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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 (10 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
7.7.9.1 $x^{7} + 14 x^{3} + 7$ $7$ $7$ $1$ $9$ $D_{7}$ (as 7T2) $1$ $2$ $[3/2]$ $[3/2]_{2}$ $t + 4$ $x^{7} + 14 x^{3} + 7$ $[3, 0]$ $[1]$
7.7.9.4 $x^{7} + 35 x^{3} + 7$ $7$ $7$ $1$ $9$ $D_{7}$ (as 7T2) $1$ $2$ $[3/2]$ $[3/2]_{2}$ $t + 4$ $x^{7} + 35 x^{3} + 7$ $[3, 0]$ $[1]$
7.7.12.10 $x^{7} + 7 x^{6} + 7$ $7$ $7$ $1$ $12$ $D_{7}$ (as 7T2) $2$ $1$ $[2]$ $[2]^{2}$ $t + 4$ $x^{7} + 7 x^{6} + 7$ $[6, 0]$ $[2]$
13.7.6.1 $x^{7} + 13$ $13$ $7$ $1$ $6$ $D_{7}$ (as 7T2) $2$ $7$ $[\ ]$ $[\ ]_{7}^{2}$ $t + 11$ $x^{7} + 13$ $[0]$ $[2]$
41.7.6.1 $x^{7} + 41$ $41$ $7$ $1$ $6$ $D_{7}$ (as 7T2) $2$ $7$ $[\ ]$ $[\ ]_{7}^{2}$ $t + 35$ $x^{7} + 41$ $[0]$ $[2]$
83.7.6.1 $x^{7} + 83$ $83$ $7$ $1$ $6$ $D_{7}$ (as 7T2) $2$ $7$ $[\ ]$ $[\ ]_{7}^{2}$ $t + 81$ $x^{7} + 83$ $[0]$ $[2]$
97.7.6.1 $x^{7} + 97$ $97$ $7$ $1$ $6$ $D_{7}$ (as 7T2) $2$ $7$ $[\ ]$ $[\ ]_{7}^{2}$ $t + 92$ $x^{7} + 97$ $[0]$ $[2]$
139.7.6.1 $x^{7} + 139$ $139$ $7$ $1$ $6$ $D_{7}$ (as 7T2) $2$ $7$ $[\ ]$ $[\ ]_{7}^{2}$ $t + 137$ $x^{7} + 139$ $[0]$ $[2]$
167.7.6.1 $x^{7} + 167$ $167$ $7$ $1$ $6$ $D_{7}$ (as 7T2) $2$ $7$ $[\ ]$ $[\ ]_{7}^{2}$ $t + 162$ $x^{7} + 167$ $[0]$ $[2]$
181.7.6.1 $x^{7} + 181$ $181$ $7$ $1$ $6$ $D_{7}$ (as 7T2) $2$ $7$ $[\ ]$ $[\ ]_{7}^{2}$ $t + 179$ $x^{7} + 181$ $[0]$ $[2]$
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