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Degree Residue characteristic Galois group Galois unramified degree Assoc. Inertia
Ramification index Discriminant exponent Inertia subgroup Galois tame degree Indices
Residue field degree Top slope Wild Visible Wild inertia subgroup
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Results (24 matches)

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Label Polynomial $p$ $e$ $f$ $c$ Galois group $u$ $t$ Visible slopes Slope content Unram. Ext. Eisen. Poly. Ind. of Insep. Assoc. Inertia
2.7.6.1 $x^{7} + 2$ $2$ $7$ $1$ $6$ $C_7:C_3$ (as 7T3) $3$ $7$ $[\ ]$ $[\ ]_{7}^{3}$ $t + 1$ $x^{7} + 2$ $[0]$ $[3]$
7.7.8.1 $x^{7} + 14 x^{2} + 7$ $7$ $7$ $1$ $8$ $C_7:C_3$ (as 7T3) $1$ $3$ $[4/3]$ $[4/3]_{3}$ $t + 4$ $x^{7} + 14 x^{2} + 7$ $[2, 0]$ $[1]$
7.7.8.2 $x^{7} + 7 x^{2} + 7$ $7$ $7$ $1$ $8$ $C_7:C_3$ (as 7T3) $1$ $3$ $[4/3]$ $[4/3]_{3}$ $t + 4$ $x^{7} + 7 x^{2} + 7$ $[2, 0]$ $[1]$
7.7.8.3 $x^{7} + 28 x^{2} + 7$ $7$ $7$ $1$ $8$ $C_7:C_3$ (as 7T3) $1$ $3$ $[4/3]$ $[4/3]_{3}$ $t + 4$ $x^{7} + 28 x^{2} + 7$ $[2, 0]$ $[1]$
7.7.10.1 $x^{7} + 28 x^{4} + 7$ $7$ $7$ $1$ $10$ $C_7:C_3$ (as 7T3) $1$ $3$ $[5/3]$ $[5/3]_{3}$ $t + 4$ $x^{7} + 28 x^{4} + 7$ $[4, 0]$ $[1]$
7.7.10.2 $x^{7} + 7 x^{4} + 7$ $7$ $7$ $1$ $10$ $C_7:C_3$ (as 7T3) $1$ $3$ $[5/3]$ $[5/3]_{3}$ $t + 4$ $x^{7} + 7 x^{4} + 7$ $[4, 0]$ $[1]$
7.7.10.3 $x^{7} + 14 x^{4} + 7$ $7$ $7$ $1$ $10$ $C_7:C_3$ (as 7T3) $1$ $3$ $[5/3]$ $[5/3]_{3}$ $t + 4$ $x^{7} + 14 x^{4} + 7$ $[4, 0]$ $[1]$
7.7.12.8 $x^{7} + 21 x^{6} + 7$ $7$ $7$ $1$ $12$ $C_7:C_3$ (as 7T3) $3$ $1$ $[2]$ $[2]^{3}$ $t + 4$ $x^{7} + 21 x^{6} + 7$ $[6, 0]$ $[3]$
7.7.12.9 $x^{7} + 35 x^{6} + 7$ $7$ $7$ $1$ $12$ $C_7:C_3$ (as 7T3) $3$ $1$ $[2]$ $[2]^{3}$ $t + 4$ $x^{7} + 35 x^{6} + 7$ $[6, 0]$ $[3]$
11.7.6.1 $x^{7} + 11$ $11$ $7$ $1$ $6$ $C_7:C_3$ (as 7T3) $3$ $7$ $[\ ]$ $[\ ]_{7}^{3}$ $t + 9$ $x^{7} + 11$ $[0]$ $[3]$
23.7.6.1 $x^{7} + 23$ $23$ $7$ $1$ $6$ $C_7:C_3$ (as 7T3) $3$ $7$ $[\ ]$ $[\ ]_{7}^{3}$ $t + 18$ $x^{7} + 23$ $[0]$ $[3]$
37.7.6.1 $x^{7} + 37$ $37$ $7$ $1$ $6$ $C_7:C_3$ (as 7T3) $3$ $7$ $[\ ]$ $[\ ]_{7}^{3}$ $t + 35$ $x^{7} + 37$ $[0]$ $[3]$
53.7.6.1 $x^{7} + 53$ $53$ $7$ $1$ $6$ $C_7:C_3$ (as 7T3) $3$ $7$ $[\ ]$ $[\ ]_{7}^{3}$ $t + 51$ $x^{7} + 53$ $[0]$ $[3]$
67.7.6.1 $x^{7} + 67$ $67$ $7$ $1$ $6$ $C_7:C_3$ (as 7T3) $3$ $7$ $[\ ]$ $[\ ]_{7}^{3}$ $t + 65$ $x^{7} + 67$ $[0]$ $[3]$
79.7.6.1 $x^{7} + 79$ $79$ $7$ $1$ $6$ $C_7:C_3$ (as 7T3) $3$ $7$ $[\ ]$ $[\ ]_{7}^{3}$ $t + 76$ $x^{7} + 79$ $[0]$ $[3]$
107.7.6.1 $x^{7} + 107$ $107$ $7$ $1$ $6$ $C_7:C_3$ (as 7T3) $3$ $7$ $[\ ]$ $[\ ]_{7}^{3}$ $t + 105$ $x^{7} + 107$ $[0]$ $[3]$
109.7.6.1 $x^{7} + 109$ $109$ $7$ $1$ $6$ $C_7:C_3$ (as 7T3) $3$ $7$ $[\ ]$ $[\ ]_{7}^{3}$ $t + 103$ $x^{7} + 109$ $[0]$ $[3]$
137.7.6.1 $x^{7} + 137$ $137$ $7$ $1$ $6$ $C_7:C_3$ (as 7T3) $3$ $7$ $[\ ]$ $[\ ]_{7}^{3}$ $t + 134$ $x^{7} + 137$ $[0]$ $[3]$
149.7.6.1 $x^{7} + 149$ $149$ $7$ $1$ $6$ $C_7:C_3$ (as 7T3) $3$ $7$ $[\ ]$ $[\ ]_{7}^{3}$ $t + 147$ $x^{7} + 149$ $[0]$ $[3]$
151.7.6.1 $x^{7} + 151$ $151$ $7$ $1$ $6$ $C_7:C_3$ (as 7T3) $3$ $7$ $[\ ]$ $[\ ]_{7}^{3}$ $t + 145$ $x^{7} + 151$ $[0]$ $[3]$
163.7.6.1 $x^{7} + 163$ $163$ $7$ $1$ $6$ $C_7:C_3$ (as 7T3) $3$ $7$ $[\ ]$ $[\ ]_{7}^{3}$ $t + 161$ $x^{7} + 163$ $[0]$ $[3]$
179.7.6.1 $x^{7} + 179$ $179$ $7$ $1$ $6$ $C_7:C_3$ (as 7T3) $3$ $7$ $[\ ]$ $[\ ]_{7}^{3}$ $t + 177$ $x^{7} + 179$ $[0]$ $[3]$
191.7.6.1 $x^{7} + 191$ $191$ $7$ $1$ $6$ $C_7:C_3$ (as 7T3) $3$ $7$ $[\ ]$ $[\ ]_{7}^{3}$ $t + 172$ $x^{7} + 191$ $[0]$ $[3]$
193.7.6.1 $x^{7} + 193$ $193$ $7$ $1$ $6$ $C_7:C_3$ (as 7T3) $3$ $7$ $[\ ]$ $[\ ]_{7}^{3}$ $t + 188$ $x^{7} + 193$ $[0]$ $[3]$
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