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Degree Residue characteristic Galois group Galois unramified degree Assoc. Inertia
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Results (24 matches)

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Label Polynomial $p$ $e$ $f$ $c$ Galois group Visible slopes Slope content Unram. Ext. Eisen. Poly.
2.8.8.3 $x^{8} + 2 x^{7} + 32 x^{6} + 116 x^{5} + 456 x^{4} + 696 x^{3} + 1152 x^{2} + 432 x + 1296$ $2$ $2$ $4$ $8$ $C_2^3: C_4$ (as 8T20) $[2]$ $[2, 2, 2]^{4}$ $t^{4} + t + 1$ $x^{2} + \left(2 t^{3} + 2 t^{2} + 2\right) x + 6$
2.8.12.4 $x^{8} + 8 x^{6} - 16 x^{5} - 376 x^{4} - 128 x^{3} + 8928 x^{2} + 21056 x + 13008$ $2$ $2$ $4$ $12$ $C_2^3: C_4$ (as 8T20) $[3]$ $[2, 2, 3]^{4}$ $t^{4} + t + 1$ $x^{2} + 4 t x + 4 t^{2} + 12 t + 2$
2.8.16.18 $x^{8} + 12 x^{6} + 4 x^{5} + 52 x^{4} + 24 x^{3} + 112 x^{2} + 56 x + 76$ $2$ $4$ $2$ $16$ $C_2^3: C_4$ (as 8T20) $[2, 3]$ $[2, 3, 3]^{4}$ $t^{2} + t + 1$ $x^{4} + 6 x^{2} + \left(4 t + 4\right) x + 4 t + 10$
2.8.16.19 $x^{8} + 8 x^{7} + 16 x^{6} - 4 x^{5} + 12 x^{4} + 88 x^{3} + 40 x^{2} - 8 x + 76$ $2$ $4$ $2$ $16$ $C_2^3: C_4$ (as 8T20) $[2, 3]$ $[2, 3, 3]^{4}$ $t^{2} + t + 1$ $x^{4} + 4 x^{3} + \left(4 t + 2\right) x^{2} + 4 t x + 4 t + 10$
2.8.20.10 $x^{8} + 8 x^{7} + 40 x^{6} + 112 x^{5} + 204 x^{4} + 176 x^{3} + 16 x^{2} - 32 x + 52$ $2$ $4$ $2$ $20$ $C_2^3: C_4$ (as 8T20) $[3, 7/2]$ $[2, 2, 3, 7/2]^{2}$ $t^{2} + t + 1$ $x^{4} + 4 x^{3} + 12 x^{2} + 8 x + 8 t + 2$
2.8.20.11 $x^{8} + 8 x^{7} + 4 x^{6} - 48 x^{5} + 152 x^{4} + 32 x^{3} + 168 x^{2} + 124$ $2$ $4$ $2$ $20$ $C_2^3: C_4$ (as 8T20) $[3, 7/2]$ $[2, 2, 3, 7/2]^{2}$ $t^{2} + t + 1$ $x^{4} + 4 x^{3} + 12 t x^{2} + 12 t + 10$
2.8.20.12 $x^{8} + 8 x^{7} + 32 x^{6} + 72 x^{5} + 92 x^{4} + 48 x^{3} + 32 x^{2} + 80 x + 52$ $2$ $4$ $2$ $20$ $C_2^3: C_4$ (as 8T20) $[3, 7/2]$ $[2, 2, 3, 7/2]^{2}$ $t^{2} + t + 1$ $x^{4} + 4 x^{3} + 8 x^{2} + \left(8 t + 8\right) x + 8 t + 2$
2.8.20.9 $x^{8} + 8 x^{7} + 36 x^{6} + 80 x^{5} + 112 x^{4} + 24 x^{2} + 12$ $2$ $4$ $2$ $20$ $C_2^3: C_4$ (as 8T20) $[3, 7/2]$ $[2, 2, 3, 7/2]^{2}$ $t^{2} + t + 1$ $x^{4} + 4 x^{3} + \left(4 t + 12\right) x^{2} + 4 t + 2$
2.8.28.13 $x^{8} + 8 x^{7} + 8 x^{5} + 12 x^{4} + 24 x^{2} + 10$ $2$ $8$ $1$ $28$ $C_2^3: C_4$ (as 8T20) $[3, 4, 17/4]$ $[2, 3, 7/2, 4, 17/4]$ $t + 1$ $x^{8} + 8 x^{7} + 8 x^{5} + 12 x^{4} + 24 x^{2} + 10$
2.8.28.14 $x^{8} + 8 x^{7} + 8 x^{5} + 12 x^{4} + 8 x^{2} + 2$ $2$ $8$ $1$ $28$ $C_2^3: C_4$ (as 8T20) $[3, 4, 17/4]$ $[2, 3, 7/2, 4, 17/4]$ $t + 1$ $x^{8} + 8 x^{7} + 8 x^{5} + 12 x^{4} + 8 x^{2} + 2$
2.8.28.17 $x^{8} + 8 x^{7} + 8 x^{5} + 12 x^{4} + 8 x^{2} + 26$ $2$ $8$ $1$ $28$ $C_2^3: C_4$ (as 8T20) $[3, 4, 17/4]$ $[2, 3, 7/2, 4, 17/4]$ $t + 1$ $x^{8} + 8 x^{7} + 8 x^{5} + 12 x^{4} + 8 x^{2} + 26$
2.8.28.18 $x^{8} + 8 x^{7} + 8 x^{5} + 12 x^{4} + 24 x^{2} + 18$ $2$ $8$ $1$ $28$ $C_2^3: C_4$ (as 8T20) $[3, 4, 17/4]$ $[2, 3, 7/2, 4, 17/4]$ $t + 1$ $x^{8} + 8 x^{7} + 8 x^{5} + 12 x^{4} + 24 x^{2} + 18$
2.8.28.19 $x^{8} + 8 x^{5} + 12 x^{4} + 24 x^{2} + 10$ $2$ $8$ $1$ $28$ $C_2^3: C_4$ (as 8T20) $[3, 4, 17/4]$ $[2, 3, 7/2, 4, 17/4]$ $t + 1$ $x^{8} + 8 x^{5} + 12 x^{4} + 24 x^{2} + 10$
2.8.28.20 $x^{8} + 8 x^{5} + 12 x^{4} + 8 x^{2} + 2$ $2$ $8$ $1$ $28$ $C_2^3: C_4$ (as 8T20) $[3, 4, 17/4]$ $[2, 3, 7/2, 4, 17/4]$ $t + 1$ $x^{8} + 8 x^{5} + 12 x^{4} + 8 x^{2} + 2$
2.8.28.25 $x^{8} + 8 x^{5} + 12 x^{4} + 24 x^{2} + 2$ $2$ $8$ $1$ $28$ $C_2^3: C_4$ (as 8T20) $[3, 4, 17/4]$ $[2, 3, 7/2, 4, 17/4]$ $t + 1$ $x^{8} + 8 x^{5} + 12 x^{4} + 24 x^{2} + 2$
2.8.28.26 $x^{8} + 8 x^{5} + 12 x^{4} + 8 x^{2} + 26$ $2$ $8$ $1$ $28$ $C_2^3: C_4$ (as 8T20) $[3, 4, 17/4]$ $[2, 3, 7/2, 4, 17/4]$ $t + 1$ $x^{8} + 8 x^{5} + 12 x^{4} + 8 x^{2} + 26$
2.8.28.27 $x^{8} + 8 x^{7} + 8 x^{5} + 12 x^{4} + 8 x^{2} + 18$ $2$ $8$ $1$ $28$ $C_2^3: C_4$ (as 8T20) $[3, 4, 17/4]$ $[2, 3, 7/2, 4, 17/4]$ $t + 1$ $x^{8} + 8 x^{7} + 8 x^{5} + 12 x^{4} + 8 x^{2} + 18$
2.8.28.3 $x^{8} + 8 x^{5} + 12 x^{4} + 24 x^{2} + 26$ $2$ $8$ $1$ $28$ $C_2^3: C_4$ (as 8T20) $[3, 4, 17/4]$ $[2, 3, 7/2, 4, 17/4]$ $t + 1$ $x^{8} + 8 x^{5} + 12 x^{4} + 24 x^{2} + 26$
2.8.28.31 $x^{8} + 8 x^{5} + 12 x^{4} + 24 x^{2} + 18$ $2$ $8$ $1$ $28$ $C_2^3: C_4$ (as 8T20) $[3, 4, 17/4]$ $[2, 3, 7/2, 4, 17/4]$ $t + 1$ $x^{8} + 8 x^{5} + 12 x^{4} + 24 x^{2} + 18$
2.8.28.32 $x^{8} + 8 x^{7} + 8 x^{5} + 12 x^{4} + 8 x^{2} + 10$ $2$ $8$ $1$ $28$ $C_2^3: C_4$ (as 8T20) $[3, 4, 17/4]$ $[2, 3, 7/2, 4, 17/4]$ $t + 1$ $x^{8} + 8 x^{7} + 8 x^{5} + 12 x^{4} + 8 x^{2} + 10$
2.8.28.4 $x^{8} + 8 x^{7} + 8 x^{5} + 12 x^{4} + 24 x^{2} + 2$ $2$ $8$ $1$ $28$ $C_2^3: C_4$ (as 8T20) $[3, 4, 17/4]$ $[2, 3, 7/2, 4, 17/4]$ $t + 1$ $x^{8} + 8 x^{7} + 8 x^{5} + 12 x^{4} + 24 x^{2} + 2$
2.8.28.5 $x^{8} + 8 x^{7} + 8 x^{5} + 12 x^{4} + 24 x^{2} + 26$ $2$ $8$ $1$ $28$ $C_2^3: C_4$ (as 8T20) $[3, 4, 17/4]$ $[2, 3, 7/2, 4, 17/4]$ $t + 1$ $x^{8} + 8 x^{7} + 8 x^{5} + 12 x^{4} + 24 x^{2} + 26$
2.8.28.6 $x^{8} + 8 x^{5} + 12 x^{4} + 8 x^{2} + 18$ $2$ $8$ $1$ $28$ $C_2^3: C_4$ (as 8T20) $[3, 4, 17/4]$ $[2, 3, 7/2, 4, 17/4]$ $t + 1$ $x^{8} + 8 x^{5} + 12 x^{4} + 8 x^{2} + 18$
2.8.28.7 $x^{8} + 8 x^{5} + 12 x^{4} + 8 x^{2} + 10$ $2$ $8$ $1$ $28$ $C_2^3: C_4$ (as 8T20) $[3, 4, 17/4]$ $[2, 3, 7/2, 4, 17/4]$ $t + 1$ $x^{8} + 8 x^{5} + 12 x^{4} + 8 x^{2} + 10$
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