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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 (15 matches)

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Label Polynomial $p$ $e$ $f$ $c$ Galois group Visible slopes Slope content
17.8.0.1 x8 + 11x4 + 12x3 + 6x + 3 $17$ $1$ $8$ $0$ $C_8$ (as 8T1) $[\ ]$ $[\ ]^{8}$
17.8.4.1 x8 + 612x7 + 140536x6 + 14363966x5 + 553913435x4 + 345855654x3 + 4032327212x2 + 6379401496x + 2294776272 $17$ $2$ $4$ $4$ $C_4\times C_2$ (as 8T2) $[\ ]$ $[\ ]_{2}^{4}$
17.8.4.2 x8 + 2023x4 - 49130x2 + 250563 $17$ $2$ $4$ $4$ $C_8$ (as 8T1) $[\ ]$ $[\ ]_{2}^{4}$
17.8.6.1 x8 + 64x7 + 1548x6 + 16960x5 + 74840x4 + 51968x3 + 39432x2 + 270464x + 1062564 $17$ $4$ $2$ $6$ $C_4\times C_2$ (as 8T2) $[\ ]$ $[\ ]_{4}^{2}$
17.8.6.2 x8 + 204x4 - 7225 $17$ $4$ $2$ $6$ $C_4\times C_2$ (as 8T2) $[\ ]$ $[\ ]_{4}^{2}$
17.8.6.3 x8 - 272x4 + 867 $17$ $4$ $2$ $6$ $C_8$ (as 8T1) $[\ ]$ $[\ ]_{4}^{2}$
17.8.6.4 x8 - 3604x4 - 719321 $17$ $4$ $2$ $6$ $C_8$ (as 8T1) $[\ ]$ $[\ ]_{4}^{2}$
17.8.7.1 x8 + 68 $17$ $8$ $1$ $7$ $C_8$ (as 8T1) $[\ ]$ $[\ ]_{8}$
17.8.7.2 x8 + 136 $17$ $8$ $1$ $7$ $C_8$ (as 8T1) $[\ ]$ $[\ ]_{8}$
17.8.7.3 x8 + 17 $17$ $8$ $1$ $7$ $C_8$ (as 8T1) $[\ ]$ $[\ ]_{8}$
17.8.7.4 x8 + 34 $17$ $8$ $1$ $7$ $C_8$ (as 8T1) $[\ ]$ $[\ ]_{8}$
17.8.7.5 x8 + 119 $17$ $8$ $1$ $7$ $C_8$ (as 8T1) $[\ ]$ $[\ ]_{8}$
17.8.7.6 x8 + 102 $17$ $8$ $1$ $7$ $C_8$ (as 8T1) $[\ ]$ $[\ ]_{8}$
17.8.7.7 x8 + 51 $17$ $8$ $1$ $7$ $C_8$ (as 8T1) $[\ ]$ $[\ ]_{8}$
17.8.7.8 x8 + 85 $17$ $8$ $1$ $7$ $C_8$ (as 8T1) $[\ ]$ $[\ ]_{8}$
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