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Results (8 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
3.8.0.1 $x^{8} + 2 x^{5} + x^{4} + 2 x^{2} + 2 x + 2$ $3$ $1$ $8$ $0$ $C_8$ (as 8T1) $8$ $1$ $[\ ]$ $[\ ]^{8}$ $t^{8} + 2 t^{5} + t^{4} + 2 t^{2} + 2 t + 2$ $x - 3$ $[0]$ $[\ ]$
3.8.4.1 $x^{8} + 4 x^{7} + 16 x^{6} + 36 x^{5} + 94 x^{4} + 116 x^{3} + 144 x^{2} + 36 x + 229$ $3$ $2$ $4$ $4$ $C_4\times C_2$ (as 8T2) $4$ $2$ $[\ ]$ $[\ ]_{2}^{4}$ $t^{4} + 2 t^{3} + 2$ $x^{2} + 3$ $[0]$ $[1]$
3.8.4.2 $x^{8} - 6 x^{6} + 162$ $3$ $2$ $4$ $4$ $C_8$ (as 8T1) $4$ $2$ $[\ ]$ $[\ ]_{2}^{4}$ $t^{4} + 2 t^{3} + 2$ $x^{2} + 3 t$ $[0]$ $[1]$
3.8.6.1 $x^{8} + 9$ $3$ $4$ $2$ $6$ $Q_8$ (as 8T5) $2$ $4$ $[\ ]$ $[\ ]_{4}^{2}$ $t^{2} + 2 t + 2$ $x^{4} + 3 t + 3$ $[0]$ $[1]$
3.8.6.2 $x^{8} + 6 x^{5} + 6 x^{4} + 18 x^{2} + 18 x + 9$ $3$ $4$ $2$ $6$ $D_4$ (as 8T4) $2$ $4$ $[\ ]$ $[\ ]_{4}^{2}$ $t^{2} + 2 t + 2$ $x^{4} + \left(3 t + 6\right) x + 3$ $[0]$ $[1]$
3.8.6.3 $x^{8} - 6 x^{4} + 18$ $3$ $4$ $2$ $6$ $C_8:C_2$ (as 8T7) $4$ $4$ $[\ ]$ $[\ ]_{4}^{4}$ $t^{2} + 2 t + 2$ $x^{4} + 3 t$ $[0]$ $[1]$
3.8.7.1 $x^{8} + 3$ $3$ $8$ $1$ $7$ $QD_{16}$ (as 8T8) $2$ $8$ $[\ ]$ $[\ ]_{8}^{2}$ $t + 1$ $x^{8} + 3$ $[0]$ $[2]$
3.8.7.2 $x^{8} + 6$ $3$ $8$ $1$ $7$ $QD_{16}$ (as 8T8) $2$ $8$ $[\ ]$ $[\ ]_{8}^{2}$ $t + 1$ $x^{8} + 6$ $[0]$ $[2]$
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