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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 (42 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
2.1.5.4a1.1 $x^{5} + 2$ $2$ $1$ $5$ $4$ $F_5$ (as 5T3) $4$ $5$ $[\ ]$ $[\ ]$ $[\ ]_{5}^{4}$ $[\ ]_{5}^{4}$ $[\ ]^{4}$ $[\ ]^{4}$ $t + 1$ $x^{5} + 2$ $[0]$ $[4]$ $z^4 + z^3 + 1$ $[5]$
3.1.5.4a1.1 $x^{5} + 3$ $3$ $1$ $5$ $4$ $F_5$ (as 5T3) $4$ $5$ $[\ ]$ $[\ ]$ $[\ ]_{5}^{4}$ $[\ ]_{5}^{4}$ $[\ ]^{4}$ $[\ ]^{4}$ $t + 1$ $x^{5} + 3$ $[0]$ $[4]$ $z^4 + 2 z^3 + z^2 + z + 2$ undefined
5.1.5.5a1.1 $x^{5} + 5 x + 5$ $5$ $1$ $5$ $5$ $F_5$ (as 5T3) $1$ $4$ $[\frac{5}{4}]$ $[\frac{1}{4}]$ $[\frac{5}{4}]_{4}$ $[\frac{1}{4}]_{4}$ $[\ ]_{4}$ $[\ ]_{4}$ $t + 3$ $x^{5} + 5 x + 5$ $[1, 0]$ $[1]$ $z + 4$ undefined
5.1.5.5a1.2 $x^{5} + 10 x + 5$ $5$ $1$ $5$ $5$ $F_5$ (as 5T3) $1$ $4$ $[\frac{5}{4}]$ $[\frac{1}{4}]$ $[\frac{5}{4}]_{4}$ $[\frac{1}{4}]_{4}$ $[\ ]_{4}$ $[\ ]_{4}$ $t + 3$ $x^{5} + 10 x + 5$ $[1, 0]$ $[1]$ $z + 3$ undefined
5.1.5.5a1.3 $x^{5} + 15 x + 5$ $5$ $1$ $5$ $5$ $F_5$ (as 5T3) $1$ $4$ $[\frac{5}{4}]$ $[\frac{1}{4}]$ $[\frac{5}{4}]_{4}$ $[\frac{1}{4}]_{4}$ $[\ ]_{4}$ $[\ ]_{4}$ $t + 3$ $x^{5} + 15 x + 5$ $[1, 0]$ $[1]$ $z + 2$ undefined
5.1.5.5a1.4 $x^{5} + 20 x + 5$ $5$ $1$ $5$ $5$ $F_5$ (as 5T3) $1$ $4$ $[\frac{5}{4}]$ $[\frac{1}{4}]$ $[\frac{5}{4}]_{4}$ $[\frac{1}{4}]_{4}$ $[\ ]_{4}$ $[\ ]_{4}$ $t + 3$ $x^{5} + 20 x + 5$ $[1, 0]$ $[1]$ $z + 1$ undefined
5.1.5.6a2.1 $x^{5} + 5 x^{2} + 5$ $5$ $1$ $5$ $6$ $F_5$ (as 5T3) $2$ $2$ $[\frac{3}{2}]$ $[\frac{1}{2}]$ $[\frac{3}{2}]_{2}^{2}$ $[\frac{1}{2}]_{2}^{2}$ $[\ ]^{2}_{2}$ $[\ ]^{2}_{2}$ $t + 3$ $x^{5} + 5 x^{2} + 5$ $[2, 0]$ $[2]$ $z^2 + 3$ undefined
5.1.5.6a2.2 $x^{5} + 20 x^{2} + 5$ $5$ $1$ $5$ $6$ $F_5$ (as 5T3) $2$ $2$ $[\frac{3}{2}]$ $[\frac{1}{2}]$ $[\frac{3}{2}]_{2}^{2}$ $[\frac{1}{2}]_{2}^{2}$ $[\ ]^{2}_{2}$ $[\ ]^{2}_{2}$ $t + 3$ $x^{5} + 20 x^{2} + 5$ $[2, 0]$ $[2]$ $z^2 + 2$ undefined
5.1.5.7a1.1 $x^{5} + 5 x^{3} + 5$ $5$ $1$ $5$ $7$ $F_5$ (as 5T3) $1$ $4$ $[\frac{7}{4}]$ $[\frac{3}{4}]$ $[\frac{7}{4}]_{4}$ $[\frac{3}{4}]_{4}$ $[\ ]_{4}$ $[\ ]_{4}$ $t + 3$ $x^{5} + 5 x^{3} + 5$ $[3, 0]$ $[1]$ $z + 2$ undefined
5.1.5.7a1.2 $x^{5} + 10 x^{3} + 5$ $5$ $1$ $5$ $7$ $F_5$ (as 5T3) $1$ $4$ $[\frac{7}{4}]$ $[\frac{3}{4}]$ $[\frac{7}{4}]_{4}$ $[\frac{3}{4}]_{4}$ $[\ ]_{4}$ $[\ ]_{4}$ $t + 3$ $x^{5} + 10 x^{3} + 5$ $[3, 0]$ $[1]$ $z + 4$ undefined
5.1.5.7a1.3 $x^{5} + 15 x^{3} + 5$ $5$ $1$ $5$ $7$ $F_5$ (as 5T3) $1$ $4$ $[\frac{7}{4}]$ $[\frac{3}{4}]$ $[\frac{7}{4}]_{4}$ $[\frac{3}{4}]_{4}$ $[\ ]_{4}$ $[\ ]_{4}$ $t + 3$ $x^{5} + 15 x^{3} + 5$ $[3, 0]$ $[1]$ $z + 1$ undefined
5.1.5.7a1.4 $x^{5} + 20 x^{3} + 5$ $5$ $1$ $5$ $7$ $F_5$ (as 5T3) $1$ $4$ $[\frac{7}{4}]$ $[\frac{3}{4}]$ $[\frac{7}{4}]_{4}$ $[\frac{3}{4}]_{4}$ $[\ ]_{4}$ $[\ ]_{4}$ $t + 3$ $x^{5} + 20 x^{3} + 5$ $[3, 0]$ $[1]$ $z + 3$ undefined
5.1.5.8a2.1 $x^{5} + 10 x^{4} + 5$ $5$ $1$ $5$ $8$ $F_5$ (as 5T3) $4$ $1$ $[2]$ $[1]$ $[2]^{4}$ $[1]^{4}$ $[\ ]^{4}$ $[\ ]^{4}$ $t + 3$ $x^{5} + 10 x^{4} + 5$ $[4, 0]$ $[4]$ $z^4 + 2$ undefined
5.1.5.8a3.1 $x^{5} + 15 x^{4} + 5$ $5$ $1$ $5$ $8$ $F_5$ (as 5T3) $4$ $1$ $[2]$ $[1]$ $[2]^{4}$ $[1]^{4}$ $[\ ]^{4}$ $[\ ]^{4}$ $t + 3$ $x^{5} + 15 x^{4} + 5$ $[4, 0]$ $[4]$ $z^4 + 3$ undefined
5.1.5.9a1.1 $x^{5} + 5$ $5$ $1$ $5$ $9$ $F_5$ (as 5T3) $1$ $4$ $[\frac{9}{4}]$ $[\frac{5}{4}]$ $[\frac{9}{4}]_{4}$ $[\frac{5}{4}]_{4}$ $[\ ]_{4}$ $[\ ]_{4}$ $t + 3$ $x^{5} + 5$ $[5, 0]$ $[1]$ $z + 4$ undefined
5.1.5.9a1.2 $x^{5} + 25 x + 5$ $5$ $1$ $5$ $9$ $F_5$ (as 5T3) $1$ $4$ $[\frac{9}{4}]$ $[\frac{5}{4}]$ $[\frac{9}{4}]_{4}$ $[\frac{5}{4}]_{4}$ $[\ ]_{4}$ $[\ ]_{4}$ $t + 3$ $x^{5} + 25 x + 5$ $[5, 0]$ $[1]$ $z + 4$ undefined
5.1.5.9a1.3 $x^{5} + 50 x + 5$ $5$ $1$ $5$ $9$ $F_5$ (as 5T3) $1$ $4$ $[\frac{9}{4}]$ $[\frac{5}{4}]$ $[\frac{9}{4}]_{4}$ $[\frac{5}{4}]_{4}$ $[\ ]_{4}$ $[\ ]_{4}$ $t + 3$ $x^{5} + 50 x + 5$ $[5, 0]$ $[1]$ $z + 4$ undefined
5.1.5.9a1.4 $x^{5} + 75 x + 5$ $5$ $1$ $5$ $9$ $F_5$ (as 5T3) $1$ $4$ $[\frac{9}{4}]$ $[\frac{5}{4}]$ $[\frac{9}{4}]_{4}$ $[\frac{5}{4}]_{4}$ $[\ ]_{4}$ $[\ ]_{4}$ $t + 3$ $x^{5} + 75 x + 5$ $[5, 0]$ $[1]$ $z + 4$ undefined
5.1.5.9a1.5 $x^{5} + 100 x + 5$ $5$ $1$ $5$ $9$ $F_5$ (as 5T3) $1$ $4$ $[\frac{9}{4}]$ $[\frac{5}{4}]$ $[\frac{9}{4}]_{4}$ $[\frac{5}{4}]_{4}$ $[\ ]_{4}$ $[\ ]_{4}$ $t + 3$ $x^{5} + 100 x + 5$ $[5, 0]$ $[1]$ $z + 4$ undefined
7.1.5.4a1.1 $x^{5} + 7$ $7$ $1$ $5$ $4$ $F_5$ (as 5T3) $4$ $5$ $[\ ]$ $[\ ]$ $[\ ]_{5}^{4}$ $[\ ]_{5}^{4}$ $[\ ]^{4}$ $[\ ]^{4}$ $t + 4$ $x^{5} + 7$ $[0]$ $[4]$ $z^4 + 5 z^3 + 3 z^2 + 3 z + 5$ undefined
13.1.5.4a1.1 $x^{5} + 13$ $13$ $1$ $5$ $4$ $F_5$ (as 5T3) $4$ $5$ $[\ ]$ $[\ ]$ $[\ ]_{5}^{4}$ $[\ ]_{5}^{4}$ $[\ ]^{4}$ $[\ ]^{4}$ $t + 11$ $x^{5} + 13$ $[0]$ $[4]$ $z^4 + 5 z^3 + 10 z^2 + 10 z + 5$ undefined
17.1.5.4a1.1 $x^{5} + 17$ $17$ $1$ $5$ $4$ $F_5$ (as 5T3) $4$ $5$ $[\ ]$ $[\ ]$ $[\ ]_{5}^{4}$ $[\ ]_{5}^{4}$ $[\ ]^{4}$ $[\ ]^{4}$ $t + 14$ $x^{5} + 17$ $[0]$ $[4]$ $z^4 + 5 z^3 + 10 z^2 + 10 z + 5$ undefined
23.1.5.4a1.1 $x^{5} + 23$ $23$ $1$ $5$ $4$ $F_5$ (as 5T3) $4$ $5$ $[\ ]$ $[\ ]$ $[\ ]_{5}^{4}$ $[\ ]_{5}^{4}$ $[\ ]^{4}$ $[\ ]^{4}$ $t + 18$ $x^{5} + 23$ $[0]$ $[4]$ $z^4 + 5 z^3 + 10 z^2 + 10 z + 5$ undefined
37.1.5.4a1.1 $x^{5} + 37$ $37$ $1$ $5$ $4$ $F_5$ (as 5T3) $4$ $5$ $[\ ]$ $[\ ]$ $[\ ]_{5}^{4}$ $[\ ]_{5}^{4}$ $[\ ]^{4}$ $[\ ]^{4}$ $t + 35$ $x^{5} + 37$ $[0]$ $[4]$ $z^4 + 5 z^3 + 10 z^2 + 10 z + 5$ undefined
43.1.5.4a1.1 $x^{5} + 43$ $43$ $1$ $5$ $4$ $F_5$ (as 5T3) $4$ $5$ $[\ ]$ $[\ ]$ $[\ ]_{5}^{4}$ $[\ ]_{5}^{4}$ $[\ ]^{4}$ $[\ ]^{4}$ $t + 40$ $x^{5} + 43$ $[0]$ $[4]$ $z^4 + 5 z^3 + 10 z^2 + 10 z + 5$ undefined
47.1.5.4a1.1 $x^{5} + 47$ $47$ $1$ $5$ $4$ $F_5$ (as 5T3) $4$ $5$ $[\ ]$ $[\ ]$ $[\ ]_{5}^{4}$ $[\ ]_{5}^{4}$ $[\ ]^{4}$ $[\ ]^{4}$ $t + 42$ $x^{5} + 47$ $[0]$ $[4]$ $z^4 + 5 z^3 + 10 z^2 + 10 z + 5$ undefined
53.1.5.4a1.1 $x^{5} + 53$ $53$ $1$ $5$ $4$ $F_5$ (as 5T3) $4$ $5$ $[\ ]$ $[\ ]$ $[\ ]_{5}^{4}$ $[\ ]_{5}^{4}$ $[\ ]^{4}$ $[\ ]^{4}$ $t + 51$ $x^{5} + 53$ $[0]$ $[4]$ $z^4 + 5 z^3 + 10 z^2 + 10 z + 5$ undefined
67.1.5.4a1.1 $x^{5} + 67$ $67$ $1$ $5$ $4$ $F_5$ (as 5T3) $4$ $5$ $[\ ]$ $[\ ]$ $[\ ]_{5}^{4}$ $[\ ]_{5}^{4}$ $[\ ]^{4}$ $[\ ]^{4}$ $t + 65$ $x^{5} + 67$ $[0]$ $[4]$ $z^4 + 5 z^3 + 10 z^2 + 10 z + 5$ undefined
73.1.5.4a1.1 $x^{5} + 73$ $73$ $1$ $5$ $4$ $F_5$ (as 5T3) $4$ $5$ $[\ ]$ $[\ ]$ $[\ ]_{5}^{4}$ $[\ ]_{5}^{4}$ $[\ ]^{4}$ $[\ ]^{4}$ $t + 68$ $x^{5} + 73$ $[0]$ $[4]$ $z^4 + 5 z^3 + 10 z^2 + 10 z + 5$ undefined
83.1.5.4a1.1 $x^{5} + 83$ $83$ $1$ $5$ $4$ $F_5$ (as 5T3) $4$ $5$ $[\ ]$ $[\ ]$ $[\ ]_{5}^{4}$ $[\ ]_{5}^{4}$ $[\ ]^{4}$ $[\ ]^{4}$ $t + 81$ $x^{5} + 83$ $[0]$ $[4]$ $z^4 + 5 z^3 + 10 z^2 + 10 z + 5$ undefined
97.1.5.4a1.1 $x^{5} + 97$ $97$ $1$ $5$ $4$ $F_5$ (as 5T3) $4$ $5$ $[\ ]$ $[\ ]$ $[\ ]_{5}^{4}$ $[\ ]_{5}^{4}$ $[\ ]^{4}$ $[\ ]^{4}$ $t + 92$ $x^{5} + 97$ $[0]$ $[4]$ $z^4 + 5 z^3 + 10 z^2 + 10 z + 5$ undefined
103.1.5.4a1.1 $x^{5} + 103$ $103$ $1$ $5$ $4$ $F_5$ (as 5T3) $4$ $5$ $[\ ]$ $[\ ]$ $[\ ]_{5}^{4}$ $[\ ]_{5}^{4}$ $[\ ]^{4}$ $[\ ]^{4}$ $t + 98$ $x^{5} + 103$ $[0]$ $[4]$ $z^4 + 5 z^3 + 10 z^2 + 10 z + 5$ undefined
107.1.5.4a1.1 $x^{5} + 107$ $107$ $1$ $5$ $4$ $F_5$ (as 5T3) $4$ $5$ $[\ ]$ $[\ ]$ $[\ ]_{5}^{4}$ $[\ ]_{5}^{4}$ $[\ ]^{4}$ $[\ ]^{4}$ $t + 105$ $x^{5} + 107$ $[0]$ $[4]$ $z^4 + 5 z^3 + 10 z^2 + 10 z + 5$ undefined
113.1.5.4a1.1 $x^{5} + 113$ $113$ $1$ $5$ $4$ $F_5$ (as 5T3) $4$ $5$ $[\ ]$ $[\ ]$ $[\ ]_{5}^{4}$ $[\ ]_{5}^{4}$ $[\ ]^{4}$ $[\ ]^{4}$ $t + 110$ $x^{5} + 113$ $[0]$ $[4]$ $z^4 + 5 z^3 + 10 z^2 + 10 z + 5$ undefined
127.1.5.4a1.1 $x^{5} + 127$ $127$ $1$ $5$ $4$ $F_5$ (as 5T3) $4$ $5$ $[\ ]$ $[\ ]$ $[\ ]_{5}^{4}$ $[\ ]_{5}^{4}$ $[\ ]^{4}$ $[\ ]^{4}$ $t + 124$ $x^{5} + 127$ $[0]$ $[4]$ $z^4 + 5 z^3 + 10 z^2 + 10 z + 5$ undefined
137.1.5.4a1.1 $x^{5} + 137$ $137$ $1$ $5$ $4$ $F_5$ (as 5T3) $4$ $5$ $[\ ]$ $[\ ]$ $[\ ]_{5}^{4}$ $[\ ]_{5}^{4}$ $[\ ]^{4}$ $[\ ]^{4}$ $t + 134$ $x^{5} + 137$ $[0]$ $[4]$ $z^4 + 5 z^3 + 10 z^2 + 10 z + 5$ undefined
157.1.5.4a1.1 $x^{5} + 157$ $157$ $1$ $5$ $4$ $F_5$ (as 5T3) $4$ $5$ $[\ ]$ $[\ ]$ $[\ ]_{5}^{4}$ $[\ ]_{5}^{4}$ $[\ ]^{4}$ $[\ ]^{4}$ $t + 152$ $x^{5} + 157$ $[0]$ $[4]$ $z^4 + 5 z^3 + 10 z^2 + 10 z + 5$ undefined
163.1.5.4a1.1 $x^{5} + 163$ $163$ $1$ $5$ $4$ $F_5$ (as 5T3) $4$ $5$ $[\ ]$ $[\ ]$ $[\ ]_{5}^{4}$ $[\ ]_{5}^{4}$ $[\ ]^{4}$ $[\ ]^{4}$ $t + 161$ $x^{5} + 163$ $[0]$ $[4]$ $z^4 + 5 z^3 + 10 z^2 + 10 z + 5$ undefined
167.1.5.4a1.1 $x^{5} + 167$ $167$ $1$ $5$ $4$ $F_5$ (as 5T3) $4$ $5$ $[\ ]$ $[\ ]$ $[\ ]_{5}^{4}$ $[\ ]_{5}^{4}$ $[\ ]^{4}$ $[\ ]^{4}$ $t + 162$ $x^{5} + 167$ $[0]$ $[4]$ $z^4 + 5 z^3 + 10 z^2 + 10 z + 5$ undefined
173.1.5.4a1.1 $x^{5} + 173$ $173$ $1$ $5$ $4$ $F_5$ (as 5T3) $4$ $5$ $[\ ]$ $[\ ]$ $[\ ]_{5}^{4}$ $[\ ]_{5}^{4}$ $[\ ]^{4}$ $[\ ]^{4}$ $t + 171$ $x^{5} + 173$ $[0]$ $[4]$ $z^4 + 5 z^3 + 10 z^2 + 10 z + 5$ undefined
193.1.5.4a1.1 $x^{5} + 193$ $193$ $1$ $5$ $4$ $F_5$ (as 5T3) $4$ $5$ $[\ ]$ $[\ ]$ $[\ ]_{5}^{4}$ $[\ ]_{5}^{4}$ $[\ ]^{4}$ $[\ ]^{4}$ $t + 188$ $x^{5} + 193$ $[0]$ $[4]$ $z^4 + 5 z^3 + 10 z^2 + 10 z + 5$ undefined
197.1.5.4a1.1 $x^{5} + 197$ $197$ $1$ $5$ $4$ $F_5$ (as 5T3) $4$ $5$ $[\ ]$ $[\ ]$ $[\ ]_{5}^{4}$ $[\ ]_{5}^{4}$ $[\ ]^{4}$ $[\ ]^{4}$ $t + 195$ $x^{5} + 197$ $[0]$ $[4]$ $z^4 + 5 z^3 + 10 z^2 + 10 z + 5$ undefined
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