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Degree	Residue characteristic	Galois group	Galois unramified degree	Assoc. Inertia

Ramification index	Discriminant exponent	Inertia subgroup	Galois tame degree	Indices

Residue field degree	Top slope	Wild	Visible	Wild inertia subgroup

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Results (1-50 of 158 matches)

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Label	$n$	Polynomial	$p$	$e$	$f$	$c$	Galois group	$u$	$t$	Visible slopes	Slope content	Ind. of Insep.	Assoc. Inertia
2.10.0.1	$10$	x¹⁰ + x⁶ + x⁵ + x³ + x² + x + 1	$2$	$1$	$10$	$0$	$C_{10}$ (as 10T1)	$10$	$1$	$[\ ]$	$[\ ]^{10}$	$[0]$	$[]$
2.10.8.1	$10$	x¹⁰ + 5x⁹ + 15x⁸ + 30x⁷ + 45x⁶ + 55x⁵ + 55x⁴ + 10x³ - 25x² - 5x + 7	$2$	$5$	$2$	$8$	$F_5$ (as 10T4)	$4$	$5$	$[\ ]$	$[\ ]_{5}^{4}$	$[0]$	$[2]$
2.10.10.1	$10$	x¹⁰ + 4x⁹ + 6x⁸ + 80x⁷ + 616x⁶ + 2352x⁵ + 6000x⁴ + 11136x³ + 13776x² + 9472x + 2784	$2$	$2$	$5$	$10$	$C_2^4 : C_5$ (as 10T8)	$5$	$1$	$[2]$	$[2, 2, 2, 2]^{5}$	$[1, 0]$	$[1]$
2.10.10.10	$10$	x¹⁰ + 10x⁹ + 22x⁸ + 160x⁶ + 1200x⁵ + 3168x⁴ + 4480x³ + 3760x² + 1824x + 416	$2$	$2$	$5$	$10$	$C_2 \times (C_2^4 : C_5)$ (as 10T14)	$5$	$1$	$[2]$	$[2, 2, 2, 2, 2]^{5}$	$[1, 0]$	$[1]$
2.10.10.11	$10$	x¹⁰ + 10x⁹ + 38x⁸ + 64x⁷ + 152x⁶ + 688x⁵ + 912x⁴ - 1024x³ - 1968x² + 32x - 32	$2$	$2$	$5$	$10$	$C_{10}$ (as 10T1)	$5$	$1$	$[2]$	$[2]^{5}$	$[1, 0]$	$[1]$
2.10.10.12	$10$	x¹⁰ + 10x⁹ + 34x⁸ + 112x⁷ + 328x⁶ + 640x⁵ + 1360x⁴ + 2176x³ + 1168x² + 1888x - 1248	$2$	$2$	$5$	$10$	$C_2 \times (C_2^4 : C_5)$ (as 10T14)	$5$	$1$	$[2]$	$[2, 2, 2, 2, 2]^{5}$	$[1, 0]$	$[1]$
2.10.10.13	$10$	x¹⁰ + 10x⁹ + 10x⁸ + 56x⁷ + 192x⁶ + 800x⁵ + 1536x⁴ + 2208x³ + 2224x² + 96x - 1056	$2$	$2$	$5$	$10$	$C_2 \times (C_2^4 : C_5)$ (as 10T14)	$5$	$1$	$[2]$	$[2, 2, 2, 2, 2]^{5}$	$[1, 0]$	$[1]$
2.10.10.14	$10$	x¹⁰ + 4x⁹ - 6x⁸ + 176x⁷ + 848x⁶ + 2256x⁵ + 1216x⁴ - 1088x³ - 5392x² - 5120x - 3616	$2$	$2$	$5$	$10$	$C_2 \times (C_2^4 : C_5)$ (as 10T14)	$5$	$1$	$[2]$	$[2, 2, 2, 2, 2]^{5}$	$[1, 0]$	$[1]$
2.10.10.15	$10$	x¹⁰ + 2x + 2	$2$	$10$	$1$	$10$	$(C_2^4 : C_5):C_4$ (as 10T24)	$4$	$5$	$[6/5]$	$[6/5, 6/5, 6/5, 6/5]_{5}^{4}$	$[1, 0]$	$[1, 4]$
2.10.10.16	$10$	x¹⁰ + 2x² + 2x + 2	$2$	$10$	$1$	$10$	$(C_2^4 : C_5):C_4$ (as 10T25)	$4$	$5$	$[6/5]$	$[6/5, 6/5, 6/5, 6/5]_{5}^{4}$	$[1, 0]$	$[1, 4]$
2.10.10.2	$10$	x¹⁰ + 4x⁹ + 46x⁸ + 328x⁷ + 1232x⁶ + 4048x⁵ + 5824x⁴ + 6496x³ - 8272x² - 14336x - 17632	$2$	$2$	$5$	$10$	$C_2^4 : C_5$ (as 10T8)	$5$	$1$	$[2]$	$[2, 2, 2, 2]^{5}$	$[1, 0]$	$[1]$
2.10.10.3	$10$	x¹⁰ + 10x⁹ + 74x⁸ + 320x⁷ + 1104x⁶ + 2752x⁵ + 6176x⁴ + 12096x³ + 17712x² + 15968x + 8416	$2$	$2$	$5$	$10$	$C_2^4 : C_5$ (as 10T8)	$5$	$1$	$[2]$	$[2, 2, 2, 2]^{5}$	$[1, 0]$	$[1]$
2.10.10.4	$10$	x¹⁰ - 2x⁸ + 16x⁷ - 8x⁶ - 432x⁵ - 176x⁴ - 960x³ - 1776x² - 448x - 32	$2$	$2$	$5$	$10$	$C_2 \times (C_2^4 : C_5)$ (as 10T14)	$10$	$1$	$[2]$	$[2, 2, 2, 2]^{10}$	$[1, 0]$	$[1]$
2.10.10.5	$10$	x¹⁰ + 34x⁸ - 24x⁷ + 368x⁶ - 496x⁵ + 1568x⁴ - 1760x³ + 2992x² - 1856x + 352	$2$	$2$	$5$	$10$	$C_2 \times (C_2^4 : C_5)$ (as 10T14)	$10$	$1$	$[2]$	$[2, 2, 2, 2]^{10}$	$[1, 0]$	$[1]$
2.10.10.6	$10$	x¹⁰ - 6x⁹ + 42x⁸ - 104x⁷ - 256x⁶ - 112x⁵ - 1568x⁴ - 2016x³ - 2832x² - 4960x - 3616	$2$	$2$	$5$	$10$	$C_2 \times (C_2^4 : C_5)$ (as 10T14)	$10$	$1$	$[2]$	$[2, 2, 2, 2]^{10}$	$[1, 0]$	$[1]$
2.10.10.7	$10$	x¹⁰ + 10x⁹ + 50x⁸ + 160x⁷ + 360x⁶ + 592x⁵ + 656x⁴ + 384x³ - 112x² - 352x - 1248	$2$	$2$	$5$	$10$	$C_{10}$ (as 10T1)	$5$	$1$	$[2]$	$[2]^{5}$	$[1, 0]$	$[1]$
2.10.10.8	$10$	x¹⁰ + 4x⁹ + 14x⁸ + 240x⁷ + 928x⁶ + 4400x⁵ + 6368x⁴ + 13888x³ - 336x² + 2432x - 17632	$2$	$2$	$5$	$10$	$C_2 \times (C_2^4 : C_5)$ (as 10T14)	$5$	$1$	$[2]$	$[2, 2, 2, 2, 2]^{5}$	$[1, 0]$	$[1]$
2.10.10.9	$10$	x¹⁰ + 10x⁹ + 22x⁸ - 8x⁷ + 72x⁶ + 1328x⁵ + 4496x⁴ + 3680x³ - 3696x² - 96x - 32	$2$	$2$	$5$	$10$	$C_2 \times (C_2^4 : C_5)$ (as 10T14)	$5$	$1$	$[2]$	$[2, 2, 2, 2, 2]^{5}$	$[1, 0]$	$[1]$
2.10.12.1	$10$	x¹⁰ + 2x⁶ + 2x³ + 2	$2$	$10$	$1$	$12$	$(C_2^4 : C_5):C_4$ (as 10T24)	$4$	$5$	$[8/5]$	$[8/5, 8/5, 8/5, 8/5]_{5}^{4}$	$[3, 0]$	$[1, 4]$
2.10.12.2	$10$	x¹⁰ + 2x⁶ + 2x⁵ + 2x³ + 2	$2$	$10$	$1$	$12$	$(C_2^4 : C_5):C_4$ (as 10T24)	$4$	$5$	$[8/5]$	$[8/5, 8/5, 8/5, 8/5]_{5}^{4}$	$[3, 0]$	$[1, 4]$
2.10.12.3	$10$	x¹⁰ + 2x³ + 2	$2$	$10$	$1$	$12$	$(C_2^4 : C_5):C_4$ (as 10T25)	$4$	$5$	$[8/5]$	$[8/5, 8/5, 8/5, 8/5]_{5}^{4}$	$[3, 0]$	$[1, 4]$
2.10.12.4	$10$	x¹⁰ + 2x⁵ + 2x³ + 2	$2$	$10$	$1$	$12$	$(C_2^4 : C_5):C_4$ (as 10T25)	$4$	$5$	$[8/5]$	$[8/5, 8/5, 8/5, 8/5]_{5}^{4}$	$[3, 0]$	$[1, 4]$
2.10.14.1	$10$	x¹⁰ + 2x⁸ + 2x⁷ + 2x⁶ + 2x⁵ + 2x⁴ + 2	$2$	$10$	$1$	$14$	$F_{5}\times C_2$ (as 10T5)	$4$	$5$	$[2]$	$[2]_{5}^{4}$	$[5, 0]$	$[1, 4]$
2.10.14.2	$10$	x¹⁰ + 2x⁹ + 2x⁵ + 2	$2$	$10$	$1$	$14$	$((C_2^4 : C_5):C_4)\times C_2$ (as 10T29)	$4$	$5$	$[2]$	$[6/5, 6/5, 6/5, 6/5, 2]_{5}^{4}$	$[5, 0]$	$[1, 4]$
2.10.14.3	$10$	x¹⁰ + 2x⁹ + 2x⁸ + 2x⁷ + 2x⁵ + 2	$2$	$10$	$1$	$14$	$((C_2^4 : C_5):C_4)\times C_2$ (as 10T29)	$4$	$5$	$[2]$	$[8/5, 8/5, 8/5, 8/5, 2]_{5}^{4}$	$[5, 0]$	$[1, 4]$
2.10.14.4	$10$	x¹⁰ + 2x⁸ + 2x⁷ + 2x⁵ + 2	$2$	$10$	$1$	$14$	$((C_2^4 : C_5):C_4)\times C_2$ (as 10T29)	$4$	$5$	$[2]$	$[8/5, 8/5, 8/5, 8/5, 2]_{5}^{4}$	$[5, 0]$	$[1, 4]$
2.10.14.5	$10$	x¹⁰ + 2x⁵ + 6	$2$	$10$	$1$	$14$	$F_{5}\times C_2$ (as 10T5)	$4$	$5$	$[2]$	$[2]_{5}^{4}$	$[5, 0]$	$[1, 4]$
2.10.14.6	$10$	x¹⁰ + 2x⁹ + 2x⁷ + 2x⁵ + 2x⁴ + 6	$2$	$10$	$1$	$14$	$((C_2^4 : C_5):C_4)\times C_2$ (as 10T29)	$4$	$5$	$[2]$	$[6/5, 6/5, 6/5, 6/5, 2]_{5}^{4}$	$[5, 0]$	$[1, 4]$
2.10.14.7	$10$	x¹⁰ + 2x⁹ + 2x⁸ + 2x⁶ + 2x⁵ + 2x⁴ + 2	$2$	$10$	$1$	$14$	$((C_2^4 : C_5):C_4)\times C_2$ (as 10T29)	$4$	$5$	$[2]$	$[8/5, 8/5, 8/5, 8/5, 2]_{5}^{4}$	$[5, 0]$	$[1, 4]$
2.10.14.8	$10$	x¹⁰ + 2x⁵ + 2x⁴ + 6	$2$	$10$	$1$	$14$	$((C_2^4 : C_5):C_4)\times C_2$ (as 10T29)	$4$	$5$	$[2]$	$[8/5, 8/5, 8/5, 8/5, 2]_{5}^{4}$	$[5, 0]$	$[1, 4]$
2.10.15.1	$10$	x¹⁰ + 70x⁸ + 2x⁷ + 1960x⁶ - 26x⁵ + 27441x⁴ - 2240x³ + 192110x² - 14504x + 537993	$2$	$2$	$5$	$15$	$C_{10}$ (as 10T1)	$5$	$1$	$[3]$	$[3]^{5}$	$[2, 0]$	$[1]$
2.10.15.10	$10$	x¹⁰ - 12x⁹ + 110x⁸ - 416x⁷ + 4264x⁶ - 11936x⁵ + 27504x⁴ - 98432x³ + 20560x² - 83648x + 9568	$2$	$2$	$5$	$15$	$C_2 \times (C_2^4 : C_5)$ (as 10T14)	$5$	$1$	$[3]$	$[2, 2, 2, 2, 3]^{5}$	$[2, 0]$	$[1]$
2.10.15.11	$10$	x¹⁰ + 20x⁹ + 222x⁸ + 1632x⁷ + 8392x⁶ + 35680x⁵ + 129840x⁴ + 366464x³ + 703952x² + 802624x + 377696	$2$	$2$	$5$	$15$	$C_2 \times (C_2^4 : C_5)$ (as 10T14)	$5$	$1$	$[3]$	$[2, 2, 2, 2, 3]^{5}$	$[2, 0]$	$[1]$
2.10.15.12	$10$	x¹⁰ - 12x⁹ + 30x⁸ - 96x⁷ + 2440x⁶ + 5728x⁵ + 31664x⁴ + 22656x³ + 16080x² + 26944x + 9568	$2$	$2$	$5$	$15$	$C_2 \times (C_2^4 : C_5)$ (as 10T14)	$5$	$1$	$[3]$	$[2, 2, 2, 2, 3]^{5}$	$[2, 0]$	$[1]$
2.10.15.13	$10$	x¹⁰ - 12x⁹ + 174x⁸ - 640x⁷ - 40x⁶ + 11424x⁵ - 7984x⁴ - 79360x³ + 84112x² + 955968x + 1404384	$2$	$2$	$5$	$15$	$C_{10}$ (as 10T1)	$5$	$1$	$[3]$	$[3]^{5}$	$[2, 0]$	$[1]$
2.10.15.14	$10$	x¹⁰ - 12x⁹ + 54x⁸ - 320x⁷ + 3784x⁶ + 6816x⁵ + 104176x⁴ + 90624x³ + 798672x² + 117824x + 1510112	$2$	$2$	$5$	$15$	$C_2 \times (C_2^4 : C_5)$ (as 10T14)	$5$	$1$	$[3]$	$[2, 2, 2, 2, 3]^{5}$	$[2, 0]$	$[1]$
2.10.15.15	$10$	x¹⁰ - 12x⁹ + 70x⁸ + 32x⁷ + 1832x⁶ + 2528x⁵ - 9424x⁴ - 73600x³ - 157616x² - 129216x - 23328	$2$	$2$	$5$	$15$	$C_2 \times (C_2^4 : C_5)$ (as 10T14)	$5$	$1$	$[3]$	$[2, 2, 2, 2, 3]^{5}$	$[2, 0]$	$[1]$
2.10.15.16	$10$	x¹⁰ + 20x⁹ + 182x⁸ + 992x⁷ + 3336x⁶ + 10848x⁵ + 51312x⁴ + 168320x³ + 262864x² + 156480x - 23328	$2$	$2$	$5$	$15$	$C_2 \times (C_2^4 : C_5)$ (as 10T14)	$5$	$1$	$[3]$	$[2, 2, 2, 2, 3]^{5}$	$[2, 0]$	$[1]$
2.10.15.2	$10$	x¹⁰ + 8x⁹ + 102x⁸ + 832x⁷ + 6440x⁶ + 35904x⁵ + 191792x⁴ + 594688x³ + 1067088x² + 999040x + 445152	$2$	$2$	$5$	$15$	$C_2 \times (C_2^4 : C_5)$ (as 10T14)	$5$	$1$	$[3]$	$[2, 2, 2, 2, 3]^{5}$	$[2, 0]$	$[1]$
2.10.15.3	$10$	x¹⁰ - 12x⁹ + 82x⁸ - 32x⁷ + 1976x⁶ + 8544x⁵ + 38064x⁴ + 155008x³ + 517392x² + 885056x + 574496	$2$	$2$	$5$	$15$	$C_2 \times (C_2^4 : C_5)$ (as 10T14)	$5$	$1$	$[3]$	$[2, 2, 2, 2, 3]^{5}$	$[2, 0]$	$[1]$
2.10.15.4	$10$	x¹⁰ + 14x⁸ + 952x⁶ + 15696x⁴ + 92432x² + 183776	$2$	$2$	$5$	$15$	$C_2 \times (C_2^4 : C_5)$ (as 10T14)	$5$	$1$	$[3]$	$[2, 2, 2, 2, 3]^{5}$	$[2, 0]$	$[1]$
2.10.15.5	$10$	x¹⁰ + 46x⁸ + 808x⁶ + 6768x⁴ + 27216x² + 9568	$2$	$2$	$5$	$15$	$C_{10}$ (as 10T1)	$5$	$1$	$[3]$	$[3]^{5}$	$[2, 0]$	$[1]$
2.10.15.6	$10$	x¹⁰ - 12x⁹ + 34x⁸ + 1040x⁷ - 168x⁶ + 19712x⁵ - 16464x⁴ + 66752x³ - 45424x² + 23232x - 17632	$2$	$2$	$5$	$15$	$C_2 \times (C_2^4 : C_5)$ (as 10T14)	$5$	$1$	$[3]$	$[2, 2, 2, 2, 3]^{5}$	$[2, 0]$	$[1]$
2.10.15.7	$10$	x¹⁰ + 62x⁸ - 96x⁷ + 840x⁶ + 64x⁵ + 22832x⁴ + 70528x³ + 199632x² + 445184x + 361824	$2$	$2$	$5$	$15$	$C_2 \times (C_2^4 : C_5)$ (as 10T14)	$5$	$1$	$[3]$	$[2, 2, 2, 2, 3]^{5}$	$[2, 0]$	$[1]$
2.10.15.8	$10$	x¹⁰ + 20x⁹ + 234x⁸ + 2512x⁷ + 17000x⁶ + 100480x⁵ + 430224x⁴ + 1312448x³ + 2519632x² + 2593984x + 1080096	$2$	$2$	$5$	$15$	$C_2 \times (C_2^4 : C_5)$ (as 10T14)	$5$	$1$	$[3]$	$[2, 2, 2, 2, 3]^{5}$	$[2, 0]$	$[1]$
2.10.15.9	$10$	x¹⁰ + 20x⁹ + 206x⁸ + 1376x⁷ + 6504x⁶ + 22496x⁵ + 57328x⁴ + 105856x³ + 135504x² + 108864x + 9568	$2$	$2$	$5$	$15$	$C_{10}$ (as 10T1)	$5$	$1$	$[3]$	$[3]^{5}$	$[2, 0]$	$[1]$
2.10.16.1	$10$	x¹⁰ + 2x⁷ + 4x⁴ + 4x² + 2	$2$	$10$	$1$	$16$	$(C_2^4 : C_5):C_4$ (as 10T24)	$4$	$5$	$[12/5]$	$[12/5, 12/5, 12/5, 12/5]_{5}^{4}$	$[7, 0]$	$[1, 4]$
2.10.16.10	$10$	x¹⁰ + 2x⁸ + 2x⁷ + 2x⁶ + 2x⁴ + 4x³ + 4x² + 4x + 2	$2$	$10$	$1$	$16$	$((C_2^4 : C_5):C_4)\times C_2$ (as 10T29)	$4$	$5$	$[12/5]$	$[2, 12/5, 12/5, 12/5, 12/5]_{5}^{4}$	$[7, 0]$	$[1, 4]$
2.10.16.11	$10$	x¹⁰ + 2x⁹ + 2x⁷ + 4x³ + 6	$2$	$10$	$1$	$16$	$((C_2^4 : C_5):C_4)\times C_2$ (as 10T29)	$4$	$5$	$[12/5]$	$[2, 12/5, 12/5, 12/5, 12/5]_{5}^{4}$	$[7, 0]$	$[1, 4]$
2.10.16.12	$10$	x¹⁰ + 2x⁸ + 2x⁷ + 2x⁴ + 4x³ + 4x² + 2	$2$	$10$	$1$	$16$	$((C_2^4 : C_5):C_4)\times C_2$ (as 10T29)	$4$	$5$	$[12/5]$	$[2, 12/5, 12/5, 12/5, 12/5]_{5}^{4}$	$[7, 0]$	$[1, 4]$

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