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Results (11 matches)

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Label Polynomial $p$ $e$ $f$ $c$ Galois group Visible slopes Slope content Unram. Ext. Eisen. Poly.
5.8.0.1 $x^{8} + x^{4} + 3 x^{2} + 4 x + 2$ $5$ $1$ $8$ $0$ $C_8$ (as 8T1) $[\ ]$ $[\ ]^{8}$ $t^{8} + t^{4} + 3 t^{2} + 4 t + 2$ $x - 5$
5.8.4.1 $x^{8} + 80 x^{7} + 2428 x^{6} + 33688 x^{5} + 195810 x^{4} + 305952 x^{3} + 870132 x^{2} + 1037416 x + 503089$ $5$ $2$ $4$ $4$ $C_4\times C_2$ (as 8T2) $[\ ]$ $[\ ]_{2}^{4}$ $t^{4} + 4 t^{2} + 4 t + 2$ $x^{2} + 20 x + 5$
5.8.4.2 $x^{8} + 100 x^{4} - 500 x^{2} + 1250$ $5$ $2$ $4$ $4$ $C_8$ (as 8T1) $[\ ]$ $[\ ]_{2}^{4}$ $t^{4} + 4 t^{2} + 4 t + 2$ $x^{2} + 5 t$
5.8.6.1 $x^{8} + 16 x^{7} + 104 x^{6} + 352 x^{5} + 674 x^{4} + 784 x^{3} + 776 x^{2} + 928 x + 721$ $5$ $4$ $2$ $6$ $C_4\times C_2$ (as 8T2) $[\ ]$ $[\ ]_{4}^{2}$ $t^{2} + 4 t + 2$ $x^{4} + 5$
5.8.6.2 $x^{8} + 10 x^{4} - 25$ $5$ $4$ $2$ $6$ $C_4\times C_2$ (as 8T2) $[\ ]$ $[\ ]_{4}^{2}$ $t^{2} + 4 t + 2$ $x^{4} + 5 t + 15$
5.8.6.3 $x^{8} - 50 x^{4} - 175$ $5$ $4$ $2$ $6$ $C_8$ (as 8T1) $[\ ]$ $[\ ]_{4}^{2}$ $t^{2} + 4 t + 2$ $x^{4} + 20 t + 15$
5.8.6.4 $x^{8} - 20 x^{4} + 50$ $5$ $4$ $2$ $6$ $C_8$ (as 8T1) $[\ ]$ $[\ ]_{4}^{2}$ $t^{2} + 4 t + 2$ $x^{4} + 5 t$
5.8.7.1 $x^{8} + 20$ $5$ $8$ $1$ $7$ $C_8:C_2$ (as 8T7) $[\ ]$ $[\ ]_{8}^{2}$ $t + 3$ $x^{8} + 20$
5.8.7.2 $x^{8} + 5$ $5$ $8$ $1$ $7$ $C_8:C_2$ (as 8T7) $[\ ]$ $[\ ]_{8}^{2}$ $t + 3$ $x^{8} + 5$
5.8.7.3 $x^{8} + 10$ $5$ $8$ $1$ $7$ $C_8:C_2$ (as 8T7) $[\ ]$ $[\ ]_{8}^{2}$ $t + 3$ $x^{8} + 10$
5.8.7.4 $x^{8} + 15$ $5$ $8$ $1$ $7$ $C_8:C_2$ (as 8T7) $[\ ]$ $[\ ]_{8}^{2}$ $t + 3$ $x^{8} + 15$
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