79$ $7$ $1$ $0$ $C_7$ (as 7T1) $7$ $1$ $[\ ]$ $[\ ]$ $[\ ]^{7}$ $[\ ]^{7}$ $[\ ]$ $[\ ]$ $t^{7} + 4 t + 76$ $x - 79$ $[0]$ $[\ ]$ undefined
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