$p$-adic field search results

Results (47 matches)

 

Label	$n$	Polynomial	$p$	$e$	$f$	$c$	Galois group	$u$	$t$	Visible slopes	Slope content	Ind. of Insep.	Assoc. Inertia
2.6.0.1	$6$	x^6 + x^4 + x^3 + x + 1	$2$	$1$	$6$	$0$	$C_6$ (as 6T1)	$6$	$1$	$[\ ]$	$[\ ]^{6}$	$[0]$	$[]$
2.6.4.1	$6$	x^6 + 3x^5 + 10x^4 + 19x^3 + 22x^2 + 11x + 7	$2$	$3$	$2$	$4$	$S_3$ (as 6T2)	$2$	$3$	$[\ ]$	$[\ ]_{3}^{2}$	$[0]$	$[1]$
2.6.4.2	$6$	x^6 - 2x^3 + 4	$2$	$3$	$2$	$4$	$S_3\times C_3$ (as 6T5)	$6$	$3$	$[\ ]$	$[\ ]_{3}^{6}$	$[0]$	$[1]$
2.6.6.1	$6$	x^6 + 6x^5 + 34x^4 + 80x^3 + 204x^2 + 216x + 216	$2$	$2$	$3$	$6$	$A_4$ (as 6T4)	$3$	$1$	$[2]$	$[2, 2]^{3}$	$[1, 0]$	$[1]$
2.6.6.2	$6$	x^6 + 6x^5 + 14x^4 + 24x^3 + 44x^2 + 8x + 72	$2$	$2$	$3$	$6$	$A_4\times C_2$ (as 6T6)	$6$	$1$	$[2]$	$[2, 2]^{6}$	$[1, 0]$	$[1]$
2.6.6.3	$6$	x^6 + 6x^5 + 20x^4 + 42x^3 + 55x^2 + 36x + 9	$2$	$2$	$3$	$6$	$C_6$ (as 6T1)	$3$	$1$	$[2]$	$[2]^{3}$	$[1, 0]$	$[1]$
2.6.6.4	$6$	x^6 - 4x^5 + 14x^4 - 24x^3 + 100x^2 + 48x + 88	$2$	$2$	$3$	$6$	$A_4\times C_2$ (as 6T6)	$3$	$1$	$[2]$	$[2, 2, 2]^{3}$	$[1, 0]$	$[1]$
2.6.6.5	$6$	x^6 + 6x^5 + 32x^4 + 90x^3 + 199x^2 + 204x + 149	$2$	$2$	$3$	$6$	$C_6$ (as 6T1)	$3$	$1$	$[2]$	$[2]^{3}$	$[1, 0]$	$[1]$
2.6.6.6	$6$	x^6 - 4x^5 + 30x^4 - 16x^3 + 164x^2 + 160x + 88	$2$	$2$	$3$	$6$	$A_4\times C_2$ (as 6T6)	$3$	$1$	$[2]$	$[2, 2, 2]^{3}$	$[1, 0]$	$[1]$
2.6.6.7	$6$	x^6 + 2x^2 + 2x + 2	$2$	$6$	$1$	$6$	$S_4$ (as 6T7)	$2$	$3$	$[4/3]$	$[4/3, 4/3]_{3}^{2}$	$[1, 0]$	$[1, 2]$
2.6.6.8	$6$	x^6 + 2x + 2	$2$	$6$	$1$	$6$	$S_4$ (as 6T8)	$2$	$3$	$[4/3]$	$[4/3, 4/3]_{3}^{2}$	$[1, 0]$	$[1, 2]$
2.6.8.1	$6$	x^6 + 2x^3 + 2	$2$	$6$	$1$	$8$	$D_{6}$ (as 6T3)	$2$	$3$	$[2]$	$[2]_{3}^{2}$	$[3, 0]$	$[1, 2]$
2.6.8.2	$6$	x^6 + 2x^4 + 2x^3 + 2	$2$	$6$	$1$	$8$	$S_4\times C_2$ (as 6T11)	$2$	$3$	$[2]$	$[4/3, 4/3, 2]_{3}^{2}$	$[3, 0]$	$[1, 2]$
2.6.8.3	$6$	x^6 + 2x^3 + 6	$2$	$6$	$1$	$8$	$D_{6}$ (as 6T3)	$2$	$3$	$[2]$	$[2]_{3}^{2}$	$[3, 0]$	$[1, 2]$
2.6.8.4	$6$	x^6 + 2x^4 + 2x^3 + 6	$2$	$6$	$1$	$8$	$S_4\times C_2$ (as 6T11)	$2$	$3$	$[2]$	$[4/3, 4/3, 2]_{3}^{2}$	$[3, 0]$	$[1, 2]$
2.6.9.1	$6$	x^6 + 44x^4 + 2x^3 + 589x^2 - 82x + 2367	$2$	$2$	$3$	$9$	$C_6$ (as 6T1)	$3$	$1$	$[3]$	$[3]^{3}$	$[2, 0]$	$[1]$
2.6.9.2	$6$	x^6 + 4x^5 - 10x^4 + 160x^3 + 1212x^2 + 2160x - 1048	$2$	$2$	$3$	$9$	$A_4\times C_2$ (as 6T6)	$3$	$1$	$[3]$	$[2, 2, 3]^{3}$	$[2, 0]$	$[1]$
2.6.9.3	$6$	x^6 + 12x^5 + 86x^4 + 352x^3 + 892x^2 + 1552x + 1384	$2$	$2$	$3$	$9$	$C_6$ (as 6T1)	$3$	$1$	$[3]$	$[3]^{3}$	$[2, 0]$	$[1]$
2.6.9.4	$6$	x^6 + 4x^5 + 14x^4 + 224x^3 + 1244x^2 + 3184x + 2376	$2$	$2$	$3$	$9$	$A_4\times C_2$ (as 6T6)	$3$	$1$	$[3]$	$[2, 2, 3]^{3}$	$[2, 0]$	$[1]$
2.6.9.5	$6$	x^6 + 12x^5 + 68x^4 + 226x^3 + 457x^2 + 514x + 243	$2$	$2$	$3$	$9$	$C_6$ (as 6T1)	$3$	$1$	$[3]$	$[3]^{3}$	$[2, 0]$	$[1]$
2.6.9.6	$6$	x^6 - 8x^5 + 86x^4 + 96x^3 + 860x^2 + 2976x + 2728	$2$	$2$	$3$	$9$	$A_4\times C_2$ (as 6T6)	$3$	$1$	$[3]$	$[2, 2, 3]^{3}$	$[2, 0]$	$[1]$
2.6.9.7	$6$	x^6 + 32x^4 + 2x^3 + 301x^2 - 58x + 811	$2$	$2$	$3$	$9$	$C_6$ (as 6T1)	$3$	$1$	$[3]$	$[3]^{3}$	$[2, 0]$	$[1]$
2.6.9.8	$6$	x^6 - 8x^5 + 62x^4 + 224x^3 + 316x^2 + 1184x + 1608	$2$	$2$	$3$	$9$	$A_4\times C_2$ (as 6T6)	$3$	$1$	$[3]$	$[2, 2, 3]^{3}$	$[2, 0]$	$[1]$
2.6.10.1	$6$	x^6 + 2x^5 + 4x^2 + 4x + 2	$2$	$6$	$1$	$10$	$S_4$ (as 6T7)	$2$	$3$	$[8/3]$	$[8/3, 8/3]_{3}^{2}$	$[5, 0]$	$[1, 2]$
2.6.10.2	$6$	x^6 + 2x^5 + 4x^4 + 4x + 2	$2$	$6$	$1$	$10$	$S_4$ (as 6T7)	$2$	$3$	$[8/3]$	$[8/3, 8/3]_{3}^{2}$	$[5, 0]$	$[1, 2]$
2.6.10.3	$6$	x^6 + 2x^5 + 4x + 2	$2$	$6$	$1$	$10$	$S_4$ (as 6T8)	$2$	$3$	$[8/3]$	$[8/3, 8/3]_{3}^{2}$	$[5, 0]$	$[1, 2]$
2.6.10.4	$6$	x^6 + 2x^5 + 4x^3 + 4x + 2	$2$	$6$	$1$	$10$	$S_4$ (as 6T8)	$2$	$3$	$[8/3]$	$[8/3, 8/3]_{3}^{2}$	$[5, 0]$	$[1, 2]$
2.6.10.5	$6$	x^6 + 2x^5 + 4x^3 + 4x^2 + 2	$2$	$6$	$1$	$10$	$S_4\times C_2$ (as 6T11)	$2$	$3$	$[8/3]$	$[2, 8/3, 8/3]_{3}^{2}$	$[5, 0]$	$[1, 2]$
2.6.10.6	$6$	x^6 + 2x^5 + 4x^2 + 2	$2$	$6$	$1$	$10$	$S_4\times C_2$ (as 6T11)	$2$	$3$	$[8/3]$	$[2, 8/3, 8/3]_{3}^{2}$	$[5, 0]$	$[1, 2]$
2.6.10.7	$6$	x^6 + 2x^5 + 4x^3 + 2	$2$	$6$	$1$	$10$	$S_4\times C_2$ (as 6T11)	$2$	$3$	$[8/3]$	$[2, 8/3, 8/3]_{3}^{2}$	$[5, 0]$	$[1, 2]$
2.6.10.8	$6$	x^6 + 2x^5 + 2	$2$	$6$	$1$	$10$	$S_4\times C_2$ (as 6T11)	$2$	$3$	$[8/3]$	$[2, 8/3, 8/3]_{3}^{2}$	$[5, 0]$	$[1, 2]$
2.6.11.1	$6$	x^6 + 4x^3 + 2	$2$	$6$	$1$	$11$	$D_{6}$ (as 6T3)	$2$	$3$	$[3]$	$[3]_{3}^{2}$	$[6, 0]$	$[1, 2]$
2.6.11.10	$6$	x^6 + 4x^2 + 2	$2$	$6$	$1$	$11$	$S_4\times C_2$ (as 6T11)	$2$	$3$	$[3]$	$[4/3, 4/3, 3]_{3}^{2}$	$[6, 0]$	$[1, 2]$
2.6.11.11	$6$	x^6 + 4x^4 + 4x + 14	$2$	$6$	$1$	$11$	$S_4\times C_2$ (as 6T11)	$2$	$3$	$[3]$	$[8/3, 8/3, 3]_{3}^{2}$	$[6, 0]$	$[1, 2]$
2.6.11.12	$6$	x^6 + 4x^4 + 4x^3 + 4x + 10	$2$	$6$	$1$	$11$	$S_4\times C_2$ (as 6T11)	$2$	$3$	$[3]$	$[8/3, 8/3, 3]_{3}^{2}$	$[6, 0]$	$[1, 2]$
2.6.11.13	$6$	x^6 + 10	$2$	$6$	$1$	$11$	$D_{6}$ (as 6T3)	$2$	$3$	$[3]$	$[3]_{3}^{2}$	$[6, 0]$	$[1, 2]$
2.6.11.14	$6$	x^6 + 4x^2 + 10	$2$	$6$	$1$	$11$	$S_4\times C_2$ (as 6T11)	$2$	$3$	$[3]$	$[4/3, 4/3, 3]_{3}^{2}$	$[6, 0]$	$[1, 2]$
2.6.11.15	$6$	x^6 + 4x^4 + 4x + 6	$2$	$6$	$1$	$11$	$S_4\times C_2$ (as 6T11)	$2$	$3$	$[3]$	$[8/3, 8/3, 3]_{3}^{2}$	$[6, 0]$	$[1, 2]$
2.6.11.16	$6$	x^6 + 4x^4 + 4x^3 + 4x + 2	$2$	$6$	$1$	$11$	$S_4\times C_2$ (as 6T11)	$2$	$3$	$[3]$	$[8/3, 8/3, 3]_{3}^{2}$	$[6, 0]$	$[1, 2]$
2.6.11.2	$6$	x^6 + 4x^5 + 4x^4 + 4x^3 + 4x^2 + 2	$2$	$6$	$1$	$11$	$S_4\times C_2$ (as 6T11)	$2$	$3$	$[3]$	$[4/3, 4/3, 3]_{3}^{2}$	$[6, 0]$	$[1, 2]$
2.6.11.3	$6$	x^6 + 4x^2 + 4x + 10	$2$	$6$	$1$	$11$	$S_4\times C_2$ (as 6T11)	$2$	$3$	$[3]$	$[8/3, 8/3, 3]_{3}^{2}$	$[6, 0]$	$[1, 2]$
2.6.11.4	$6$	x^6 + 4x^4 + 4x^2 + 4x + 2	$2$	$6$	$1$	$11$	$S_4\times C_2$ (as 6T11)	$2$	$3$	$[3]$	$[8/3, 8/3, 3]_{3}^{2}$	$[6, 0]$	$[1, 2]$
2.6.11.5	$6$	x^6 + 4x^3 + 10	$2$	$6$	$1$	$11$	$D_{6}$ (as 6T3)	$2$	$3$	$[3]$	$[3]_{3}^{2}$	$[6, 0]$	$[1, 2]$
2.6.11.6	$6$	x^6 + 4x^5 + 4x^4 + 4x^3 + 4x^2 + 10	$2$	$6$	$1$	$11$	$S_4\times C_2$ (as 6T11)	$2$	$3$	$[3]$	$[4/3, 4/3, 3]_{3}^{2}$	$[6, 0]$	$[1, 2]$
2.6.11.7	$6$	x^6 + 4x^2 + 4x + 2	$2$	$6$	$1$	$11$	$S_4\times C_2$ (as 6T11)	$2$	$3$	$[3]$	$[8/3, 8/3, 3]_{3}^{2}$	$[6, 0]$	$[1, 2]$
2.6.11.8	$6$	x^6 + 4x^5 + 4x^2 + 4x + 2	$2$	$6$	$1$	$11$	$S_4\times C_2$ (as 6T11)	$2$	$3$	$[3]$	$[8/3, 8/3, 3]_{3}^{2}$	$[6, 0]$	$[1, 2]$
2.6.11.9	$6$	x^6 + 4x^5 + 4x^2 + 2	$2$	$6$	$1$	$11$	$D_{6}$ (as 6T3)	$2$	$3$	$[3]$	$[3]_{3}^{2}$	$[6, 0]$	$[1, 2]$