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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 97 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
2.17.1.0a1.1 $x^{17} + x^{3} + 1$ $2$ $17$ $1$ $0$ $C_{17}$ (as 17T1) $17$ $1$ $[\ ]$ $[\ ]$ $[\ ]^{17}$ $[\ ]^{17}$ $[\ ]$ $[\ ]$ $t^{17} + t^{3} + 1$ $x - 2$ $[0]$ $[\ ]$ $[1]$
3.17.1.0a1.1 $x^{17} + 2 x + 1$ $3$ $17$ $1$ $0$ $C_{17}$ (as 17T1) $17$ $1$ $[\ ]$ $[\ ]$ $[\ ]^{17}$ $[\ ]^{17}$ $[\ ]$ $[\ ]$ $t^{17} + 2 t + 1$ $x - 3$ $[0]$ $[\ ]$ undefined
5.17.1.0a1.1 $x^{17} + 3 x^{2} + 2 x + 3$ $5$ $17$ $1$ $0$ $C_{17}$ (as 17T1) $17$ $1$ $[\ ]$ $[\ ]$ $[\ ]^{17}$ $[\ ]^{17}$ $[\ ]$ $[\ ]$ $t^{17} + 3 t^{2} + 2 t + 3$ $x - 5$ $[0]$ $[\ ]$ undefined
7.17.1.0a1.1 $x^{17} + x + 4$ $7$ $17$ $1$ $0$ $C_{17}$ (as 17T1) $17$ $1$ $[\ ]$ $[\ ]$ $[\ ]^{17}$ $[\ ]^{17}$ $[\ ]$ $[\ ]$ $t^{17} + t + 4$ $x - 7$ $[0]$ $[\ ]$ undefined
11.17.1.0a1.1 $x^{17} + 4 x + 9$ $11$ $17$ $1$ $0$ $C_{17}$ (as 17T1) $17$ $1$ $[\ ]$ $[\ ]$ $[\ ]^{17}$ $[\ ]^{17}$ $[\ ]$ $[\ ]$ $t^{17} + 4 t + 9$ $x - 11$ $[0]$ $[\ ]$ undefined
13.17.1.0a1.1 $x^{17} + 10 x^{2} + 6 x + 11$ $13$ $17$ $1$ $0$ $C_{17}$ (as 17T1) $17$ $1$ $[\ ]$ $[\ ]$ $[\ ]^{17}$ $[\ ]^{17}$ $[\ ]$ $[\ ]$ $t^{17} + 10 t^{2} + 6 t + 11$ $x - 13$ $[0]$ $[\ ]$ undefined
17.17.1.0a1.1 $x^{17} + 16 x + 14$ $17$ $17$ $1$ $0$ $C_{17}$ (as 17T1) $17$ $1$ $[\ ]$ $[\ ]$ $[\ ]^{17}$ $[\ ]^{17}$ $[\ ]$ $[\ ]$ $t^{17} + 16 t + 14$ $x - 17$ $[0]$ $[\ ]$ undefined
17.1.17.32a16.1 $x^{17} + 272 x^{16} + 17$ $17$ $1$ $17$ $32$ $C_{17}$ (as 17T1) $1$ $1$ $[2]$ $[1]$ $[2]$ $[1]$ $[\ ]$ $[\ ]$ $t + 14$ $x^{17} + 272 x^{16} + 17$ $[16, 0]$ $[1]$ $z^{16} + 16$ undefined
17.1.17.32a16.2 $x^{17} + 272 x^{16} + 306$ $17$ $1$ $17$ $32$ $C_{17}$ (as 17T1) $1$ $1$ $[2]$ $[1]$ $[2]$ $[1]$ $[\ ]$ $[\ ]$ $t + 14$ $x^{17} + 272 x^{16} + 306$ $[16, 0]$ $[1]$ $z^{16} + 16$ undefined
17.1.17.32a16.3 $x^{17} + 272 x^{16} + 595$ $17$ $1$ $17$ $32$ $C_{17}$ (as 17T1) $1$ $1$ $[2]$ $[1]$ $[2]$ $[1]$ $[\ ]$ $[\ ]$ $t + 14$ $x^{17} + 272 x^{16} + 595$ $[16, 0]$ $[1]$ $z^{16} + 16$ undefined
17.1.17.32a16.4 $x^{17} + 272 x^{16} + 884$ $17$ $1$ $17$ $32$ $C_{17}$ (as 17T1) $1$ $1$ $[2]$ $[1]$ $[2]$ $[1]$ $[\ ]$ $[\ ]$ $t + 14$ $x^{17} + 272 x^{16} + 884$ $[16, 0]$ $[1]$ $z^{16} + 16$ undefined
17.1.17.32a16.5 $x^{17} + 272 x^{16} + 1173$ $17$ $1$ $17$ $32$ $C_{17}$ (as 17T1) $1$ $1$ $[2]$ $[1]$ $[2]$ $[1]$ $[\ ]$ $[\ ]$ $t + 14$ $x^{17} + 272 x^{16} + 1173$ $[16, 0]$ $[1]$ $z^{16} + 16$ undefined
17.1.17.32a16.6 $x^{17} + 272 x^{16} + 1462$ $17$ $1$ $17$ $32$ $C_{17}$ (as 17T1) $1$ $1$ $[2]$ $[1]$ $[2]$ $[1]$ $[\ ]$ $[\ ]$ $t + 14$ $x^{17} + 272 x^{16} + 1462$ $[16, 0]$ $[1]$ $z^{16} + 16$ undefined
17.1.17.32a16.7 $x^{17} + 272 x^{16} + 1751$ $17$ $1$ $17$ $32$ $C_{17}$ (as 17T1) $1$ $1$ $[2]$ $[1]$ $[2]$ $[1]$ $[\ ]$ $[\ ]$ $t + 14$ $x^{17} + 272 x^{16} + 1751$ $[16, 0]$ $[1]$ $z^{16} + 16$ undefined
17.1.17.32a16.8 $x^{17} + 272 x^{16} + 2040$ $17$ $1$ $17$ $32$ $C_{17}$ (as 17T1) $1$ $1$ $[2]$ $[1]$ $[2]$ $[1]$ $[\ ]$ $[\ ]$ $t + 14$ $x^{17} + 272 x^{16} + 2040$ $[16, 0]$ $[1]$ $z^{16} + 16$ undefined
17.1.17.32a16.9 $x^{17} + 272 x^{16} + 2329$ $17$ $1$ $17$ $32$ $C_{17}$ (as 17T1) $1$ $1$ $[2]$ $[1]$ $[2]$ $[1]$ $[\ ]$ $[\ ]$ $t + 14$ $x^{17} + 272 x^{16} + 2329$ $[16, 0]$ $[1]$ $z^{16} + 16$ undefined
17.1.17.32a16.10 $x^{17} + 272 x^{16} + 2618$ $17$ $1$ $17$ $32$ $C_{17}$ (as 17T1) $1$ $1$ $[2]$ $[1]$ $[2]$ $[1]$ $[\ ]$ $[\ ]$ $t + 14$ $x^{17} + 272 x^{16} + 2618$ $[16, 0]$ $[1]$ $z^{16} + 16$ undefined
17.1.17.32a16.11 $x^{17} + 272 x^{16} + 2907$ $17$ $1$ $17$ $32$ $C_{17}$ (as 17T1) $1$ $1$ $[2]$ $[1]$ $[2]$ $[1]$ $[\ ]$ $[\ ]$ $t + 14$ $x^{17} + 272 x^{16} + 2907$ $[16, 0]$ $[1]$ $z^{16} + 16$ undefined
17.1.17.32a16.12 $x^{17} + 272 x^{16} + 3196$ $17$ $1$ $17$ $32$ $C_{17}$ (as 17T1) $1$ $1$ $[2]$ $[1]$ $[2]$ $[1]$ $[\ ]$ $[\ ]$ $t + 14$ $x^{17} + 272 x^{16} + 3196$ $[16, 0]$ $[1]$ $z^{16} + 16$ undefined
17.1.17.32a16.13 $x^{17} + 272 x^{16} + 3485$ $17$ $1$ $17$ $32$ $C_{17}$ (as 17T1) $1$ $1$ $[2]$ $[1]$ $[2]$ $[1]$ $[\ ]$ $[\ ]$ $t + 14$ $x^{17} + 272 x^{16} + 3485$ $[16, 0]$ $[1]$ $z^{16} + 16$ undefined
17.1.17.32a16.14 $x^{17} + 272 x^{16} + 3774$ $17$ $1$ $17$ $32$ $C_{17}$ (as 17T1) $1$ $1$ $[2]$ $[1]$ $[2]$ $[1]$ $[\ ]$ $[\ ]$ $t + 14$ $x^{17} + 272 x^{16} + 3774$ $[16, 0]$ $[1]$ $z^{16} + 16$ undefined
17.1.17.32a16.15 $x^{17} + 272 x^{16} + 4063$ $17$ $1$ $17$ $32$ $C_{17}$ (as 17T1) $1$ $1$ $[2]$ $[1]$ $[2]$ $[1]$ $[\ ]$ $[\ ]$ $t + 14$ $x^{17} + 272 x^{16} + 4063$ $[16, 0]$ $[1]$ $z^{16} + 16$ undefined
17.1.17.32a16.16 $x^{17} + 272 x^{16} + 4352$ $17$ $1$ $17$ $32$ $C_{17}$ (as 17T1) $1$ $1$ $[2]$ $[1]$ $[2]$ $[1]$ $[\ ]$ $[\ ]$ $t + 14$ $x^{17} + 272 x^{16} + 4352$ $[16, 0]$ $[1]$ $z^{16} + 16$ undefined
17.1.17.32a16.17 $x^{17} + 272 x^{16} + 4641$ $17$ $1$ $17$ $32$ $C_{17}$ (as 17T1) $1$ $1$ $[2]$ $[1]$ $[2]$ $[1]$ $[\ ]$ $[\ ]$ $t + 14$ $x^{17} + 272 x^{16} + 4641$ $[16, 0]$ $[1]$ $z^{16} + 16$ undefined
19.17.1.0a1.1 $x^{17} + 2 x + 17$ $19$ $17$ $1$ $0$ $C_{17}$ (as 17T1) $17$ $1$ $[\ ]$ $[\ ]$ $[\ ]^{17}$ $[\ ]^{17}$ $[\ ]$ $[\ ]$ $t^{17} + 2 t + 17$ $x - 19$ $[0]$ $[\ ]$ undefined
23.17.1.0a1.1 $x^{17} + 20 x + 18$ $23$ $17$ $1$ $0$ $C_{17}$ (as 17T1) $17$ $1$ $[\ ]$ $[\ ]$ $[\ ]^{17}$ $[\ ]^{17}$ $[\ ]$ $[\ ]$ $t^{17} + 20 t + 18$ $x - 23$ $[0]$ $[\ ]$ undefined
29.17.1.0a1.1 $x^{17} + 2 x + 27$ $29$ $17$ $1$ $0$ $C_{17}$ (as 17T1) $17$ $1$ $[\ ]$ $[\ ]$ $[\ ]^{17}$ $[\ ]^{17}$ $[\ ]$ $[\ ]$ $t^{17} + 2 t + 27$ $x - 29$ $[0]$ $[\ ]$ undefined
31.17.1.0a1.1 $x^{17} + 10 x + 28$ $31$ $17$ $1$ $0$ $C_{17}$ (as 17T1) $17$ $1$ $[\ ]$ $[\ ]$ $[\ ]^{17}$ $[\ ]^{17}$ $[\ ]$ $[\ ]$ $t^{17} + 10 t + 28$ $x - 31$ $[0]$ $[\ ]$ undefined
37.17.1.0a1.1 $x^{17} + 3 x + 35$ $37$ $17$ $1$ $0$ $C_{17}$ (as 17T1) $17$ $1$ $[\ ]$ $[\ ]$ $[\ ]^{17}$ $[\ ]^{17}$ $[\ ]$ $[\ ]$ $t^{17} + 3 t + 35$ $x - 37$ $[0]$ $[\ ]$ undefined
41.17.1.0a1.1 $x^{17} + 4 x + 35$ $41$ $17$ $1$ $0$ $C_{17}$ (as 17T1) $17$ $1$ $[\ ]$ $[\ ]$ $[\ ]^{17}$ $[\ ]^{17}$ $[\ ]$ $[\ ]$ $t^{17} + 4 t + 35$ $x - 41$ $[0]$ $[\ ]$ undefined
43.17.1.0a1.1 $x^{17} + 36 x + 40$ $43$ $17$ $1$ $0$ $C_{17}$ (as 17T1) $17$ $1$ $[\ ]$ $[\ ]$ $[\ ]^{17}$ $[\ ]^{17}$ $[\ ]$ $[\ ]$ $t^{17} + 36 t + 40$ $x - 43$ $[0]$ $[\ ]$ undefined
47.17.1.0a1.1 $x^{17} + 16 x + 42$ $47$ $17$ $1$ $0$ $C_{17}$ (as 17T1) $17$ $1$ $[\ ]$ $[\ ]$ $[\ ]^{17}$ $[\ ]^{17}$ $[\ ]$ $[\ ]$ $t^{17} + 16 t + 42$ $x - 47$ $[0]$ $[\ ]$ undefined
53.17.1.0a1.1 $x^{17} + 12 x + 51$ $53$ $17$ $1$ $0$ $C_{17}$ (as 17T1) $17$ $1$ $[\ ]$ $[\ ]$ $[\ ]^{17}$ $[\ ]^{17}$ $[\ ]$ $[\ ]$ $t^{17} + 12 t + 51$ $x - 53$ $[0]$ $[\ ]$ undefined
59.17.1.0a1.1 $x^{17} + 9 x + 57$ $59$ $17$ $1$ $0$ $C_{17}$ (as 17T1) $17$ $1$ $[\ ]$ $[\ ]$ $[\ ]^{17}$ $[\ ]^{17}$ $[\ ]$ $[\ ]$ $t^{17} + 9 t + 57$ $x - 59$ $[0]$ $[\ ]$ undefined
61.17.1.0a1.1 $x^{17} + 10 x + 59$ $61$ $17$ $1$ $0$ $C_{17}$ (as 17T1) $17$ $1$ $[\ ]$ $[\ ]$ $[\ ]^{17}$ $[\ ]^{17}$ $[\ ]$ $[\ ]$ $t^{17} + 10 t + 59$ $x - 61$ $[0]$ $[\ ]$ undefined
67.17.1.0a1.1 $x^{17} + 5 x + 65$ $67$ $17$ $1$ $0$ $C_{17}$ (as 17T1) $17$ $1$ $[\ ]$ $[\ ]$ $[\ ]^{17}$ $[\ ]^{17}$ $[\ ]$ $[\ ]$ $t^{17} + 5 t + 65$ $x - 67$ $[0]$ $[\ ]$ undefined
71.17.1.0a1.1 $x^{17} + 3 x + 64$ $71$ $17$ $1$ $0$ $C_{17}$ (as 17T1) $17$ $1$ $[\ ]$ $[\ ]$ $[\ ]^{17}$ $[\ ]^{17}$ $[\ ]$ $[\ ]$ $t^{17} + 3 t + 64$ $x - 71$ $[0]$ $[\ ]$ undefined
73.17.1.0a1.1 $x^{17} + 8 x + 68$ $73$ $17$ $1$ $0$ $C_{17}$ (as 17T1) $17$ $1$ $[\ ]$ $[\ ]$ $[\ ]^{17}$ $[\ ]^{17}$ $[\ ]$ $[\ ]$ $t^{17} + 8 t + 68$ $x - 73$ $[0]$ $[\ ]$ undefined
79.17.1.0a1.1 $x^{17} + 25 x + 76$ $79$ $17$ $1$ $0$ $C_{17}$ (as 17T1) $17$ $1$ $[\ ]$ $[\ ]$ $[\ ]^{17}$ $[\ ]^{17}$ $[\ ]$ $[\ ]$ $t^{17} + 25 t + 76$ $x - 79$ $[0]$ $[\ ]$ undefined
83.17.1.0a1.1 $x^{17} + 7 x + 81$ $83$ $17$ $1$ $0$ $C_{17}$ (as 17T1) $17$ $1$ $[\ ]$ $[\ ]$ $[\ ]^{17}$ $[\ ]^{17}$ $[\ ]$ $[\ ]$ $t^{17} + 7 t + 81$ $x - 83$ $[0]$ $[\ ]$ undefined
89.17.1.0a1.1 $x^{17} + 20 x + 86$ $89$ $17$ $1$ $0$ $C_{17}$ (as 17T1) $17$ $1$ $[\ ]$ $[\ ]$ $[\ ]^{17}$ $[\ ]^{17}$ $[\ ]$ $[\ ]$ $t^{17} + 20 t + 86$ $x - 89$ $[0]$ $[\ ]$ undefined
97.17.1.0a1.1 $x^{17} + 5 x + 92$ $97$ $17$ $1$ $0$ $C_{17}$ (as 17T1) $17$ $1$ $[\ ]$ $[\ ]$ $[\ ]^{17}$ $[\ ]^{17}$ $[\ ]$ $[\ ]$ $t^{17} + 5 t + 92$ $x - 97$ $[0]$ $[\ ]$ undefined
101.17.1.0a1.1 $x^{17} + 31 x + 99$ $101$ $17$ $1$ $0$ $C_{17}$ (as 17T1) $17$ $1$ $[\ ]$ $[\ ]$ $[\ ]^{17}$ $[\ ]^{17}$ $[\ ]$ $[\ ]$ $t^{17} + 31 t + 99$ $x - 101$ $[0]$ $[\ ]$ undefined
103.17.1.0a1.1 $x^{17} + 102 x^{2} + 8 x + 98$ $103$ $17$ $1$ $0$ $C_{17}$ (as 17T1) $17$ $1$ $[\ ]$ $[\ ]$ $[\ ]^{17}$ $[\ ]^{17}$ $[\ ]$ $[\ ]$ $t^{17} + 102 t^{2} + 8 t + 98$ $x - 103$ $[0]$ $[\ ]$ undefined
103.1.17.16a1.1 $x^{17} + 103$ $103$ $1$ $17$ $16$ $C_{17}$ (as 17T1) $1$ $17$ $[\ ]$ $[\ ]$ $[\ ]_{17}$ $[\ ]_{17}$ $[\ ]$ $[\ ]$ $t + 98$ $x^{17} + 103$ $[0]$ $[1]$ $z^{16} + 17 z^{15} + 33 z^{14} + 62 z^{13} + 11 z^{12} + 8 z^{11} + 16 z^{10} + 84 z^9 + 2 z^8 + 2 z^7 + 84 z^6 + 16 z^5 + 8 z^4 + 11 z^3 + 62 z^2 + 33 z + 17$ undefined
103.1.17.16a1.2 $x^{17} + 515$ $103$ $1$ $17$ $16$ $C_{17}$ (as 17T1) $1$ $17$ $[\ ]$ $[\ ]$ $[\ ]_{17}$ $[\ ]_{17}$ $[\ ]$ $[\ ]$ $t + 98$ $x^{17} + 515$ $[0]$ $[1]$ $z^{16} + 17 z^{15} + 33 z^{14} + 62 z^{13} + 11 z^{12} + 8 z^{11} + 16 z^{10} + 84 z^9 + 2 z^8 + 2 z^7 + 84 z^6 + 16 z^5 + 8 z^4 + 11 z^3 + 62 z^2 + 33 z + 17$ undefined
103.1.17.16a1.3 $x^{17} + 721$ $103$ $1$ $17$ $16$ $C_{17}$ (as 17T1) $1$ $17$ $[\ ]$ $[\ ]$ $[\ ]_{17}$ $[\ ]_{17}$ $[\ ]$ $[\ ]$ $t + 98$ $x^{17} + 721$ $[0]$ $[1]$ $z^{16} + 17 z^{15} + 33 z^{14} + 62 z^{13} + 11 z^{12} + 8 z^{11} + 16 z^{10} + 84 z^9 + 2 z^8 + 2 z^7 + 84 z^6 + 16 z^5 + 8 z^4 + 11 z^3 + 62 z^2 + 33 z + 17$ undefined
103.1.17.16a1.4 $x^{17} + 2266$ $103$ $1$ $17$ $16$ $C_{17}$ (as 17T1) $1$ $17$ $[\ ]$ $[\ ]$ $[\ ]_{17}$ $[\ ]_{17}$ $[\ ]$ $[\ ]$ $t + 98$ $x^{17} + 2266$ $[0]$ $[1]$ $z^{16} + 17 z^{15} + 33 z^{14} + 62 z^{13} + 11 z^{12} + 8 z^{11} + 16 z^{10} + 84 z^9 + 2 z^8 + 2 z^7 + 84 z^6 + 16 z^5 + 8 z^4 + 11 z^3 + 62 z^2 + 33 z + 17$ undefined
103.1.17.16a1.5 $x^{17} + 2575$ $103$ $1$ $17$ $16$ $C_{17}$ (as 17T1) $1$ $17$ $[\ ]$ $[\ ]$ $[\ ]_{17}$ $[\ ]_{17}$ $[\ ]$ $[\ ]$ $t + 98$ $x^{17} + 2575$ $[0]$ $[1]$ $z^{16} + 17 z^{15} + 33 z^{14} + 62 z^{13} + 11 z^{12} + 8 z^{11} + 16 z^{10} + 84 z^9 + 2 z^8 + 2 z^7 + 84 z^6 + 16 z^5 + 8 z^4 + 11 z^3 + 62 z^2 + 33 z + 17$ undefined
103.1.17.16a1.6 $x^{17} + 2678$ $103$ $1$ $17$ $16$ $C_{17}$ (as 17T1) $1$ $17$ $[\ ]$ $[\ ]$ $[\ ]_{17}$ $[\ ]_{17}$ $[\ ]$ $[\ ]$ $t + 98$ $x^{17} + 2678$ $[0]$ $[1]$ $z^{16} + 17 z^{15} + 33 z^{14} + 62 z^{13} + 11 z^{12} + 8 z^{11} + 16 z^{10} + 84 z^9 + 2 z^8 + 2 z^7 + 84 z^6 + 16 z^5 + 8 z^4 + 11 z^3 + 62 z^2 + 33 z + 17$ undefined
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