$p$-adic field search results

Degree	Residue characteristic	Galois group	Galois unramified degree
Ramification index	Discriminant exponent	Inertia subgroup	Galois tame degree
Residue field degree	Top slope	Wild inertia subgroup

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Results (1-50 of 105 matches)

 

Label	$n$	Polynomial	$p$	$e$	$f$	$c$	Galois group	$u$	$t$	Visible slopes	Slope content
2.8.8.1	$8$	x^8 + 28x^4 + 144	$2$	$2$	$4$	$8$	$C_4\times C_2$ (as 8T2)	$4$	$1$	$[2]$	$[2]^{4}$
2.8.12.1	$8$	x^8 + 6x^6 + 8x^5 + 16	$2$	$2$	$4$	$12$	$C_4\times C_2$ (as 8T2)	$4$	$1$	$[3]$	$[3]^{4}$
2.8.12.2	$8$	x^8 + 2x^6 + 8x^4 + 16	$2$	$2$	$4$	$12$	$C_4\times C_2$ (as 8T2)	$4$	$1$	$[3]$	$[3]^{4}$
2.8.16.1	$8$	x^8 + 6x^6 + 2x^4 + 4x^2 + 8x + 12	$2$	$4$	$2$	$16$	$C_4\times C_2$ (as 8T2)	$2$	$1$	$[2,3]$	$[2, 3]^{2}$
2.8.16.2	$8$	x^8 + 2x^6 + 6x^4 + 4x^2 + 8x + 20	$2$	$4$	$2$	$16$	$C_4\times C_2$ (as 8T2)	$2$	$1$	$[2,3]$	$[2, 3]^{2}$
2.8.16.3	$8$	x^8 + 2x^6 + 6x^4 + 4x^2 + 8x + 28	$2$	$4$	$2$	$16$	$C_4\times C_2$ (as 8T2)	$2$	$1$	$[2,3]$	$[2, 3]^{2}$
2.8.22.2	$8$	x^8 + 10x^4 + 16x + 4	$2$	$4$	$2$	$22$	$C_4\times C_2$ (as 8T2)	$2$	$1$	$[3,4]$	$[3, 4]^{2}$
2.8.22.5	$8$	x^8 + 10x^4 + 16x + 36	$2$	$4$	$2$	$22$	$C_4\times C_2$ (as 8T2)	$2$	$1$	$[3,4]$	$[3, 4]^{2}$
2.8.22.6	$8$	x^8 + 4x^6 + 6x^4 + 16x^3 + 24x^2 + 36	$2$	$4$	$2$	$22$	$C_4\times C_2$ (as 8T2)	$2$	$1$	$[3,4]$	$[3, 4]^{2}$
2.8.22.7	$8$	x^8 + 2x^4 + 16x + 4	$2$	$4$	$2$	$22$	$C_4\times C_2$ (as 8T2)	$2$	$1$	$[3,4]$	$[3, 4]^{2}$
2.8.24.1	$8$	x^8 + 14x^4 + 4x^2 + 8x + 22	$2$	$8$	$1$	$24$	$C_4\times C_2$ (as 8T2)	$1$	$1$	$[2,3,4]$	$[2, 3, 4]$
2.8.24.10	$8$	x^8 + 16	$2$	$8$	$1$	$24$	$C_4\times C_2$ (as 8T2)	$1$	$1$	$[2,3,4]$	$[2, 3, 4]$
2.8.24.11	$8$	x^8 + 8x^7 + 8x^5 + 2x^4 + 12x^2 + 8x + 26	$2$	$8$	$1$	$24$	$C_4\times C_2$ (as 8T2)	$1$	$1$	$[2,3,4]$	$[2, 3, 4]$
2.8.24.13	$8$	x^8 + 28x^4 + 36	$2$	$8$	$1$	$24$	$C_4\times C_2$ (as 8T2)	$1$	$1$	$[2,3,4]$	$[2, 3, 4]$
2.8.24.2	$8$	x^8 + 14x^4 + 4x^2 + 8x + 6	$2$	$8$	$1$	$24$	$C_4\times C_2$ (as 8T2)	$1$	$1$	$[2,3,4]$	$[2, 3, 4]$
2.8.24.5	$8$	x^8 - 15	$2$	$8$	$1$	$24$	$C_4\times C_2$ (as 8T2)	$1$	$1$	$[2,3,4]$	$[2, 3, 4]$
2.8.24.7	$8$	x^8 + 8x^7 + 12x^6 + 10x^4 + 8x^3 + 4x^2 + 8x + 14	$2$	$8$	$1$	$24$	$C_4\times C_2$ (as 8T2)	$1$	$1$	$[2,3,4]$	$[2, 3, 4]$
2.8.24.9	$8$	x^8 + 8x^7 + 14x^4 + 4x^2 + 8x + 30	$2$	$8$	$1$	$24$	$C_4\times C_2$ (as 8T2)	$1$	$1$	$[2,3,4]$	$[2, 3, 4]$
3.8.4.1	$8$	x^8 + 36x^4 - 27x^2 + 324	$3$	$2$	$4$	$4$	$C_4\times C_2$ (as 8T2)	$4$	$2$	$[\ ]$	$[\ ]_{2}^{4}$
5.8.4.1	$8$	x^8 + 10x^6 + 125x^4 + 2500	$5$	$2$	$4$	$4$	$C_4\times C_2$ (as 8T2)	$4$	$2$	$[\ ]$	$[\ ]_{2}^{4}$
5.8.6.1	$8$	x^8 - 5x^4 + 400	$5$	$4$	$2$	$6$	$C_4\times C_2$ (as 8T2)	$2$	$4$	$[\ ]$	$[\ ]_{4}^{2}$
5.8.6.2	$8$	x^8 + 15x^4 + 100	$5$	$4$	$2$	$6$	$C_4\times C_2$ (as 8T2)	$2$	$4$	$[\ ]$	$[\ ]_{4}^{2}$
7.8.4.1	$8$	x^8 + 14x^6 + 539x^4 + 343x^2 + 60025	$7$	$2$	$4$	$4$	$C_4\times C_2$ (as 8T2)	$4$	$2$	$[\ ]$	$[\ ]_{2}^{4}$
11.8.4.1	$8$	x^8 + 484x^4 - 1331x^2 + 58564	$11$	$2$	$4$	$4$	$C_4\times C_2$ (as 8T2)	$4$	$2$	$[\ ]$	$[\ ]_{2}^{4}$
13.8.4.1	$8$	x^8 + 26x^6 + 845x^4 + 6591x^2 + 114244	$13$	$2$	$4$	$4$	$C_4\times C_2$ (as 8T2)	$4$	$2$	$[\ ]$	$[\ ]_{2}^{4}$
13.8.6.1	$8$	x^8 - 13x^4 + 2704	$13$	$4$	$2$	$6$	$C_4\times C_2$ (as 8T2)	$2$	$4$	$[\ ]$	$[\ ]_{4}^{2}$
13.8.6.2	$8$	x^8 + 39x^4 + 676	$13$	$4$	$2$	$6$	$C_4\times C_2$ (as 8T2)	$2$	$4$	$[\ ]$	$[\ ]_{4}^{2}$
17.8.4.1	$8$	x^8 + 6358x^4 - 4913x^2 + 10106041	$17$	$2$	$4$	$4$	$C_4\times C_2$ (as 8T2)	$4$	$2$	$[\ ]$	$[\ ]_{2}^{4}$
17.8.6.1	$8$	x^8 - 119x^4 + 23409	$17$	$4$	$2$	$6$	$C_4\times C_2$ (as 8T2)	$2$	$4$	$[\ ]$	$[\ ]_{4}^{2}$
17.8.6.2	$8$	x^8 + 85x^4 + 2601	$17$	$4$	$2$	$6$	$C_4\times C_2$ (as 8T2)	$2$	$4$	$[\ ]$	$[\ ]_{4}^{2}$
19.8.4.1	$8$	x^8 + 7220x^4 - 27436x^2 + 13032100	$19$	$2$	$4$	$4$	$C_4\times C_2$ (as 8T2)	$4$	$2$	$[\ ]$	$[\ ]_{2}^{4}$
23.8.4.1	$8$	x^8 + 11638x^4 - 12167x^2 + 33860761	$23$	$2$	$4$	$4$	$C_4\times C_2$ (as 8T2)	$4$	$2$	$[\ ]$	$[\ ]_{2}^{4}$
29.8.4.1	$8$	x^8 + 31958x^4 - 24389x^2 + 255328441	$29$	$2$	$4$	$4$	$C_4\times C_2$ (as 8T2)	$4$	$2$	$[\ ]$	$[\ ]_{2}^{4}$
29.8.6.1	$8$	x^8 - 203x^4 + 68121	$29$	$4$	$2$	$6$	$C_4\times C_2$ (as 8T2)	$2$	$4$	$[\ ]$	$[\ ]_{4}^{2}$
29.8.6.2	$8$	x^8 + 145x^4 + 7569	$29$	$4$	$2$	$6$	$C_4\times C_2$ (as 8T2)	$2$	$4$	$[\ ]$	$[\ ]_{4}^{2}$
31.8.4.1	$8$	x^8 + 32674x^4 - 119164x^2 + 266897569	$31$	$2$	$4$	$4$	$C_4\times C_2$ (as 8T2)	$4$	$2$	$[\ ]$	$[\ ]_{2}^{4}$
37.8.4.1	$8$	x^8 + 5476x^4 - 50653x^2 + 7496644	$37$	$2$	$4$	$4$	$C_4\times C_2$ (as 8T2)	$4$	$2$	$[\ ]$	$[\ ]_{2}^{4}$
37.8.6.1	$8$	x^8 - 1147x^4 + 855625	$37$	$4$	$2$	$6$	$C_4\times C_2$ (as 8T2)	$2$	$4$	$[\ ]$	$[\ ]_{4}^{2}$
37.8.6.2	$8$	x^8 + 333x^4 + 34225	$37$	$4$	$2$	$6$	$C_4\times C_2$ (as 8T2)	$2$	$4$	$[\ ]$	$[\ ]_{4}^{2}$
41.8.4.1	$8$	x^8 + 57154x^4 - 68921x^2 + 816644929	$41$	$2$	$4$	$4$	$C_4\times C_2$ (as 8T2)	$4$	$2$	$[\ ]$	$[\ ]_{2}^{4}$
41.8.6.1	$8$	x^8 - 9881x^4 + 34857216	$41$	$4$	$2$	$6$	$C_4\times C_2$ (as 8T2)	$2$	$4$	$[\ ]$	$[\ ]_{4}^{2}$
41.8.6.2	$8$	x^8 + 943x^4 + 242064	$41$	$4$	$2$	$6$	$C_4\times C_2$ (as 8T2)	$2$	$4$	$[\ ]$	$[\ ]_{4}^{2}$
43.8.4.1	$8$	x^8 + 73960x^4 - 79507x^2 + 1367520400	$43$	$2$	$4$	$4$	$C_4\times C_2$ (as 8T2)	$4$	$2$	$[\ ]$	$[\ ]_{2}^{4}$
47.8.4.1	$8$	x^8 + 172302x^4 - 103823x^2 + 7421994801	$47$	$2$	$4$	$4$	$C_4\times C_2$ (as 8T2)	$4$	$2$	$[\ ]$	$[\ ]_{2}^{4}$
53.8.4.1	$8$	x^8 + 101124x^4 - 148877x^2 + 2556515844	$53$	$2$	$4$	$4$	$C_4\times C_2$ (as 8T2)	$4$	$2$	$[\ ]$	$[\ ]_{2}^{4}$
53.8.6.1	$8$	x^8 - 1643x^4 + 1755625	$53$	$4$	$2$	$6$	$C_4\times C_2$ (as 8T2)	$2$	$4$	$[\ ]$	$[\ ]_{4}^{2}$
53.8.6.2	$8$	x^8 + 477x^4 + 70225	$53$	$4$	$2$	$6$	$C_4\times C_2$ (as 8T2)	$2$	$4$	$[\ ]$	$[\ ]_{4}^{2}$
59.8.4.1	$8$	x^8 + 97468x^4 - 205379x^2 + 2375002756	$59$	$2$	$4$	$4$	$C_4\times C_2$ (as 8T2)	$4$	$2$	$[\ ]$	$[\ ]_{2}^{4}$
61.8.4.1	$8$	x^8 + 14884x^4 - 226981x^2 + 55383364	$61$	$2$	$4$	$4$	$C_4\times C_2$ (as 8T2)	$4$	$2$	$[\ ]$	$[\ ]_{2}^{4}$
61.8.6.1	$8$	x^8 - 61x^4 + 59536	$61$	$4$	$2$	$6$	$C_4\times C_2$ (as 8T2)	$2$	$4$	$[\ ]$	$[\ ]_{4}^{2}$