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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 Unram. Ext. Eisen. Poly.
2.10.10.16 $x^{10} + 2 x^{2} + 2 x + 2$ $2$ $10$ $1$ $10$ $(C_2^4 : C_5):C_4$ (as 10T25) $[6/5]$ $[6/5, 6/5, 6/5, 6/5]_{5}^{4}$ $t + 1$ $x^{10} + 2 x^{2} + 2 x + 2$
2.10.12.3 $x^{10} + 2 x^{3} + 2$ $2$ $10$ $1$ $12$ $(C_2^4 : C_5):C_4$ (as 10T25) $[8/5]$ $[8/5, 8/5, 8/5, 8/5]_{5}^{4}$ $t + 1$ $x^{10} + 2 x^{3} + 2$
2.10.12.4 $x^{10} + 2 x^{5} + 2 x^{3} + 2$ $2$ $10$ $1$ $12$ $(C_2^4 : C_5):C_4$ (as 10T25) $[8/5]$ $[8/5, 8/5, 8/5, 8/5]_{5}^{4}$ $t + 1$ $x^{10} + 2 x^{5} + 2 x^{3} + 2$
2.10.16.5 $x^{10} + 2 x^{9} + 2 x^{8} + 2 x^{7} + 2 x^{6} + 2 x^{4} + 4 x^{3} + 4 x^{2} + 2$ $2$ $10$ $1$ $16$ $(C_2^4 : C_5):C_4$ (as 10T25) $[12/5]$ $[12/5, 12/5, 12/5, 12/5]_{5}^{4}$ $t + 1$ $x^{10} + 2 x^{9} + 2 x^{8} + 2 x^{7} + 2 x^{6} + 2 x^{4} + 4 x^{3} + 4 x^{2} + 2$
2.10.16.6 $x^{10} + 2 x^{8} + 2 x^{7} + 4 x^{4} + 4 x + 2$ $2$ $10$ $1$ $16$ $(C_2^4 : C_5):C_4$ (as 10T25) $[12/5]$ $[12/5, 12/5, 12/5, 12/5]_{5}^{4}$ $t + 1$ $x^{10} + 2 x^{8} + 2 x^{7} + 4 x^{4} + 4 x + 2$
2.10.16.7 $x^{10} + 2 x^{9} + 2 x^{8} + 2 x^{7} + 2 x^{6} + 2 x^{4} + 4 x^{3} + 4 x + 6$ $2$ $10$ $1$ $16$ $(C_2^4 : C_5):C_4$ (as 10T25) $[12/5]$ $[12/5, 12/5, 12/5, 12/5]_{5}^{4}$ $t + 1$ $x^{10} + 2 x^{9} + 2 x^{8} + 2 x^{7} + 2 x^{6} + 2 x^{4} + 4 x^{3} + 4 x + 6$
2.10.16.8 $x^{10} + 2 x^{9} + 2 x^{8} + 2 x^{7} + 2 x^{4} + 4 x^{2} + 4 x + 6$ $2$ $10$ $1$ $16$ $(C_2^4 : C_5):C_4$ (as 10T25) $[12/5]$ $[12/5, 12/5, 12/5, 12/5]_{5}^{4}$ $t + 1$ $x^{10} + 2 x^{9} + 2 x^{8} + 2 x^{7} + 2 x^{4} + 4 x^{2} + 4 x + 6$
2.10.18.10 $x^{10} + 2 x^{9} + 2 x^{8} + 4 x^{6} + 4 x + 2$ $2$ $10$ $1$ $18$ $(C_2^4 : C_5):C_4$ (as 10T25) $[14/5]$ $[14/5, 14/5, 14/5, 14/5]_{5}^{4}$ $t + 1$ $x^{10} + 2 x^{9} + 2 x^{8} + 4 x^{6} + 4 x + 2$
2.10.18.11 $x^{10} + 2 x^{9} + 4 x^{8} + 4 x^{7} + 4 x^{6} + 4 x^{4} + 4 x^{3} + 2$ $2$ $10$ $1$ $18$ $(C_2^4 : C_5):C_4$ (as 10T25) $[14/5]$ $[14/5, 14/5, 14/5, 14/5]_{5}^{4}$ $t + 1$ $x^{10} + 2 x^{9} + 4 x^{8} + 4 x^{7} + 4 x^{6} + 4 x^{4} + 4 x^{3} + 2$
2.10.18.12 $x^{10} + 2 x^{9} + 4 x^{8} + 4 x^{7} + 4 x^{6} + 4 x^{5} + 4 x^{4} + 4 x^{3} + 2$ $2$ $10$ $1$ $18$ $(C_2^4 : C_5):C_4$ (as 10T25) $[14/5]$ $[14/5, 14/5, 14/5, 14/5]_{5}^{4}$ $t + 1$ $x^{10} + 2 x^{9} + 4 x^{8} + 4 x^{7} + 4 x^{6} + 4 x^{5} + 4 x^{4} + 4 x^{3} + 2$
2.10.18.13 $x^{10} + 2 x^{9} + 2 x^{8} + 4 x^{7} + 4 x^{6} + 4 x + 2$ $2$ $10$ $1$ $18$ $(C_2^4 : C_5):C_4$ (as 10T25) $[14/5]$ $[14/5, 14/5, 14/5, 14/5]_{5}^{4}$ $t + 1$ $x^{10} + 2 x^{9} + 2 x^{8} + 4 x^{7} + 4 x^{6} + 4 x + 2$
2.10.18.14 $x^{10} + 2 x^{9} + 2 x^{8} + 4 x^{7} + 4 x^{6} + 4 x^{5} + 4 x + 2$ $2$ $10$ $1$ $18$ $(C_2^4 : C_5):C_4$ (as 10T25) $[14/5]$ $[14/5, 14/5, 14/5, 14/5]_{5}^{4}$ $t + 1$ $x^{10} + 2 x^{9} + 2 x^{8} + 4 x^{7} + 4 x^{6} + 4 x^{5} + 4 x + 2$
2.10.18.15 $x^{10} + 2 x^{9} + 4 x^{8} + 4 x^{6} + 4 x^{5} + 4 x^{4} + 4 x^{3} + 2$ $2$ $10$ $1$ $18$ $(C_2^4 : C_5):C_4$ (as 10T25) $[14/5]$ $[14/5, 14/5, 14/5, 14/5]_{5}^{4}$ $t + 1$ $x^{10} + 2 x^{9} + 4 x^{8} + 4 x^{6} + 4 x^{5} + 4 x^{4} + 4 x^{3} + 2$
2.10.18.16 $x^{10} + 2 x^{9} + 2 x^{8} + 4 x^{6} + 4 x^{5} + 4 x + 2$ $2$ $10$ $1$ $18$ $(C_2^4 : C_5):C_4$ (as 10T25) $[14/5]$ $[14/5, 14/5, 14/5, 14/5]_{5}^{4}$ $t + 1$ $x^{10} + 2 x^{9} + 2 x^{8} + 4 x^{6} + 4 x^{5} + 4 x + 2$
2.10.18.9 $x^{10} + 2 x^{9} + 4 x^{8} + 4 x^{6} + 4 x^{4} + 4 x^{3} + 2$ $2$ $10$ $1$ $18$ $(C_2^4 : C_5):C_4$ (as 10T25) $[14/5]$ $[14/5, 14/5, 14/5, 14/5]_{5}^{4}$ $t + 1$ $x^{10} + 2 x^{9} + 4 x^{8} + 4 x^{6} + 4 x^{4} + 4 x^{3} + 2$
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