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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
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Results (14 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
2.1.8.8a1.1 $x^{8} + 2 x + 2$ $2$ $1$ $8$ $8$ $C_2^3:(C_7: C_3)$ (as 8T36) $3$ $7$ $[\frac{8}{7}, \frac{8}{7}, \frac{8}{7}]$ $[\frac{1}{7},\frac{1}{7},\frac{1}{7}]$ $[\frac{8}{7}, \frac{8}{7}, \frac{8}{7}]_{7}^{3}$ $[\frac{1}{7},\frac{1}{7},\frac{1}{7}]_{7}^{3}$ $[\ ]^{3}_{7}$ $[\ ]^{3}_{7}$ $t + 1$ $x^{8} + 2 x + 2$ $[1, 1, 1, 0]$ $[1]$ $z + 1$ $[1, 2, 4, 9]$
2.1.8.10a1.1 $x^{8} + 2 x^{3} + 2$ $2$ $1$ $8$ $10$ $C_2^3:(C_7: C_3)$ (as 8T36) $3$ $7$ $[\frac{10}{7}, \frac{10}{7}, \frac{10}{7}]$ $[\frac{3}{7},\frac{3}{7},\frac{3}{7}]$ $[\frac{10}{7}, \frac{10}{7}, \frac{10}{7}]_{7}^{3}$ $[\frac{3}{7},\frac{3}{7},\frac{3}{7}]_{7}^{3}$ $[\ ]^{3}_{7}$ $[\ ]^{3}_{7}$ $t + 1$ $x^{8} + 2 x^{3} + 2$ $[3, 3, 3, 0]$ $[1]$ $z + 1$ $[1, 2, 4, 11]$
2.1.8.12a1.1 $x^{8} + 2 x^{5} + 2$ $2$ $1$ $8$ $12$ $C_2^3:(C_7: C_3)$ (as 8T36) $3$ $7$ $[\frac{12}{7}, \frac{12}{7}, \frac{12}{7}]$ $[\frac{5}{7},\frac{5}{7},\frac{5}{7}]$ $[\frac{12}{7}, \frac{12}{7}, \frac{12}{7}]_{7}^{3}$ $[\frac{5}{7},\frac{5}{7},\frac{5}{7}]_{7}^{3}$ $[\ ]^{3}_{7}$ $[\ ]^{3}_{7}$ $t + 1$ $x^{8} + 2 x^{5} + 2$ $[5, 5, 5, 0]$ $[1]$ $z + 1$ $[1, 3, 6, 13]$
2.1.8.12a1.2 $x^{8} + 2 x^{5} + 2 x^{4} + 2$ $2$ $1$ $8$ $12$ $C_2^3:(C_7: C_3)$ (as 8T36) $3$ $7$ $[\frac{12}{7}, \frac{12}{7}, \frac{12}{7}]$ $[\frac{5}{7},\frac{5}{7},\frac{5}{7}]$ $[\frac{12}{7}, \frac{12}{7}, \frac{12}{7}]_{7}^{3}$ $[\frac{5}{7},\frac{5}{7},\frac{5}{7}]_{7}^{3}$ $[\ ]^{3}_{7}$ $[\ ]^{3}_{7}$ $t + 1$ $x^{8} + 2 x^{5} + 2 x^{4} + 2$ $[5, 5, 4, 0]$ $[1]$ $z + 1$ $[1, 2, 4, 13]$
2.1.8.16a1.1 $x^{8} + 4 x + 2$ $2$ $1$ $8$ $16$ $C_2^3:(C_7: C_3)$ (as 8T36) $3$ $7$ $[\frac{16}{7}, \frac{16}{7}, \frac{16}{7}]$ $[\frac{9}{7},\frac{9}{7},\frac{9}{7}]$ $[\frac{16}{7}, \frac{16}{7}, \frac{16}{7}]_{7}^{3}$ $[\frac{9}{7},\frac{9}{7},\frac{9}{7}]_{7}^{3}$ $[\ ]^{3}_{7}$ $[\ ]^{3}_{7}$ $t + 1$ $x^{8} + 4 x + 2$ $[9, 9, 8, 0]$ $[1]$ $z + 1$ $[1, 3, 7, 15]$
2.1.8.16a1.2 $x^{8} + 4 x^{2} + 4 x + 2$ $2$ $1$ $8$ $16$ $C_2^3:(C_7: C_3)$ (as 8T36) $3$ $7$ $[\frac{16}{7}, \frac{16}{7}, \frac{16}{7}]$ $[\frac{9}{7},\frac{9}{7},\frac{9}{7}]$ $[\frac{16}{7}, \frac{16}{7}, \frac{16}{7}]_{7}^{3}$ $[\frac{9}{7},\frac{9}{7},\frac{9}{7}]_{7}^{3}$ $[\ ]^{3}_{7}$ $[\ ]^{3}_{7}$ $t + 1$ $x^{8} + 4 x^{2} + 4 x + 2$ $[9, 9, 8, 0]$ $[1]$ $z + 1$ $[1, 3, 7, 15]$
2.1.8.18a1.1 $x^{8} + 4 x^{3} + 2$ $2$ $1$ $8$ $18$ $C_2^3:(C_7: C_3)$ (as 8T36) $3$ $7$ $[\frac{18}{7}, \frac{18}{7}, \frac{18}{7}]$ $[\frac{11}{7},\frac{11}{7},\frac{11}{7}]$ $[\frac{18}{7}, \frac{18}{7}, \frac{18}{7}]_{7}^{3}$ $[\frac{11}{7},\frac{11}{7},\frac{11}{7}]_{7}^{3}$ $[\ ]^{3}_{7}$ $[\ ]^{3}_{7}$ $t + 1$ $x^{8} + 4 x^{3} + 2$ $[11, 11, 8, 0]$ $[1]$ $z + 1$ $[1, 3, 7, 15]$
2.1.8.18a1.2 $x^{8} + 4 x^{4} + 4 x^{3} + 2$ $2$ $1$ $8$ $18$ $C_2^3:(C_7: C_3)$ (as 8T36) $3$ $7$ $[\frac{18}{7}, \frac{18}{7}, \frac{18}{7}]$ $[\frac{11}{7},\frac{11}{7},\frac{11}{7}]$ $[\frac{18}{7}, \frac{18}{7}, \frac{18}{7}]_{7}^{3}$ $[\frac{11}{7},\frac{11}{7},\frac{11}{7}]_{7}^{3}$ $[\ ]^{3}_{7}$ $[\ ]^{3}_{7}$ $t + 1$ $x^{8} + 4 x^{4} + 4 x^{3} + 2$ $[11, 11, 8, 0]$ $[1]$ $z + 1$ $[1, 3, 7, 15]$
2.1.8.18a1.3 $x^{8} + 4 x^{3} + 4 x^{2} + 2$ $2$ $1$ $8$ $18$ $C_2^3:(C_7: C_3)$ (as 8T36) $3$ $7$ $[\frac{18}{7}, \frac{18}{7}, \frac{18}{7}]$ $[\frac{11}{7},\frac{11}{7},\frac{11}{7}]$ $[\frac{18}{7}, \frac{18}{7}, \frac{18}{7}]_{7}^{3}$ $[\frac{11}{7},\frac{11}{7},\frac{11}{7}]_{7}^{3}$ $[\ ]^{3}_{7}$ $[\ ]^{3}_{7}$ $t + 1$ $x^{8} + 4 x^{3} + 4 x^{2} + 2$ $[11, 10, 8, 0]$ $[1]$ $z + 1$ $[1, 3, 7, 15]$
2.1.8.18a1.4 $x^{8} + 4 x^{4} + 4 x^{3} + 4 x^{2} + 2$ $2$ $1$ $8$ $18$ $C_2^3:(C_7: C_3)$ (as 8T36) $3$ $7$ $[\frac{18}{7}, \frac{18}{7}, \frac{18}{7}]$ $[\frac{11}{7},\frac{11}{7},\frac{11}{7}]$ $[\frac{18}{7}, \frac{18}{7}, \frac{18}{7}]_{7}^{3}$ $[\frac{11}{7},\frac{11}{7},\frac{11}{7}]_{7}^{3}$ $[\ ]^{3}_{7}$ $[\ ]^{3}_{7}$ $t + 1$ $x^{8} + 4 x^{4} + 4 x^{3} + 4 x^{2} + 2$ $[11, 10, 8, 0]$ $[1]$ $z + 1$ $[1, 3, 7, 15]$
2.1.8.20a1.1 $x^{8} + 4 x^{5} + 2$ $2$ $1$ $8$ $20$ $C_2^3:(C_7: C_3)$ (as 8T36) $3$ $7$ $[\frac{20}{7}, \frac{20}{7}, \frac{20}{7}]$ $[\frac{13}{7},\frac{13}{7},\frac{13}{7}]$ $[\frac{20}{7}, \frac{20}{7}, \frac{20}{7}]_{7}^{3}$ $[\frac{13}{7},\frac{13}{7},\frac{13}{7}]_{7}^{3}$ $[\ ]^{3}_{7}$ $[\ ]^{3}_{7}$ $t + 1$ $x^{8} + 4 x^{5} + 2$ $[13, 13, 8, 0]$ $[1]$ $z + 1$ $[1, 3, 7, 15]$
2.1.8.20a1.2 $x^{8} + 4 x^{6} + 4 x^{5} + 2$ $2$ $1$ $8$ $20$ $C_2^3:(C_7: C_3)$ (as 8T36) $3$ $7$ $[\frac{20}{7}, \frac{20}{7}, \frac{20}{7}]$ $[\frac{13}{7},\frac{13}{7},\frac{13}{7}]$ $[\frac{20}{7}, \frac{20}{7}, \frac{20}{7}]_{7}^{3}$ $[\frac{13}{7},\frac{13}{7},\frac{13}{7}]_{7}^{3}$ $[\ ]^{3}_{7}$ $[\ ]^{3}_{7}$ $t + 1$ $x^{8} + 4 x^{6} + 4 x^{5} + 2$ $[13, 13, 8, 0]$ $[1]$ $z + 1$ $[1, 3, 7, 15]$
2.1.8.20a1.3 $x^{8} + 4 x^{5} + 4 x^{4} + 2$ $2$ $1$ $8$ $20$ $C_2^3:(C_7: C_3)$ (as 8T36) $3$ $7$ $[\frac{20}{7}, \frac{20}{7}, \frac{20}{7}]$ $[\frac{13}{7},\frac{13}{7},\frac{13}{7}]$ $[\frac{20}{7}, \frac{20}{7}, \frac{20}{7}]_{7}^{3}$ $[\frac{13}{7},\frac{13}{7},\frac{13}{7}]_{7}^{3}$ $[\ ]^{3}_{7}$ $[\ ]^{3}_{7}$ $t + 1$ $x^{8} + 4 x^{5} + 4 x^{4} + 2$ $[13, 13, 8, 0]$ $[1]$ $z + 1$ $[1, 3, 7, 15]$
2.1.8.20a1.4 $x^{8} + 4 x^{6} + 4 x^{5} + 4 x^{4} + 2$ $2$ $1$ $8$ $20$ $C_2^3:(C_7: C_3)$ (as 8T36) $3$ $7$ $[\frac{20}{7}, \frac{20}{7}, \frac{20}{7}]$ $[\frac{13}{7},\frac{13}{7},\frac{13}{7}]$ $[\frac{20}{7}, \frac{20}{7}, \frac{20}{7}]_{7}^{3}$ $[\frac{13}{7},\frac{13}{7},\frac{13}{7}]_{7}^{3}$ $[\ ]^{3}_{7}$ $[\ ]^{3}_{7}$ $t + 1$ $x^{8} + 4 x^{6} + 4 x^{5} + 4 x^{4} + 2$ $[13, 13, 8, 0]$ $[1]$ $z + 1$ $[1, 3, 7, 15]$
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