pp-adic field search results

Results (15 matches)

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Label	$n$	Polynomial	$p$	$e$	$f$	$c$	Galois group	$u$	$t$	Visible slopes	Slope content	Unram. Ext.	Eisen. Poly.	Ind. of Insep.	Assoc. Inertia
17.8.0.1	$8$	$x^{8} + 11 x^{4} + 12 x^{3} + 6 x + 3$	$17$	$1$	$8$	$0$	$C_8$ (as 8T1)	$8$	$1$	$[\ ]$	$[\ ]^{8}$	$t^{8} + 11 t^{4} + 12 t^{3} + 6 t + 3$	$x - 17$	$[0]$	$[\ ]$
17.8.4.1	$8$	$x^{8} + 612 x^{7} + 140536 x^{6} + 14363966 x^{5} + 553913435 x^{4} + 345855654 x^{3} + 4032327212 x^{2} + 6379401496 x + 2294776272$	$17$	$2$	$4$	$4$	$C_4\times C_2$ (as 8T2)	$4$	$2$	$[\ ]$	$[\ ]_{2}^{4}$	$t^{4} + 7 t^{2} + 10 t + 3$	$x^{2} + 153 x + 17$	$[0]$	$[1]$
17.8.4.2	$8$	$x^{8} + 2023 x^{4} - 49130 x^{2} + 250563$	$17$	$2$	$4$	$4$	$C_8$ (as 8T1)	$4$	$2$	$[\ ]$	$[\ ]_{2}^{4}$	$t^{4} + 7 t^{2} + 10 t + 3$	$x^{2} + 17 t$	$[0]$	$[1]$
17.8.6.1	$8$	$x^{8} + 64 x^{7} + 1548 x^{6} + 16960 x^{5} + 74840 x^{4} + 51968 x^{3} + 39432 x^{2} + 270464 x + 1062564$	$17$	$4$	$2$	$6$	$C_4\times C_2$ (as 8T2)	$2$	$4$	$[\ ]$	$[\ ]_{4}^{2}$	$t^{2} + 16 t + 3$	$x^{4} + 17$	$[0]$	$[1]$
17.8.6.2	$8$	$x^{8} + 204 x^{4} - 7225$	$17$	$4$	$2$	$6$	$C_4\times C_2$ (as 8T2)	$2$	$4$	$[\ ]$	$[\ ]_{4}^{2}$	$t^{2} + 16 t + 3$	$x^{4} + 17 t + 238$	$[0]$	$[1]$
17.8.6.3	$8$	$x^{8} - 272 x^{4} + 867$	$17$	$4$	$2$	$6$	$C_8$ (as 8T1)	$2$	$4$	$[\ ]$	$[\ ]_{4}^{2}$	$t^{2} + 16 t + 3$	$x^{4} + 17 t$	$[0]$	$[1]$
17.8.6.4	$8$	$x^{8} - 3604 x^{4} - 719321$	$17$	$4$	$2$	$6$	$C_8$ (as 8T1)	$2$	$4$	$[\ ]$	$[\ ]_{4}^{2}$	$t^{2} + 16 t + 3$	$x^{4} + 255 t + 238$	$[0]$	$[1]$
17.8.7.1	$8$	$x^{8} + 68$	$17$	$8$	$1$	$7$	$C_8$ (as 8T1)	$1$	$8$	$[\ ]$	$[\ ]_{8}$	$t + 14$	$x^{8} + 68$	$[0]$	$[1]$
17.8.7.2	$8$	$x^{8} + 136$	$17$	$8$	$1$	$7$	$C_8$ (as 8T1)	$1$	$8$	$[\ ]$	$[\ ]_{8}$	$t + 14$	$x^{8} + 136$	$[0]$	$[1]$
17.8.7.3	$8$	$x^{8} + 17$	$17$	$8$	$1$	$7$	$C_8$ (as 8T1)	$1$	$8$	$[\ ]$	$[\ ]_{8}$	$t + 14$	$x^{8} + 17$	$[0]$	$[1]$
17.8.7.4	$8$	$x^{8} + 34$	$17$	$8$	$1$	$7$	$C_8$ (as 8T1)	$1$	$8$	$[\ ]$	$[\ ]_{8}$	$t + 14$	$x^{8} + 34$	$[0]$	$[1]$
17.8.7.5	$8$	$x^{8} + 119$	$17$	$8$	$1$	$7$	$C_8$ (as 8T1)	$1$	$8$	$[\ ]$	$[\ ]_{8}$	$t + 14$	$x^{8} + 119$	$[0]$	$[1]$
17.8.7.6	$8$	$x^{8} + 102$	$17$	$8$	$1$	$7$	$C_8$ (as 8T1)	$1$	$8$	$[\ ]$	$[\ ]_{8}$	$t + 14$	$x^{8} + 102$	$[0]$	$[1]$
17.8.7.7	$8$	$x^{8} + 51$	$17$	$8$	$1$	$7$	$C_8$ (as 8T1)	$1$	$8$	$[\ ]$	$[\ ]_{8}$	$t + 14$	$x^{8} + 51$	$[0]$	$[1]$
17.8.7.8	$8$	$x^{8} + 85$	$17$	$8$	$1$	$7$	$C_8$ (as 8T1)	$1$	$8$	$[\ ]$	$[\ ]_{8}$	$t + 14$	$x^{8} + 85$	$[0]$	$[1]$

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