$p$-adic field search results

Results (17 matches)

 

Label	$n$	Polynomial	$p$	$e$	$f$	$c$	Galois group	$u$	$t$	Visible slopes	Slope content	Ind. of Insep.	Assoc. Inertia
5.12.0.1	$12$	x^12 + x^7 + x^6 + 4x^4 + 4x^3 + 3x^2 + 2x + 2	$5$	$1$	$12$	$0$	$C_{12}$ (as 12T1)	$12$	$1$	$[\ ]$	$[\ ]^{12}$	$[0]$	$[]$
5.12.6.1	$12$	x^12 + 120x^11 + 6032x^10 + 163208x^9 + 2529528x^8 + 21853448x^7 + 92223962x^6 + 138649448x^5 + 223472880x^4 + 401794296x^3 + 295909124x^2 + 118616440x + 126881009	$5$	$2$	$6$	$6$	$C_6\times C_2$ (as 12T2)	$6$	$2$	$[\ ]$	$[\ ]_{2}^{6}$	$[0]$	$[1]$
5.12.6.2	$12$	x^12 + 25x^8 - 500x^6 + 625x^4 + 31250	$5$	$2$	$6$	$6$	$C_{12}$ (as 12T1)	$6$	$2$	$[\ ]$	$[\ ]_{2}^{6}$	$[0]$	$[1]$
5.12.8.1	$12$	x^12 + 12x^10 + 32x^9 + 54x^8 + 96x^7 - 50x^6 + 240x^5 - 360x^4 - 884x^3 + 4044x^2 - 3912x + 4173	$5$	$3$	$4$	$8$	$C_3 : C_4$ (as 12T5)	$4$	$3$	$[\ ]$	$[\ ]_{3}^{4}$	$[0]$	$[1]$
5.12.8.2	$12$	x^12 + 100x^6 - 500x^3 + 1250	$5$	$3$	$4$	$8$	$C_3\times (C_3 : C_4)$ (as 12T19)	$12$	$3$	$[\ ]$	$[\ ]_{3}^{12}$	$[0]$	$[1]$
5.12.9.1	$12$	x^12 - 30x^8 + 225x^4 + 1125	$5$	$4$	$3$	$9$	$C_{12}$ (as 12T1)	$3$	$4$	$[\ ]$	$[\ ]_{4}^{3}$	$[0]$	$[1]$
5.12.9.2	$12$	x^12 + 12x^10 + 12x^9 + 69x^8 + 108x^7 + 42x^6 - 396x^5 + 840x^4 + 252x^3 + 1476x^2 + 684x + 1601	$5$	$4$	$3$	$9$	$C_{12}$ (as 12T1)	$3$	$4$	$[\ ]$	$[\ ]_{4}^{3}$	$[0]$	$[1]$
5.12.9.3	$12$	x^12 + 75x^4 - 375	$5$	$4$	$3$	$9$	$C_{12}$ (as 12T1)	$3$	$4$	$[\ ]$	$[\ ]_{4}^{3}$	$[0]$	$[1]$
5.12.9.4	$12$	x^12 + 30x^8 + 600x^4 + 1000	$5$	$4$	$3$	$9$	$C_{12}$ (as 12T1)	$3$	$4$	$[\ ]$	$[\ ]_{4}^{3}$	$[0]$	$[1]$
5.12.10.1	$12$	x^12 + 20x^7 + 10x^6 + 50x^2 + 100x + 25	$5$	$6$	$2$	$10$	$D_6$ (as 12T3)	$2$	$6$	$[\ ]$	$[\ ]_{6}^{2}$	$[0]$	$[1]$
5.12.10.2	$12$	x^12 - 20x^6 - 100	$5$	$6$	$2$	$10$	$C_6\times S_3$ (as 12T18)	$6$	$6$	$[\ ]$	$[\ ]_{6}^{6}$	$[0]$	$[1]$
5.12.10.3	$12$	x^12 - 50x^6 - 175	$5$	$6$	$2$	$10$	$C_3 : C_4$ (as 12T5)	$2$	$6$	$[\ ]$	$[\ ]_{6}^{2}$	$[0]$	$[1]$
5.12.10.4	$12$	x^12 - 70x^6 + 425	$5$	$6$	$2$	$10$	$C_3\times (C_3 : C_4)$ (as 12T19)	$6$	$6$	$[\ ]$	$[\ ]_{6}^{6}$	$[0]$	$[1]$
5.12.11.1	$12$	x^12 + 20	$5$	$12$	$1$	$11$	$S_3 \times C_4$ (as 12T11)	$2$	$12$	$[\ ]$	$[\ ]_{12}^{2}$	$[0]$	$[2]$
5.12.11.2	$12$	x^12 + 5	$5$	$12$	$1$	$11$	$S_3 \times C_4$ (as 12T11)	$2$	$12$	$[\ ]$	$[\ ]_{12}^{2}$	$[0]$	$[2]$
5.12.11.3	$12$	x^12 + 10	$5$	$12$	$1$	$11$	$S_3 \times C_4$ (as 12T11)	$2$	$12$	$[\ ]$	$[\ ]_{12}^{2}$	$[0]$	$[2]$
5.12.11.4	$12$	x^12 + 15	$5$	$12$	$1$	$11$	$S_3 \times C_4$ (as 12T11)	$2$	$12$	$[\ ]$	$[\ ]_{12}^{2}$	$[0]$	$[2]$