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Degree $n$ Residue characteristic $p$ Discriminant exponent $c$ Galois group Num. automorphisms
Ramification index $e$ Residue field degree $f$ Galois tame degree $t$ Galois unram. degree $u$ Intermediate field
Inertia subgroup Indices Assoc. Inertia Jump Set
Top Artin slope Galois Artin Visible Artin Wild inertia subgroup
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Results (41 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
3.1.11.10a1.1 $x^{11} + 3$ $3$ $1$ $11$ $10$ $C_{11}:C_5$ (as 11T3) $5$ $11$ $[\ ]$ $[\ ]$ $[\ ]_{11}^{5}$ $[\ ]_{11}^{5}$ $[\ ]^{5}$ $[\ ]^{5}$ $t + 1$ $x^{11} + 3$ $[0]$ $[5]$ $z^{10} + 2 z^9 + z^8 + z + 2$ undefined
5.1.11.10a1.1 $x^{11} + 5$ $5$ $1$ $11$ $10$ $C_{11}:C_5$ (as 11T3) $5$ $11$ $[\ ]$ $[\ ]$ $[\ ]_{11}^{5}$ $[\ ]_{11}^{5}$ $[\ ]^{5}$ $[\ ]^{5}$ $t + 3$ $x^{11} + 5$ $[0]$ $[5]$ $z^{10} + z^9 + 2 z^5 + 2 z^4 + 1$ undefined
11.1.11.12a2.1 $x^{11} + 22 x^{2} + 11$ $11$ $1$ $11$ $12$ $C_{11}:C_5$ (as 11T3) $1$ $5$ $[\frac{6}{5}]$ $[\frac{1}{5}]$ $[\frac{6}{5}]_{5}$ $[\frac{1}{5}]_{5}$ $[\ ]_{5}$ $[\ ]_{5}$ $t + 9$ $x^{11} + 22 x^{2} + 11$ $[2, 0]$ $[1]$ $z^2 + 2$ undefined
11.1.11.12a2.2 $x^{11} + 66 x^{2} + 11$ $11$ $1$ $11$ $12$ $C_{11}:C_5$ (as 11T3) $1$ $5$ $[\frac{6}{5}]$ $[\frac{1}{5}]$ $[\frac{6}{5}]_{5}$ $[\frac{1}{5}]_{5}$ $[\ ]_{5}$ $[\ ]_{5}$ $t + 9$ $x^{11} + 66 x^{2} + 11$ $[2, 0]$ $[1]$ $z^2 + 2$ undefined
11.1.11.12a2.3 $x^{11} + 77 x^{2} + 11$ $11$ $1$ $11$ $12$ $C_{11}:C_5$ (as 11T3) $1$ $5$ $[\frac{6}{5}]$ $[\frac{1}{5}]$ $[\frac{6}{5}]_{5}$ $[\frac{1}{5}]_{5}$ $[\ ]_{5}$ $[\ ]_{5}$ $t + 9$ $x^{11} + 77 x^{2} + 11$ $[2, 0]$ $[1]$ $z^2 + 2$ undefined
11.1.11.12a2.4 $x^{11} + 88 x^{2} + 11$ $11$ $1$ $11$ $12$ $C_{11}:C_5$ (as 11T3) $1$ $5$ $[\frac{6}{5}]$ $[\frac{1}{5}]$ $[\frac{6}{5}]_{5}$ $[\frac{1}{5}]_{5}$ $[\ ]_{5}$ $[\ ]_{5}$ $t + 9$ $x^{11} + 88 x^{2} + 11$ $[2, 0]$ $[1]$ $z^2 + 2$ undefined
11.1.11.12a2.5 $x^{11} + 110 x^{2} + 11$ $11$ $1$ $11$ $12$ $C_{11}:C_5$ (as 11T3) $1$ $5$ $[\frac{6}{5}]$ $[\frac{1}{5}]$ $[\frac{6}{5}]_{5}$ $[\frac{1}{5}]_{5}$ $[\ ]_{5}$ $[\ ]_{5}$ $t + 9$ $x^{11} + 110 x^{2} + 11$ $[2, 0]$ $[1]$ $z^2 + 2$ undefined
11.1.11.14a2.1 $x^{11} + 11 x^{4} + 11$ $11$ $1$ $11$ $14$ $C_{11}:C_5$ (as 11T3) $1$ $5$ $[\frac{7}{5}]$ $[\frac{2}{5}]$ $[\frac{7}{5}]_{5}$ $[\frac{2}{5}]_{5}$ $[\ ]_{5}$ $[\ ]_{5}$ $t + 9$ $x^{11} + 11 x^{4} + 11$ $[4, 0]$ $[1]$ $z^2 + 2$ undefined
11.1.11.14a2.2 $x^{11} + 33 x^{4} + 11$ $11$ $1$ $11$ $14$ $C_{11}:C_5$ (as 11T3) $1$ $5$ $[\frac{7}{5}]$ $[\frac{2}{5}]$ $[\frac{7}{5}]_{5}$ $[\frac{2}{5}]_{5}$ $[\ ]_{5}$ $[\ ]_{5}$ $t + 9$ $x^{11} + 33 x^{4} + 11$ $[4, 0]$ $[1]$ $z^2 + 2$ undefined
11.1.11.14a2.3 $x^{11} + 44 x^{4} + 11$ $11$ $1$ $11$ $14$ $C_{11}:C_5$ (as 11T3) $1$ $5$ $[\frac{7}{5}]$ $[\frac{2}{5}]$ $[\frac{7}{5}]_{5}$ $[\frac{2}{5}]_{5}$ $[\ ]_{5}$ $[\ ]_{5}$ $t + 9$ $x^{11} + 44 x^{4} + 11$ $[4, 0]$ $[1]$ $z^2 + 2$ undefined
11.1.11.14a2.4 $x^{11} + 55 x^{4} + 11$ $11$ $1$ $11$ $14$ $C_{11}:C_5$ (as 11T3) $1$ $5$ $[\frac{7}{5}]$ $[\frac{2}{5}]$ $[\frac{7}{5}]_{5}$ $[\frac{2}{5}]_{5}$ $[\ ]_{5}$ $[\ ]_{5}$ $t + 9$ $x^{11} + 55 x^{4} + 11$ $[4, 0]$ $[1]$ $z^2 + 2$ undefined
11.1.11.14a2.5 $x^{11} + 99 x^{4} + 11$ $11$ $1$ $11$ $14$ $C_{11}:C_5$ (as 11T3) $1$ $5$ $[\frac{7}{5}]$ $[\frac{2}{5}]$ $[\frac{7}{5}]_{5}$ $[\frac{2}{5}]_{5}$ $[\ ]_{5}$ $[\ ]_{5}$ $t + 9$ $x^{11} + 99 x^{4} + 11$ $[4, 0]$ $[1]$ $z^2 + 2$ undefined
11.1.11.16a2.1 $x^{11} + 22 x^{6} + 11$ $11$ $1$ $11$ $16$ $C_{11}:C_5$ (as 11T3) $1$ $5$ $[\frac{8}{5}]$ $[\frac{3}{5}]$ $[\frac{8}{5}]_{5}$ $[\frac{3}{5}]_{5}$ $[\ ]_{5}$ $[\ ]_{5}$ $t + 9$ $x^{11} + 22 x^{6} + 11$ $[6, 0]$ $[1]$ $z^2 + 2$ undefined
11.1.11.16a2.2 $x^{11} + 66 x^{6} + 11$ $11$ $1$ $11$ $16$ $C_{11}:C_5$ (as 11T3) $1$ $5$ $[\frac{8}{5}]$ $[\frac{3}{5}]$ $[\frac{8}{5}]_{5}$ $[\frac{3}{5}]_{5}$ $[\ ]_{5}$ $[\ ]_{5}$ $t + 9$ $x^{11} + 66 x^{6} + 11$ $[6, 0]$ $[1]$ $z^2 + 2$ undefined
11.1.11.16a2.3 $x^{11} + 77 x^{6} + 11$ $11$ $1$ $11$ $16$ $C_{11}:C_5$ (as 11T3) $1$ $5$ $[\frac{8}{5}]$ $[\frac{3}{5}]$ $[\frac{8}{5}]_{5}$ $[\frac{3}{5}]_{5}$ $[\ ]_{5}$ $[\ ]_{5}$ $t + 9$ $x^{11} + 77 x^{6} + 11$ $[6, 0]$ $[1]$ $z^2 + 2$ undefined
11.1.11.16a2.4 $x^{11} + 88 x^{6} + 11$ $11$ $1$ $11$ $16$ $C_{11}:C_5$ (as 11T3) $1$ $5$ $[\frac{8}{5}]$ $[\frac{3}{5}]$ $[\frac{8}{5}]_{5}$ $[\frac{3}{5}]_{5}$ $[\ ]_{5}$ $[\ ]_{5}$ $t + 9$ $x^{11} + 88 x^{6} + 11$ $[6, 0]$ $[1]$ $z^2 + 2$ undefined
11.1.11.16a2.5 $x^{11} + 110 x^{6} + 11$ $11$ $1$ $11$ $16$ $C_{11}:C_5$ (as 11T3) $1$ $5$ $[\frac{8}{5}]$ $[\frac{3}{5}]$ $[\frac{8}{5}]_{5}$ $[\frac{3}{5}]_{5}$ $[\ ]_{5}$ $[\ ]_{5}$ $t + 9$ $x^{11} + 110 x^{6} + 11$ $[6, 0]$ $[1]$ $z^2 + 2$ undefined
11.1.11.18a2.1 $x^{11} + 22 x^{8} + 11$ $11$ $1$ $11$ $18$ $C_{11}:C_5$ (as 11T3) $1$ $5$ $[\frac{9}{5}]$ $[\frac{4}{5}]$ $[\frac{9}{5}]_{5}$ $[\frac{4}{5}]_{5}$ $[\ ]_{5}$ $[\ ]_{5}$ $t + 9$ $x^{11} + 22 x^{8} + 11$ $[8, 0]$ $[1]$ $z^2 + 2$ undefined
11.1.11.18a2.2 $x^{11} + 66 x^{8} + 11$ $11$ $1$ $11$ $18$ $C_{11}:C_5$ (as 11T3) $1$ $5$ $[\frac{9}{5}]$ $[\frac{4}{5}]$ $[\frac{9}{5}]_{5}$ $[\frac{4}{5}]_{5}$ $[\ ]_{5}$ $[\ ]_{5}$ $t + 9$ $x^{11} + 66 x^{8} + 11$ $[8, 0]$ $[1]$ $z^2 + 2$ undefined
11.1.11.18a2.3 $x^{11} + 77 x^{8} + 11$ $11$ $1$ $11$ $18$ $C_{11}:C_5$ (as 11T3) $1$ $5$ $[\frac{9}{5}]$ $[\frac{4}{5}]$ $[\frac{9}{5}]_{5}$ $[\frac{4}{5}]_{5}$ $[\ ]_{5}$ $[\ ]_{5}$ $t + 9$ $x^{11} + 77 x^{8} + 11$ $[8, 0]$ $[1]$ $z^2 + 2$ undefined
11.1.11.18a2.4 $x^{11} + 88 x^{8} + 11$ $11$ $1$ $11$ $18$ $C_{11}:C_5$ (as 11T3) $1$ $5$ $[\frac{9}{5}]$ $[\frac{4}{5}]$ $[\frac{9}{5}]_{5}$ $[\frac{4}{5}]_{5}$ $[\ ]_{5}$ $[\ ]_{5}$ $t + 9$ $x^{11} + 88 x^{8} + 11$ $[8, 0]$ $[1]$ $z^2 + 2$ undefined
11.1.11.18a2.5 $x^{11} + 110 x^{8} + 11$ $11$ $1$ $11$ $18$ $C_{11}:C_5$ (as 11T3) $1$ $5$ $[\frac{9}{5}]$ $[\frac{4}{5}]$ $[\frac{9}{5}]_{5}$ $[\frac{4}{5}]_{5}$ $[\ ]_{5}$ $[\ ]_{5}$ $t + 9$ $x^{11} + 110 x^{8} + 11$ $[8, 0]$ $[1]$ $z^2 + 2$ undefined
11.1.11.20a2.1 $x^{11} + 22 x^{10} + 11$ $11$ $1$ $11$ $20$ $C_{11}:C_5$ (as 11T3) $5$ $1$ $[2]$ $[1]$ $[2]^{5}$ $[1]^{5}$ $[\ ]^{5}$ $[\ ]^{5}$ $t + 9$ $x^{11} + 22 x^{10} + 11$ $[10, 0]$ $[5]$ $z^{10} + 2$ undefined
11.1.11.20a6.1 $x^{11} + 66 x^{10} + 11$ $11$ $1$ $11$ $20$ $C_{11}:C_5$ (as 11T3) $5$ $1$ $[2]$ $[1]$ $[2]^{5}$ $[1]^{5}$ $[\ ]^{5}$ $[\ ]^{5}$ $t + 9$ $x^{11} + 66 x^{10} + 11$ $[10, 0]$ $[5]$ $z^{10} + 6$ undefined
11.1.11.20a7.1 $x^{11} + 77 x^{10} + 11$ $11$ $1$ $11$ $20$ $C_{11}:C_5$ (as 11T3) $5$ $1$ $[2]$ $[1]$ $[2]^{5}$ $[1]^{5}$ $[\ ]^{5}$ $[\ ]^{5}$ $t + 9$ $x^{11} + 77 x^{10} + 11$ $[10, 0]$ $[5]$ $z^{10} + 7$ undefined
11.1.11.20a8.1 $x^{11} + 88 x^{10} + 11$ $11$ $1$ $11$ $20$ $C_{11}:C_5$ (as 11T3) $5$ $1$ $[2]$ $[1]$ $[2]^{5}$ $[1]^{5}$ $[\ ]^{5}$ $[\ ]^{5}$ $t + 9$ $x^{11} + 88 x^{10} + 11$ $[10, 0]$ $[5]$ $z^{10} + 8$ undefined
31.1.11.10a1.1 $x^{11} + 31$ $31$ $1$ $11$ $10$ $C_{11}:C_5$ (as 11T3) $5$ $11$ $[\ ]$ $[\ ]$ $[\ ]_{11}^{5}$ $[\ ]_{11}^{5}$ $[\ ]^{5}$ $[\ ]^{5}$ $t + 28$ $x^{11} + 31$ $[0]$ $[5]$ $z^{10} + 11 z^9 + 24 z^8 + 10 z^7 + 20 z^6 + 28 z^5 + 28 z^4 + 20 z^3 + 10 z^2 + 24 z + 11$ undefined
37.1.11.10a1.1 $x^{11} + 37$ $37$ $1$ $11$ $10$ $C_{11}:C_5$ (as 11T3) $5$ $11$ $[\ ]$ $[\ ]$ $[\ ]_{11}^{5}$ $[\ ]_{11}^{5}$ $[\ ]^{5}$ $[\ ]^{5}$ $t + 35$ $x^{11} + 37$ $[0]$ $[5]$ $z^{10} + 11 z^9 + 18 z^8 + 17 z^7 + 34 z^6 + 18 z^5 + 18 z^4 + 34 z^3 + 17 z^2 + 18 z + 11$ undefined
47.1.11.10a1.1 $x^{11} + 47$ $47$ $1$ $11$ $10$ $C_{11}:C_5$ (as 11T3) $5$ $11$ $[\ ]$ $[\ ]$ $[\ ]_{11}^{5}$ $[\ ]_{11}^{5}$ $[\ ]^{5}$ $[\ ]^{5}$ $t + 42$ $x^{11} + 47$ $[0]$ $[5]$ $z^{10} + 11 z^9 + 8 z^8 + 24 z^7 + z^6 + 39 z^5 + 39 z^4 + z^3 + 24 z^2 + 8 z + 11$ undefined
53.1.11.10a1.1 $x^{11} + 53$ $53$ $1$ $11$ $10$ $C_{11}:C_5$ (as 11T3) $5$ $11$ $[\ ]$ $[\ ]$ $[\ ]_{11}^{5}$ $[\ ]_{11}^{5}$ $[\ ]^{5}$ $[\ ]^{5}$ $t + 51$ $x^{11} + 53$ $[0]$ $[5]$ $z^{10} + 11 z^9 + 2 z^8 + 6 z^7 + 12 z^6 + 38 z^5 + 38 z^4 + 12 z^3 + 6 z^2 + 2 z + 11$ undefined
59.1.11.10a1.1 $x^{11} + 59$ $59$ $1$ $11$ $10$ $C_{11}:C_5$ (as 11T3) $5$ $11$ $[\ ]$ $[\ ]$ $[\ ]_{11}^{5}$ $[\ ]_{11}^{5}$ $[\ ]^{5}$ $[\ ]^{5}$ $t + 57$ $x^{11} + 59$ $[0]$ $[5]$ $z^{10} + 11 z^9 + 55 z^8 + 47 z^7 + 35 z^6 + 49 z^5 + 49 z^4 + 35 z^3 + 47 z^2 + 55 z + 11$ undefined
71.1.11.10a1.1 $x^{11} + 71$ $71$ $1$ $11$ $10$ $C_{11}:C_5$ (as 11T3) $5$ $11$ $[\ ]$ $[\ ]$ $[\ ]_{11}^{5}$ $[\ ]_{11}^{5}$ $[\ ]^{5}$ $[\ ]^{5}$ $t + 64$ $x^{11} + 71$ $[0]$ $[5]$ $z^{10} + 11 z^9 + 55 z^8 + 23 z^7 + 46 z^6 + 36 z^5 + 36 z^4 + 46 z^3 + 23 z^2 + 55 z + 11$ undefined
97.1.11.10a1.1 $x^{11} + 97$ $97$ $1$ $11$ $10$ $C_{11}:C_5$ (as 11T3) $5$ $11$ $[\ ]$ $[\ ]$ $[\ ]_{11}^{5}$ $[\ ]_{11}^{5}$ $[\ ]^{5}$ $[\ ]^{5}$ $t + 92$ $x^{11} + 97$ $[0]$ $[5]$ $z^{10} + 11 z^9 + 55 z^8 + 68 z^7 + 39 z^6 + 74 z^5 + 74 z^4 + 39 z^3 + 68 z^2 + 55 z + 11$ undefined
103.1.11.10a1.1 $x^{11} + 103$ $103$ $1$ $11$ $10$ $C_{11}:C_5$ (as 11T3) $5$ $11$ $[\ ]$ $[\ ]$ $[\ ]_{11}^{5}$ $[\ ]_{11}^{5}$ $[\ ]^{5}$ $[\ ]^{5}$ $t + 98$ $x^{11} + 103$ $[0]$ $[5]$ $z^{10} + 11 z^9 + 55 z^8 + 62 z^7 + 21 z^6 + 50 z^5 + 50 z^4 + 21 z^3 + 62 z^2 + 55 z + 11$ undefined
113.1.11.10a1.1 $x^{11} + 113$ $113$ $1$ $11$ $10$ $C_{11}:C_5$ (as 11T3) $5$ $11$ $[\ ]$ $[\ ]$ $[\ ]_{11}^{5}$ $[\ ]_{11}^{5}$ $[\ ]^{5}$ $[\ ]^{5}$ $t + 110$ $x^{11} + 113$ $[0]$ $[5]$ $z^{10} + 11 z^9 + 55 z^8 + 52 z^7 + 104 z^6 + 10 z^5 + 10 z^4 + 104 z^3 + 52 z^2 + 55 z + 11$ undefined
137.1.11.10a1.1 $x^{11} + 137$ $137$ $1$ $11$ $10$ $C_{11}:C_5$ (as 11T3) $5$ $11$ $[\ ]$ $[\ ]$ $[\ ]_{11}^{5}$ $[\ ]_{11}^{5}$ $[\ ]^{5}$ $[\ ]^{5}$ $t + 134$ $x^{11} + 137$ $[0]$ $[5]$ $z^{10} + 11 z^9 + 55 z^8 + 28 z^7 + 56 z^6 + 51 z^5 + 51 z^4 + 56 z^3 + 28 z^2 + 55 z + 11$ undefined
157.1.11.10a1.1 $x^{11} + 157$ $157$ $1$ $11$ $10$ $C_{11}:C_5$ (as 11T3) $5$ $11$ $[\ ]$ $[\ ]$ $[\ ]_{11}^{5}$ $[\ ]_{11}^{5}$ $[\ ]^{5}$ $[\ ]^{5}$ $t + 152$ $x^{11} + 157$ $[0]$ $[5]$ $z^{10} + 11 z^9 + 55 z^8 + 8 z^7 + 16 z^6 + 148 z^5 + 148 z^4 + 16 z^3 + 8 z^2 + 55 z + 11$ undefined
163.1.11.10a1.1 $x^{11} + 163$ $163$ $1$ $11$ $10$ $C_{11}:C_5$ (as 11T3) $5$ $11$ $[\ ]$ $[\ ]$ $[\ ]_{11}^{5}$ $[\ ]_{11}^{5}$ $[\ ]^{5}$ $[\ ]^{5}$ $t + 161$ $x^{11} + 163$ $[0]$ $[5]$ $z^{10} + 11 z^9 + 55 z^8 + 2 z^7 + 4 z^6 + 136 z^5 + 136 z^4 + 4 z^3 + 2 z^2 + 55 z + 11$ undefined
179.1.11.10a1.1 $x^{11} + 179$ $179$ $1$ $11$ $10$ $C_{11}:C_5$ (as 11T3) $5$ $11$ $[\ ]$ $[\ ]$ $[\ ]_{11}^{5}$ $[\ ]_{11}^{5}$ $[\ ]^{5}$ $[\ ]^{5}$ $t + 177$ $x^{11} + 179$ $[0]$ $[5]$ $z^{10} + 11 z^9 + 55 z^8 + 165 z^7 + 151 z^6 + 104 z^5 + 104 z^4 + 151 z^3 + 165 z^2 + 55 z + 11$ undefined
181.1.11.10a1.1 $x^{11} + 181$ $181$ $1$ $11$ $10$ $C_{11}:C_5$ (as 11T3) $5$ $11$ $[\ ]$ $[\ ]$ $[\ ]_{11}^{5}$ $[\ ]_{11}^{5}$ $[\ ]^{5}$ $[\ ]^{5}$ $t + 179$ $x^{11} + 181$ $[0]$ $[5]$ $z^{10} + 11 z^9 + 55 z^8 + 165 z^7 + 149 z^6 + 100 z^5 + 100 z^4 + 149 z^3 + 165 z^2 + 55 z + 11$ undefined
191.1.11.10a1.1 $x^{11} + 191$ $191$ $1$ $11$ $10$ $C_{11}:C_5$ (as 11T3) $5$ $11$ $[\ ]$ $[\ ]$ $[\ ]_{11}^{5}$ $[\ ]_{11}^{5}$ $[\ ]^{5}$ $[\ ]^{5}$ $t + 172$ $x^{11} + 191$ $[0]$ $[5]$ $z^{10} + 11 z^9 + 55 z^8 + 165 z^7 + 139 z^6 + 80 z^5 + 80 z^4 + 139 z^3 + 165 z^2 + 55 z + 11$ undefined
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