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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 (24 matches)

  displayed columns for results
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
3.1.20.19a1.1 $x^{20} + 3$ $3$ $1$ $20$ $19$ $C_{20}:C_4$ (as 20T18) $4$ $20$ $[\ ]$ $[\ ]$ $[\ ]_{20}^{4}$ $[\ ]_{20}^{4}$ $[\ ]^{4}$ $[\ ]^{4}$ $t + 1$ $x^{20} + 3$ $[0]$ $[4]$ $z^{19} + 2 z^{18} + z^{17} + 2 z^{10} + z^9 + 2 z^8 + z + 2$ $[10]$
3.1.20.19a1.2 $x^{20} + 6$ $3$ $1$ $20$ $19$ $C_{20}:C_4$ (as 20T18) $4$ $20$ $[\ ]$ $[\ ]$ $[\ ]_{20}^{4}$ $[\ ]_{20}^{4}$ $[\ ]^{4}$ $[\ ]^{4}$ $t + 1$ $x^{20} + 6$ $[0]$ $[4]$ $z^{19} + 2 z^{18} + z^{17} + 2 z^{10} + z^9 + 2 z^8 + z + 2$ undefined
7.1.20.19a1.1 $x^{20} + 7$ $7$ $1$ $20$ $19$ $C_{20}:C_4$ (as 20T18) $4$ $20$ $[\ ]$ $[\ ]$ $[\ ]_{20}^{4}$ $[\ ]_{20}^{4}$ $[\ ]^{4}$ $[\ ]^{4}$ $t + 4$ $x^{20} + 7$ $[0]$ $[4]$ $z^{19} + 6 z^{18} + z^{17} + 6 z^{16} + z^{15} + 6 z^{14} + z^{13} + 2 z^{12} + 5 z^{11} + 2 z^{10} + 5 z^9 + 2 z^8 + 5 z^7 + 2 z^6 + z^5 + 6 z^4 + z^3 + 6 z^2 + z + 6$ undefined
7.1.20.19a1.2 $x^{20} + 21$ $7$ $1$ $20$ $19$ $C_{20}:C_4$ (as 20T18) $4$ $20$ $[\ ]$ $[\ ]$ $[\ ]_{20}^{4}$ $[\ ]_{20}^{4}$ $[\ ]^{4}$ $[\ ]^{4}$ $t + 4$ $x^{20} + 21$ $[0]$ $[4]$ $z^{19} + 6 z^{18} + z^{17} + 6 z^{16} + z^{15} + 6 z^{14} + z^{13} + 2 z^{12} + 5 z^{11} + 2 z^{10} + 5 z^9 + 2 z^8 + 5 z^7 + 2 z^6 + z^5 + 6 z^4 + z^3 + 6 z^2 + z + 6$ undefined
23.1.20.19a1.1 $x^{20} + 23$ $23$ $1$ $20$ $19$ $C_{20}:C_4$ (as 20T18) $4$ $20$ $[\ ]$ $[\ ]$ $[\ ]_{20}^{4}$ $[\ ]_{20}^{4}$ $[\ ]^{4}$ $[\ ]^{4}$ $t + 18$ $x^{20} + 23$ $[0]$ $[4]$ $z^{19} + 20 z^{18} + 6 z^{17} + 13 z^{16} + 15 z^{15} + 2 z^{14} + 5 z^{13} + 10 z^{12} + 22 z^{11} + 14 z^{10} + 20 z^9 + 14 z^8 + 22 z^7 + 10 z^6 + 5 z^5 + 2 z^4 + 15 z^3 + 13 z^2 + 6 z + 20$ undefined
23.1.20.19a1.2 $x^{20} + 115$ $23$ $1$ $20$ $19$ $C_{20}:C_4$ (as 20T18) $4$ $20$ $[\ ]$ $[\ ]$ $[\ ]_{20}^{4}$ $[\ ]_{20}^{4}$ $[\ ]^{4}$ $[\ ]^{4}$ $t + 18$ $x^{20} + 115$ $[0]$ $[4]$ $z^{19} + 20 z^{18} + 6 z^{17} + 13 z^{16} + 15 z^{15} + 2 z^{14} + 5 z^{13} + 10 z^{12} + 22 z^{11} + 14 z^{10} + 20 z^9 + 14 z^8 + 22 z^7 + 10 z^6 + 5 z^5 + 2 z^4 + 15 z^3 + 13 z^2 + 6 z + 20$ undefined
43.1.20.19a1.1 $x^{20} + 43$ $43$ $1$ $20$ $19$ $C_{20}:C_4$ (as 20T18) $4$ $20$ $[\ ]$ $[\ ]$ $[\ ]_{20}^{4}$ $[\ ]_{20}^{4}$ $[\ ]^{4}$ $[\ ]^{4}$ $t + 40$ $x^{20} + 43$ $[0]$ $[4]$ $z^{19} + 20 z^{18} + 18 z^{17} + 22 z^{16} + 29 z^{15} + 24 z^{14} + 17 z^{13} + 34 z^{12} + 23 z^{11} + 2 z^{10} + 28 z^9 + 2 z^8 + 23 z^7 + 34 z^6 + 17 z^5 + 24 z^4 + 29 z^3 + 22 z^2 + 18 z + 20$ undefined
43.1.20.19a1.2 $x^{20} + 129$ $43$ $1$ $20$ $19$ $C_{20}:C_4$ (as 20T18) $4$ $20$ $[\ ]$ $[\ ]$ $[\ ]_{20}^{4}$ $[\ ]_{20}^{4}$ $[\ ]^{4}$ $[\ ]^{4}$ $t + 40$ $x^{20} + 129$ $[0]$ $[4]$ $z^{19} + 20 z^{18} + 18 z^{17} + 22 z^{16} + 29 z^{15} + 24 z^{14} + 17 z^{13} + 34 z^{12} + 23 z^{11} + 2 z^{10} + 28 z^9 + 2 z^8 + 23 z^7 + 34 z^6 + 17 z^5 + 24 z^4 + 29 z^3 + 22 z^2 + 18 z + 20$ undefined
47.1.20.19a1.1 $x^{20} + 47$ $47$ $1$ $20$ $19$ $C_{20}:C_4$ (as 20T18) $4$ $20$ $[\ ]$ $[\ ]$ $[\ ]_{20}^{4}$ $[\ ]_{20}^{4}$ $[\ ]^{4}$ $[\ ]^{4}$ $t + 42$ $x^{20} + 47$ $[0]$ $[4]$ $z^{19} + 20 z^{18} + 2 z^{17} + 12 z^{16} + 4 z^{15} + 41 z^{14} + 32 z^{13} + 17 z^{12} + 10 z^{11} + 29 z^{10} + 46 z^9 + 29 z^8 + 10 z^7 + 17 z^6 + 32 z^5 + 41 z^4 + 4 z^3 + 12 z^2 + 2 z + 20$ undefined
47.1.20.19a1.2 $x^{20} + 235$ $47$ $1$ $20$ $19$ $C_{20}:C_4$ (as 20T18) $4$ $20$ $[\ ]$ $[\ ]$ $[\ ]_{20}^{4}$ $[\ ]_{20}^{4}$ $[\ ]^{4}$ $[\ ]^{4}$ $t + 42$ $x^{20} + 235$ $[0]$ $[4]$ $z^{19} + 20 z^{18} + 2 z^{17} + 12 z^{16} + 4 z^{15} + 41 z^{14} + 32 z^{13} + 17 z^{12} + 10 z^{11} + 29 z^{10} + 46 z^9 + 29 z^8 + 10 z^7 + 17 z^6 + 32 z^5 + 41 z^4 + 4 z^3 + 12 z^2 + 2 z + 20$ undefined
67.1.20.19a1.1 $x^{20} + 67$ $67$ $1$ $20$ $19$ $C_{20}:C_4$ (as 20T18) $4$ $20$ $[\ ]$ $[\ ]$ $[\ ]_{20}^{4}$ $[\ ]_{20}^{4}$ $[\ ]^{4}$ $[\ ]^{4}$ $t + 65$ $x^{20} + 67$ $[0]$ $[4]$ $z^{19} + 20 z^{18} + 56 z^{17} + z^{16} + 21 z^{15} + 27 z^{14} + 34 z^{13} + z^{12} + 10 z^{11} + 58 z^{10} + 37 z^9 + 58 z^8 + 10 z^7 + z^6 + 34 z^5 + 27 z^4 + 21 z^3 + z^2 + 56 z + 20$ undefined
67.1.20.19a1.2 $x^{20} + 134$ $67$ $1$ $20$ $19$ $C_{20}:C_4$ (as 20T18) $4$ $20$ $[\ ]$ $[\ ]$ $[\ ]_{20}^{4}$ $[\ ]_{20}^{4}$ $[\ ]^{4}$ $[\ ]^{4}$ $t + 65$ $x^{20} + 134$ $[0]$ $[4]$ $z^{19} + 20 z^{18} + 56 z^{17} + z^{16} + 21 z^{15} + 27 z^{14} + 34 z^{13} + z^{12} + 10 z^{11} + 58 z^{10} + 37 z^9 + 58 z^8 + 10 z^7 + z^6 + 34 z^5 + 27 z^4 + 21 z^3 + z^2 + 56 z + 20$ undefined
83.1.20.19a1.1 $x^{20} + 83$ $83$ $1$ $20$ $19$ $C_{20}:C_4$ (as 20T18) $4$ $20$ $[\ ]$ $[\ ]$ $[\ ]_{20}^{4}$ $[\ ]_{20}^{4}$ $[\ ]^{4}$ $[\ ]^{4}$ $t + 81$ $x^{20} + 83$ $[0]$ $[4]$ $z^{19} + 20 z^{18} + 24 z^{17} + 61 z^{16} + 31 z^{15} + 66 z^{14} + 82 z^{13} + 81 z^{12} + 59 z^{11} + 51 z^{10} + 81 z^9 + 51 z^8 + 59 z^7 + 81 z^6 + 82 z^5 + 66 z^4 + 31 z^3 + 61 z^2 + 24 z + 20$ undefined
83.1.20.19a1.2 $x^{20} + 166$ $83$ $1$ $20$ $19$ $C_{20}:C_4$ (as 20T18) $4$ $20$ $[\ ]$ $[\ ]$ $[\ ]_{20}^{4}$ $[\ ]_{20}^{4}$ $[\ ]^{4}$ $[\ ]^{4}$ $t + 81$ $x^{20} + 166$ $[0]$ $[4]$ $z^{19} + 20 z^{18} + 24 z^{17} + 61 z^{16} + 31 z^{15} + 66 z^{14} + 82 z^{13} + 81 z^{12} + 59 z^{11} + 51 z^{10} + 81 z^9 + 51 z^8 + 59 z^7 + 81 z^6 + 82 z^5 + 66 z^4 + 31 z^3 + 61 z^2 + 24 z + 20$ undefined
103.1.20.19a1.1 $x^{20} + 103$ $103$ $1$ $20$ $19$ $C_{20}:C_4$ (as 20T18) $4$ $20$ $[\ ]$ $[\ ]$ $[\ ]_{20}^{4}$ $[\ ]_{20}^{4}$ $[\ ]^{4}$ $[\ ]^{4}$ $t + 98$ $x^{20} + 103$ $[0]$ $[4]$ $z^{19} + 20 z^{18} + 87 z^{17} + 7 z^{16} + 4 z^{15} + 54 z^{14} + 32 z^{13} + 64 z^{12} + z^{11} + 70 z^{10} + 77 z^9 + 70 z^8 + z^7 + 64 z^6 + 32 z^5 + 54 z^4 + 4 z^3 + 7 z^2 + 87 z + 20$ undefined
103.1.20.19a1.2 $x^{20} + 515$ $103$ $1$ $20$ $19$ $C_{20}:C_4$ (as 20T18) $4$ $20$ $[\ ]$ $[\ ]$ $[\ ]_{20}^{4}$ $[\ ]_{20}^{4}$ $[\ ]^{4}$ $[\ ]^{4}$ $t + 98$ $x^{20} + 515$ $[0]$ $[4]$ $z^{19} + 20 z^{18} + 87 z^{17} + 7 z^{16} + 4 z^{15} + 54 z^{14} + 32 z^{13} + 64 z^{12} + z^{11} + 70 z^{10} + 77 z^9 + 70 z^8 + z^7 + 64 z^6 + 32 z^5 + 54 z^4 + 4 z^3 + 7 z^2 + 87 z + 20$ undefined
107.1.20.19a1.1 $x^{20} + 107$ $107$ $1$ $20$ $19$ $C_{20}:C_4$ (as 20T18) $4$ $20$ $[\ ]$ $[\ ]$ $[\ ]_{20}^{4}$ $[\ ]_{20}^{4}$ $[\ ]^{4}$ $[\ ]^{4}$ $t + 105$ $x^{20} + 107$ $[0]$ $[4]$ $z^{19} + 20 z^{18} + 83 z^{17} + 70 z^{16} + 30 z^{15} + 96 z^{14} + 26 z^{13} + 52 z^{12} + 31 z^{11} + 77 z^{10} + 74 z^9 + 77 z^8 + 31 z^7 + 52 z^6 + 26 z^5 + 96 z^4 + 30 z^3 + 70 z^2 + 83 z + 20$ undefined
107.1.20.19a1.2 $x^{20} + 214$ $107$ $1$ $20$ $19$ $C_{20}:C_4$ (as 20T18) $4$ $20$ $[\ ]$ $[\ ]$ $[\ ]_{20}^{4}$ $[\ ]_{20}^{4}$ $[\ ]^{4}$ $[\ ]^{4}$ $t + 105$ $x^{20} + 214$ $[0]$ $[4]$ $z^{19} + 20 z^{18} + 83 z^{17} + 70 z^{16} + 30 z^{15} + 96 z^{14} + 26 z^{13} + 52 z^{12} + 31 z^{11} + 77 z^{10} + 74 z^9 + 77 z^8 + 31 z^7 + 52 z^6 + 26 z^5 + 96 z^4 + 30 z^3 + 70 z^2 + 83 z + 20$ undefined
127.1.20.19a1.1 $x^{20} + 127$ $127$ $1$ $20$ $19$ $C_{20}:C_4$ (as 20T18) $4$ $20$ $[\ ]$ $[\ ]$ $[\ ]_{20}^{4}$ $[\ ]_{20}^{4}$ $[\ ]^{4}$ $[\ ]^{4}$ $t + 124$ $x^{20} + 127$ $[0]$ $[4]$ $z^{19} + 20 z^{18} + 63 z^{17} + 124 z^{16} + 19 z^{15} + 10 z^{14} + 25 z^{13} + 50 z^{12} + 113 z^{11} + 66 z^{10} + 98 z^9 + 66 z^8 + 113 z^7 + 50 z^6 + 25 z^5 + 10 z^4 + 19 z^3 + 124 z^2 + 63 z + 20$ undefined
127.1.20.19a1.2 $x^{20} + 381$ $127$ $1$ $20$ $19$ $C_{20}:C_4$ (as 20T18) $4$ $20$ $[\ ]$ $[\ ]$ $[\ ]_{20}^{4}$ $[\ ]_{20}^{4}$ $[\ ]^{4}$ $[\ ]^{4}$ $t + 124$ $x^{20} + 381$ $[0]$ $[4]$ $z^{19} + 20 z^{18} + 63 z^{17} + 124 z^{16} + 19 z^{15} + 10 z^{14} + 25 z^{13} + 50 z^{12} + 113 z^{11} + 66 z^{10} + 98 z^9 + 66 z^8 + 113 z^7 + 50 z^6 + 25 z^5 + 10 z^4 + 19 z^3 + 124 z^2 + 63 z + 20$ undefined
163.1.20.19a1.1 $x^{20} + 163$ $163$ $1$ $20$ $19$ $C_{20}:C_4$ (as 20T18) $4$ $20$ $[\ ]$ $[\ ]$ $[\ ]_{20}^{4}$ $[\ ]_{20}^{4}$ $[\ ]^{4}$ $[\ ]^{4}$ $t + 161$ $x^{20} + 163$ $[0]$ $[4]$ $z^{19} + 20 z^{18} + 27 z^{17} + 162 z^{16} + 118 z^{15} + 19 z^{14} + 129 z^{13} + 95 z^{12} + 134 z^{11} + 70 z^{10} + 77 z^9 + 70 z^8 + 134 z^7 + 95 z^6 + 129 z^5 + 19 z^4 + 118 z^3 + 162 z^2 + 27 z + 20$ undefined
163.1.20.19a1.2 $x^{20} + 326$ $163$ $1$ $20$ $19$ $C_{20}:C_4$ (as 20T18) $4$ $20$ $[\ ]$ $[\ ]$ $[\ ]_{20}^{4}$ $[\ ]_{20}^{4}$ $[\ ]^{4}$ $[\ ]^{4}$ $t + 161$ $x^{20} + 326$ $[0]$ $[4]$ $z^{19} + 20 z^{18} + 27 z^{17} + 162 z^{16} + 118 z^{15} + 19 z^{14} + 129 z^{13} + 95 z^{12} + 134 z^{11} + 70 z^{10} + 77 z^9 + 70 z^8 + 134 z^7 + 95 z^6 + 129 z^5 + 19 z^4 + 118 z^3 + 162 z^2 + 27 z + 20$ undefined
167.1.20.19a1.1 $x^{20} + 167$ $167$ $1$ $20$ $19$ $C_{20}:C_4$ (as 20T18) $4$ $20$ $[\ ]$ $[\ ]$ $[\ ]_{20}^{4}$ $[\ ]_{20}^{4}$ $[\ ]^{4}$ $[\ ]^{4}$ $t + 162$ $x^{20} + 167$ $[0]$ $[4]$ $z^{19} + 20 z^{18} + 23 z^{17} + 138 z^{16} + 2 z^{15} + 140 z^{14} + 16 z^{13} + 32 z^{12} + 52 z^{11} + 125 z^{10} + 54 z^9 + 125 z^8 + 52 z^7 + 32 z^6 + 16 z^5 + 140 z^4 + 2 z^3 + 138 z^2 + 23 z + 20$ undefined
167.1.20.19a1.2 $x^{20} + 835$ $167$ $1$ $20$ $19$ $C_{20}:C_4$ (as 20T18) $4$ $20$ $[\ ]$ $[\ ]$ $[\ ]_{20}^{4}$ $[\ ]_{20}^{4}$ $[\ ]^{4}$ $[\ ]^{4}$ $t + 162$ $x^{20} + 835$ $[0]$ $[4]$ $z^{19} + 20 z^{18} + 23 z^{17} + 138 z^{16} + 2 z^{15} + 140 z^{14} + 16 z^{13} + 32 z^{12} + 52 z^{11} + 125 z^{10} + 54 z^9 + 125 z^8 + 52 z^7 + 32 z^6 + 16 z^5 + 140 z^4 + 2 z^3 + 138 z^2 + 23 z + 20$ undefined
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