$p$-adic field search results

Results (20 matches)

 

Label	$n$	Polynomial	$p$	$e$	$f$	$c$	Galois group	$u$	$t$	Visible slopes	Slope content	Ind. of Insep.	Assoc. Inertia
7.12.0.1	$12$	x^12 + 2x^8 + 5x^7 + 3x^6 + 2x^5 + 4x^4 + 5x^2 + 3	$7$	$1$	$12$	$0$	$C_{12}$ (as 12T1)	$12$	$1$	$[\ ]$	$[\ ]^{12}$	$[0]$	$[]$
7.12.6.1	$12$	x^12 + 44x^10 + 10x^9 + 786x^8 + 22x^7 + 6899x^6 - 3434x^5 + 31050x^4 - 28440x^3 + 84557x^2 - 48082x + 107648	$7$	$2$	$6$	$6$	$C_6\times C_2$ (as 12T2)	$6$	$2$	$[\ ]$	$[\ ]_{2}^{6}$	$[0]$	$[1]$
7.12.6.2	$12$	x^12 + 49x^8 - 1715x^6 + 9604x^4 - 100842x^2 + 352947	$7$	$2$	$6$	$6$	$C_{12}$ (as 12T1)	$6$	$2$	$[\ ]$	$[\ ]_{2}^{6}$	$[0]$	$[1]$
7.12.8.1	$12$	x^12 + 15x^10 + 40x^9 + 84x^8 + 120x^7 + 53x^6 + 414x^5 - 1293x^4 - 1830x^3 + 10968x^2 - 13836x + 12004	$7$	$3$	$4$	$8$	$C_{12}$ (as 12T1)	$4$	$3$	$[\ ]$	$[\ ]_{3}^{4}$	$[0]$	$[1]$
7.12.8.2	$12$	x^12 - 70x^9 + 1519x^6 - 4802x^3 + 21609	$7$	$3$	$4$	$8$	$C_{12}$ (as 12T1)	$4$	$3$	$[\ ]$	$[\ ]_{3}^{4}$	$[0]$	$[1]$
7.12.8.3	$12$	x^12 + 245x^6 - 1372x^3 + 7203	$7$	$3$	$4$	$8$	$C_{12}$ (as 12T1)	$4$	$3$	$[\ ]$	$[\ ]_{3}^{4}$	$[0]$	$[1]$
7.12.9.1	$12$	x^12 + 24x^11 + 216x^10 + 880x^9 + 1605x^8 + 2064x^7 + 6576x^6 + 11904x^5 + 8307x^4 - 50984x^3 - 57096x^2 + 58128x + 76871	$7$	$4$	$3$	$9$	$D_4 \times C_3$ (as 12T14)	$6$	$4$	$[\ ]$	$[\ ]_{4}^{6}$	$[0]$	$[2]$
7.12.9.2	$12$	x^12 - 42x^8 - 1372	$7$	$4$	$3$	$9$	$D_4 \times C_3$ (as 12T14)	$6$	$4$	$[\ ]$	$[\ ]_{4}^{6}$	$[0]$	$[2]$
7.12.10.1	$12$	x^12 + 36x^11 + 558x^10 + 4860x^9 + 26055x^8 + 88776x^7 + 193010x^6 + 266580x^5 + 237645x^4 + 153900x^3 + 137808x^2 + 210600x + 184108	$7$	$6$	$2$	$10$	$C_6\times C_2$ (as 12T2)	$2$	$6$	$[\ ]$	$[\ ]_{6}^{2}$	$[0]$	$[1]$
7.12.10.2	$12$	x^12 + 14x^6 - 245	$7$	$6$	$2$	$10$	$C_6\times C_2$ (as 12T2)	$2$	$6$	$[\ ]$	$[\ ]_{6}^{2}$	$[0]$	$[1]$
7.12.10.3	$12$	x^12 - 1176	$7$	$6$	$2$	$10$	$C_6\times C_2$ (as 12T2)	$2$	$6$	$[\ ]$	$[\ ]_{6}^{2}$	$[0]$	$[1]$
7.12.10.4	$12$	x^12 - 42x^6 + 147	$7$	$6$	$2$	$10$	$C_{12}$ (as 12T1)	$2$	$6$	$[\ ]$	$[\ ]_{6}^{2}$	$[0]$	$[1]$
7.12.10.5	$12$	x^12 - 154x^6 - 1421	$7$	$6$	$2$	$10$	$C_{12}$ (as 12T1)	$2$	$6$	$[\ ]$	$[\ ]_{6}^{2}$	$[0]$	$[1]$
7.12.10.6	$12$	x^12 - 28x^6 - 98	$7$	$6$	$2$	$10$	$C_{12}$ (as 12T1)	$2$	$6$	$[\ ]$	$[\ ]_{6}^{2}$	$[0]$	$[1]$
7.12.11.1	$12$	x^12 + 14	$7$	$12$	$1$	$11$	$D_4 \times C_3$ (as 12T14)	$2$	$12$	$[\ ]$	$[\ ]_{12}^{2}$	$[0]$	$[2]$
7.12.11.2	$12$	x^12 + 7	$7$	$12$	$1$	$11$	$D_4 \times C_3$ (as 12T14)	$2$	$12$	$[\ ]$	$[\ ]_{12}^{2}$	$[0]$	$[2]$
7.12.11.3	$12$	x^12 + 28	$7$	$12$	$1$	$11$	$D_4 \times C_3$ (as 12T14)	$2$	$12$	$[\ ]$	$[\ ]_{12}^{2}$	$[0]$	$[2]$
7.12.11.4	$12$	x^12 + 42	$7$	$12$	$1$	$11$	$D_4 \times C_3$ (as 12T14)	$2$	$12$	$[\ ]$	$[\ ]_{12}^{2}$	$[0]$	$[2]$
7.12.11.5	$12$	x^12 + 21	$7$	$12$	$1$	$11$	$D_4 \times C_3$ (as 12T14)	$2$	$12$	$[\ ]$	$[\ ]_{12}^{2}$	$[0]$	$[2]$
7.12.11.6	$12$	x^12 + 35	$7$	$12$	$1$	$11$	$D_4 \times C_3$ (as 12T14)	$2$	$12$	$[\ ]$	$[\ ]_{12}^{2}$	$[0]$	$[2]$