$p$-adic field search results

Results (1-50 of 1823 matches)

 

Label	$n$	Polynomial	$p$	$e$	$f$	$c$	Galois group	$u$	$t$	Visible slopes	Slope content	Ind. of Insep.	Assoc. Inertia
2.8.0.1	$8$	x^8 + x^4 + x^3 + x^2 + 1	$2$	$1$	$8$	$0$	$C_8$ (as 8T1)	$8$	$1$	$[\ ]$	$[\ ]^{8}$	$[0]$	$[]$
2.8.8.1	$8$	x^8 + 8x^7 + 32x^6 + 82x^5 + 148x^4 + 184x^3 + 137x^2 + 44x + 5	$2$	$2$	$4$	$8$	$C_4\times C_2$ (as 8T2)	$4$	$1$	$[2]$	$[2]^{4}$	$[1, 0]$	$[1]$
2.8.8.10	$8$	x^8 - 6x^7 + 36x^6 - 60x^5 + 88x^4 + 136x^3 + 336x^2 + 400x + 144	$2$	$2$	$4$	$8$	$((C_8 : C_2):C_2):C_2$ (as 8T27)	$4$	$1$	$[2]$	$[2, 2, 2, 2]^{4}$	$[1, 0]$	$[1]$
2.8.8.11	$8$	x^8 + 4x^7 + 14x^6 + 32x^5 + 55x^4 + 60x^3 + 36x^2 + 18x + 9	$2$	$4$	$2$	$8$	$S_4$ (as 8T14)	$2$	$3$	$[4/3, 4/3]$	$[4/3, 4/3]_{3}^{2}$	$[1, 1, 0]$	$[1]$
2.8.8.12	$8$	x^8 - 2x^6 - 2x^5 + 8x^4 + 8x^3 - 4x + 4	$2$	$4$	$2$	$8$	$A_4\wr C_2$ (as 8T42)	$6$	$3$	$[4/3, 4/3]$	$[4/3, 4/3, 4/3, 4/3]_{3}^{6}$	$[1, 1, 0]$	$[1]$
2.8.8.13	$8$	x^8 + 2x + 2	$2$	$8$	$1$	$8$	$C_2^3:(C_7: C_3)$ (as 8T36)	$3$	$7$	$[8/7, 8/7, 8/7]$	$[8/7, 8/7, 8/7]_{7}^{3}$	$[1, 1, 1, 0]$	$[1]$
2.8.8.2	$8$	x^8 + 8x^7 + 56x^6 + 240x^5 + 816x^4 + 2048x^3 + 3776x^2 + 4928x + 3760	$2$	$2$	$4$	$8$	$C_2^2:C_4$ (as 8T10)	$4$	$1$	$[2]$	$[2, 2]^{4}$	$[1, 0]$	$[1]$
2.8.8.3	$8$	x^8 + 2x^7 + 32x^6 + 116x^5 + 456x^4 + 696x^3 + 1152x^2 + 432x + 1296	$2$	$2$	$4$	$8$	$C_2^3: C_4$ (as 8T20)	$4$	$1$	$[2]$	$[2, 2, 2]^{4}$	$[1, 0]$	$[1]$
2.8.8.4	$8$	x^8 + 8x^7 + 20x^6 + 8x^5 + 32x^4 + 224x^3 + 144x^2 - 224x + 752	$2$	$2$	$4$	$8$	$C_8$ (as 8T1)	$4$	$1$	$[2]$	$[2]^{4}$	$[1, 0]$	$[1]$
2.8.8.5	$8$	x^8 + 8x^7 + 56x^6 + 184x^5 + 576x^4 + 960x^3 + 1632x^2 + 1120x + 304	$2$	$2$	$4$	$8$	$C_8:C_2$ (as 8T7)	$4$	$1$	$[2]$	$[2, 2]^{4}$	$[1, 0]$	$[1]$
2.8.8.6	$8$	x^8 + 2x^7 + 24x^6 + 84x^5 + 264x^4 + 408x^3 + 384x^2 - 208x + 80	$2$	$2$	$4$	$8$	$(C_8:C_2):C_2$ (as 8T16)	$4$	$1$	$[2]$	$[2, 2, 2]^{4}$	$[1, 0]$	$[1]$
2.8.8.7	$8$	x^8 + 8x^7 + 40x^6 + 120x^5 + 232x^4 + 240x^3 + 160x^2 + 64x + 16	$2$	$2$	$4$	$8$	$((C_8 : C_2):C_2):C_2$ (as 8T27)	$4$	$1$	$[2]$	$[2, 2, 2, 2]^{4}$	$[1, 0]$	$[1]$
2.8.8.8	$8$	x^8 - 6x^7 + 40x^6 - 52x^5 + 192x^4 + 328x^3 + 1376x^2 + 1264x + 1328	$2$	$2$	$4$	$8$	$((C_8 : C_2):C_2):C_2$ (as 8T27)	$4$	$1$	$[2]$	$[2, 2, 2, 2]^{4}$	$[1, 0]$	$[1]$
2.8.8.9	$8$	x^8 + 8x^7 + 56x^6 + 216x^5 + 680x^4 + 1296x^3 + 2016x^2 + 1728x + 1296	$2$	$2$	$4$	$8$	$((C_8 : C_2):C_2):C_2$ (as 8T27)	$4$	$1$	$[2]$	$[2, 2, 2, 2]^{4}$	$[1, 0]$	$[1]$
2.8.10.1	$8$	x^8 + 2x^3 + 2	$2$	$8$	$1$	$10$	$C_2^3:(C_7: C_3)$ (as 8T36)	$3$	$7$	$[10/7, 10/7, 10/7]$	$[10/7, 10/7, 10/7]_{7}^{3}$	$[3, 3, 3, 0]$	$[1]$
2.8.10.2	$8$	x^8 + 2x^3 + 2x^2 + 2	$2$	$8$	$1$	$10$	$\textrm{GL(2,3)}$ (as 8T23)	$2$	$3$	$[4/3, 4/3, 3/2]$	$[4/3, 4/3, 3/2]_{3}^{2}$	$[3, 2, 2, 0]$	$[1, 1]$
2.8.10.3	$8$	x^8 + 2x^4 + 2x^3 + 2x^2 + 2	$2$	$8$	$1$	$10$	$\textrm{GL(2,3)}$ (as 8T23)	$2$	$3$	$[4/3, 4/3, 3/2]$	$[4/3, 4/3, 3/2]_{3}^{2}$	$[3, 2, 2, 0]$	$[1, 1]$
2.8.12.1	$8$	x^8 - 12x^7 + 52x^6 + 840x^5 + 3808x^4 + 10224x^3 + 17968x^2 + 20576x + 15216	$2$	$2$	$4$	$12$	$C_4\times C_2$ (as 8T2)	$4$	$1$	$[3]$	$[3]^{4}$	$[2, 0]$	$[1]$
2.8.12.10	$8$	x^8 + 68x^6 + 272x^5 + 928x^4 + 5376x^3 + 13680x^2 + 15552x + 92016	$2$	$2$	$4$	$12$	$((C_8 : C_2):C_2):C_2$ (as 8T27)	$4$	$1$	$[3]$	$[2, 2, 2, 3]^{4}$	$[2, 0]$	$[1]$
2.8.12.11	$8$	x^8 + 16x^7 + 92x^6 + 352x^5 + 1264x^4 + 2304x^3 + 6544x^2 - 256x + 12080	$2$	$2$	$4$	$12$	$((C_8 : C_2):C_2):C_2$ (as 8T27)	$4$	$1$	$[3]$	$[2, 2, 2, 3]^{4}$	$[2, 0]$	$[1]$
2.8.12.12	$8$	x^8 + 92x^6 + 144x^5 + 1232x^4 + 5248x^3 + 11152x^2 + 34752x + 49072	$2$	$2$	$4$	$12$	$((C_8 : C_2):C_2):C_2$ (as 8T27)	$4$	$1$	$[3]$	$[2, 2, 2, 3]^{4}$	$[2, 0]$	$[1]$
2.8.12.13	$8$	x^8 + 8x^7 + 28x^6 + 58x^5 + 87x^4 + 98x^3 + 58x^2 - 2x + 1	$2$	$4$	$2$	$12$	$D_4$ (as 8T4)	$2$	$1$	$[2, 2]$	$[2, 2]^{2}$	$[3, 3, 0]$	$[1]$
2.8.12.14	$8$	x^8 + 8x^7 + 28x^6 + 58x^5 + 95x^4 + 130x^3 + 58x^2 - 58x + 13	$2$	$4$	$2$	$12$	$D_4$ (as 8T4)	$2$	$1$	$[2, 2]$	$[2, 2]^{2}$	$[3, 3, 0]$	$[1]$
2.8.12.15	$8$	x^8 + 4x^7 + 4x^6 + 12	$2$	$4$	$2$	$12$	$C_2^2:C_4$ (as 8T10)	$4$	$1$	$[2, 2]$	$[2, 2]^{4}$	$[3, 3, 0]$	$[1]$
2.8.12.16	$8$	x^8 + 8x^7 + 32x^6 + 78x^5 + 137x^4 + 186x^3 + 128x^2 - 10x + 7	$2$	$4$	$2$	$12$	$A_4\times C_2$ (as 8T13)	$6$	$1$	$[2, 2]$	$[2, 2]^{6}$	$[3, 2, 0]$	$[3]$
2.8.12.17	$8$	x^8 + 4x^7 + 6x^6 + 4x^5 + 8x^4 + 8x^3 + 4x^2 + 4	$2$	$4$	$2$	$12$	$C_2^4:C_6$ (as 8T33)	$6$	$1$	$[2, 2]$	$[2, 2, 2, 2]^{6}$	$[3, 2, 0]$	$[3]$
2.8.12.18	$8$	x^8 - 2x^7 + 4x^6 + 8x^4 + 4x^3 + 28	$2$	$4$	$2$	$12$	$C_2^4:C_6$ (as 8T33)	$6$	$1$	$[2, 2]$	$[2, 2, 2, 2]^{6}$	$[3, 3, 0]$	$[3]$
2.8.12.19	$8$	x^8 - 2x^7 + 2x^6 + 8x^5 + 4x^4 + 12x^3 + 12x^2 + 12	$2$	$4$	$2$	$12$	$(C_8:C_2):C_2$ (as 8T16)	$4$	$1$	$[2, 2]$	$[2, 2, 2]^{4}$	$[3, 2, 0]$	$[2]$
2.8.12.2	$8$	x^8 + 16x^7 + 120x^6 + 546x^5 + 1646x^4 + 3352x^3 + 4457x^2 + 3470x + 1203	$2$	$2$	$4$	$12$	$C_4\times C_2$ (as 8T2)	$4$	$1$	$[3]$	$[3]^{4}$	$[2, 0]$	$[1]$
2.8.12.20	$8$	x^8 - 2x^7 + 2x^6 + 8x^5 + 8x^4 - 4x^3 - 4x^2 + 4	$2$	$4$	$2$	$12$	$C_2^3: C_4$ (as 8T21)	$4$	$1$	$[2, 2]$	$[2, 2, 2]^{4}$	$[3, 2, 0]$	$[2]$
2.8.12.21	$8$	x^8 + 2x^7 + 2x^6 + 4x^5 + 8x^4 + 4x^3 - 4x^2 + 4	$2$	$4$	$2$	$12$	$(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T28)	$4$	$1$	$[2, 2]$	$[2, 2, 2, 2]^{4}$	$[3, 2, 0]$	$[2]$
2.8.12.22	$8$	x^8 + 2x^7 + 8x^6 + 4x^5 + 4x^4 + 12x^3 + 12	$2$	$4$	$2$	$12$	$(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T28)	$4$	$1$	$[2, 2]$	$[2, 2, 2, 2]^{4}$	$[3, 2, 0]$	$[2]$
2.8.12.23	$8$	x^8 - 2x^7 + 8x^6 - 4x^5 + 8x^4 - 4x^3 + 8x^2 + 4	$2$	$4$	$2$	$12$	$(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T28)	$4$	$1$	$[2, 2]$	$[2, 2, 2, 2]^{4}$	$[3, 2, 0]$	$[2]$
2.8.12.24	$8$	x^8 + 2x^7 + 2x^6 + 4x^5 + 16x^4 + 12x^3 - 12x^2 + 36	$2$	$4$	$2$	$12$	$(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T28)	$4$	$1$	$[2, 2]$	$[2, 2, 2, 2]^{4}$	$[3, 2, 0]$	$[2]$
2.8.12.25	$8$	x^8 + 2x^6 + 2x^5 + 2x^2 + 2	$2$	$8$	$1$	$12$	$S_4\times C_2$ (as 8T24)	$2$	$3$	$[4/3, 4/3, 2]$	$[4/3, 4/3, 2]_{3}^{2}$	$[5, 2, 2, 0]$	$[1, 1]$
2.8.12.26	$8$	x^8 + 2x^6 + 2x^5 + 2x^2 + 6	$2$	$8$	$1$	$12$	$S_4\times C_2$ (as 8T24)	$2$	$3$	$[4/3, 4/3, 2]$	$[4/3, 4/3, 2]_{3}^{2}$	$[5, 2, 2, 0]$	$[1, 1]$
2.8.12.27	$8$	x^8 + 2x^5 + 2x^4 + 2	$2$	$8$	$1$	$12$	$C_2^3:(C_7: C_3)$ (as 8T36)	$3$	$7$	$[12/7, 12/7, 12/7]$	$[12/7, 12/7, 12/7]_{7}^{3}$	$[5, 5, 4, 0]$	$[1]$
2.8.12.28	$8$	x^8 + 2x^5 + 2	$2$	$8$	$1$	$12$	$C_2^3:(C_7: C_3)$ (as 8T36)	$3$	$7$	$[12/7, 12/7, 12/7]$	$[12/7, 12/7, 12/7]_{7}^{3}$	$[5, 5, 5, 0]$	$[1]$
2.8.12.29	$8$	x^8 + 2x^5 + 2x^2 + 6	$2$	$8$	$1$	$12$	$\textrm{GL(2,3)}$ (as 8T23)	$2$	$3$	$[4/3, 4/3, 2]$	$[4/3, 4/3, 2]_{3}^{2}$	$[5, 2, 2, 0]$	$[1, 1]$
2.8.12.3	$8$	x^8 - 12x^7 + 44x^6 + 152x^5 - 512x^4 + 560x^3 + 4432x^2 + 9376x + 21744	$2$	$2$	$4$	$12$	$C_2^2:C_4$ (as 8T10)	$4$	$1$	$[3]$	$[2, 3]^{4}$	$[2, 0]$	$[1]$
2.8.12.30	$8$	x^8 + 2x^7 + 2x^6 + 2x^5 + 2x^2 + 2	$2$	$8$	$1$	$12$	$\textrm{GL(2,3)}$ (as 8T23)	$2$	$3$	$[4/3, 4/3, 2]$	$[4/3, 4/3, 2]_{3}^{2}$	$[5, 2, 2, 0]$	$[1, 1]$
2.8.12.4	$8$	x^8 + 8x^6 - 16x^5 - 376x^4 - 128x^3 + 8928x^2 + 21056x + 13008	$2$	$2$	$4$	$12$	$C_2^3: C_4$ (as 8T20)	$4$	$1$	$[3]$	$[2, 2, 3]^{4}$	$[2, 0]$	$[1]$
2.8.12.5	$8$	x^8 + 208x^5 - 88x^4 - 1344x^3 + 13440x^2 - 16320x + 17744	$2$	$2$	$4$	$12$	$C_8$ (as 8T1)	$4$	$1$	$[3]$	$[3]^{4}$	$[2, 0]$	$[1]$
2.8.12.6	$8$	x^8 - 16x^6 + 72x^4 + 3664	$2$	$2$	$4$	$12$	$C_8$ (as 8T1)	$4$	$1$	$[3]$	$[3]^{4}$	$[2, 0]$	$[1]$
2.8.12.7	$8$	x^8 + 16x^7 + 160x^6 + 800x^5 + 2952x^4 + 7104x^3 + 12992x^2 + 14208x + 10320	$2$	$2$	$4$	$12$	$C_8:C_2$ (as 8T7)	$4$	$1$	$[3]$	$[2, 3]^{4}$	$[2, 0]$	$[1]$
2.8.12.8	$8$	x^8 - 16x^6 + 112x^5 + 56x^4 - 1280x^3 + 10176x^2 + 39744x + 40720	$2$	$2$	$4$	$12$	$(C_8:C_2):C_2$ (as 8T16)	$4$	$1$	$[3]$	$[2, 2, 3]^{4}$	$[2, 0]$	$[1]$
2.8.12.9	$8$	x^8 + 16x^7 + 68x^6 + 192x^5 + 1504x^4 + 2560x^3 + 12016x^2 + 13184x + 15216	$2$	$2$	$4$	$12$	$((C_8 : C_2):C_2):C_2$ (as 8T27)	$4$	$1$	$[3]$	$[2, 2, 2, 3]^{4}$	$[2, 0]$	$[1]$
2.8.14.1	$8$	x^8 + 2x^7 + 6	$2$	$8$	$1$	$14$	$A_4\times C_2$ (as 8T13)	$3$	$1$	$[2, 2, 2]$	$[2, 2, 2]^{3}$	$[7, 7, 7, 0]$	$[3]$
2.8.14.10	$8$	x^8 + 2x^7 + 2x^2 + 4x + 2	$2$	$8$	$1$	$14$	$C_2 \wr S_4$ (as 8T44)	$2$	$3$	$[4/3, 4/3, 5/2]$	$[4/3, 4/3, 2, 7/3, 7/3, 5/2]_{3}^{2}$	$[7, 2, 2, 0]$	$[1, 1]$
2.8.14.11	$8$	x^8 + 2x^7 + 4x^4 + 4x^3 + 2x^2 + 4x + 2	$2$	$8$	$1$	$14$	$C_2 \wr S_4$ (as 8T44)	$2$	$3$	$[4/3, 4/3, 5/2]$	$[4/3, 4/3, 2, 7/3, 7/3, 5/2]_{3}^{2}$	$[7, 2, 2, 0]$	$[1, 1]$