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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 654 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
7.14.0.1	$14$	x¹⁴ + 5x⁷ + 6x⁵ + 2x⁴ + 3x² + 6x + 3	$7$	$1$	$14$	$0$	$C_{14}$ (as 14T1)	$14$	$1$	$[\ ]$	$[\ ]^{14}$	$[0]$	$[]$
7.14.7.1	$14$	x¹⁴ + 49x¹² + 1029x¹⁰ + 12017x⁸ + 8x⁷ + 82859x⁶ - 1176x⁵ + 352947x⁴ + 13720x³ + 881203x² - 19160x + 794999	$7$	$2$	$7$	$7$	$C_{14}$ (as 14T1)	$7$	$2$	$[\ ]$	$[\ ]_{2}^{7}$	$[0]$	$[1]$
7.14.7.2	$14$	x¹⁴ - 756x¹³ + 407484x¹² - 120759324x¹¹ + 18245133144x¹⁰ - 1371646043208x⁹ + 45234910589400x⁸ - 365498518846944x⁷ - 160150981540032x⁶ - 9636001680480x⁵ - 1806831694584x⁴ - 187090145760x³ - 8419197738x² - 138355224x - 3294172	$7$	$2$	$7$	$7$	$C_{14}$ (as 14T1)	$7$	$2$	$[\ ]$	$[\ ]_{2}^{7}$	$[0]$	$[1]$
7.14.14.1	$14$	x¹⁴ + 14x⁹ - 28x⁸ + 14x⁷ - 245x⁴ - 1372x³ - 882x² - 196x + 49	$7$	$7$	$2$	$14$	$C_7^2:(C_2\times C_6)$ (as 14T24)	$2$	$6$	$[7/6]$	$[7/6, 7/6]_{6}^{2}$	$[1, 0]$	$[1]$
7.14.14.10	$14$	x¹⁴ - 14x⁹ - 70x⁸ + 14x⁷ - 245x⁴ - 1274x³ - 1519x² - 490x + 49	$7$	$7$	$2$	$14$	$C_7^2:C_{12}$ (as 14T23)	$2$	$6$	$[7/6]$	$[7/6, 7/6]_{6}^{2}$	$[1, 0]$	$[1]$
7.14.14.11	$14$	x¹⁴ - 238x⁹ - 14x⁸ + 14x⁷ + 3577x⁴ - 1862x³ - 1911x² - 98x + 49	$7$	$7$	$2$	$14$	$C_7^2:(C_2\times C_6)$ (as 14T24)	$2$	$6$	$[7/6]$	$[7/6, 7/6]_{6}^{2}$	$[1, 0]$	$[1]$
7.14.14.12	$14$	x¹⁴ - 84x⁸ + 14x⁷ + 588x² - 588x + 49	$7$	$7$	$2$	$14$	$C_7^2:C_{12}$ (as 14T23)	$2$	$6$	$[7/6]$	$[7/6, 7/6]_{6}^{2}$	$[1, 0]$	$[1]$
7.14.14.13	$14$	x¹⁴ + 28x⁹ - 154x⁸ + 14x⁷ + 196x⁴ - 2156x³ - 1225x² - 1078x + 49	$7$	$7$	$2$	$14$	$C_7^2:C_{12}$ (as 14T23)	$2$	$6$	$[7/6]$	$[7/6, 7/6]_{6}^{2}$	$[1, 0]$	$[1]$
7.14.14.14	$14$	x¹⁴ - 14x⁹ - 140x⁸ + 14x⁷ - 245x⁴ - 1372x³ + 98x² - 980x + 49	$7$	$7$	$2$	$14$	$C_7^2:(C_2\times C_6)$ (as 14T24)	$2$	$6$	$[7/6]$	$[7/6, 7/6]_{6}^{2}$	$[1, 0]$	$[1]$
7.14.14.15	$14$	x¹⁴ - 168x⁹ + 14x⁷ - 3528x⁴ - 7056x³ - 2352x² + 49	$7$	$7$	$2$	$14$	$C_7^2:(C_2\times C_6)$ (as 14T24)	$2$	$6$	$[7/6]$	$[7/6, 7/6]_{6}^{2}$	$[1, 0]$	$[1]$
7.14.14.16	$14$	x¹⁴ - 42x⁹ - 126x⁸ + 14x⁷ - 735x⁴ - 882x³ + 1029x² - 882x + 49	$7$	$7$	$2$	$14$	$C_7^2:C_{12}$ (as 14T23)	$2$	$6$	$[7/6]$	$[7/6, 7/6]_{6}^{2}$	$[1, 0]$	$[1]$
7.14.14.17	$14$	x¹⁴ - 84x⁹ - 28x⁸ + 14x⁷ + 588x⁴ - 686x² - 196x + 49	$7$	$7$	$2$	$14$	$C_7^2:C_{12}$ (as 14T23)	$2$	$6$	$[7/6]$	$[7/6, 7/6]_{6}^{2}$	$[1, 0]$	$[1]$
7.14.14.18	$14$	x¹⁴ + 28x⁸ + 14x⁷ - 98x² + 196x + 49	$7$	$7$	$2$	$14$	$C_7^2:C_{12}$ (as 14T23)	$2$	$6$	$[7/6]$	$[7/6, 7/6]_{6}^{2}$	$[1, 0]$	$[1]$
7.14.14.19	$14$	x¹⁴ - 42x⁹ + 42x⁸ + 14x⁷ - 735x⁴ - 882x³ + 147x² + 294x + 49	$7$	$7$	$2$	$14$	$F_7 \times C_2$ (as 14T7)	$2$	$6$	$[7/6]$	$[7/6]_{6}^{2}$	$[1, 0]$	$[1]$
7.14.14.2	$14$	x¹⁴ - 84x⁹ - 140x⁸ + 14x⁷ + 588x⁴ - 3038x² - 980x + 49	$7$	$7$	$2$	$14$	$C_7^2:C_{12}$ (as 14T23)	$2$	$6$	$[7/6]$	$[7/6, 7/6]_{6}^{2}$	$[1, 0]$	$[1]$
7.14.14.20	$14$	x¹⁴ - 210x⁹ - 168x⁸ + 14x⁷ + 3675x⁴ + 2940x³ - 1764x² - 1176x + 49	$7$	$7$	$2$	$14$	$C_7^2:(C_2\times C_6)$ (as 14T24)	$2$	$6$	$[7/6]$	$[7/6, 7/6]_{6}^{2}$	$[1, 0]$	$[1]$
7.14.14.21	$14$	x¹⁴ - 14x⁹ + 14x⁸ + 14x⁷ - 1127x⁴ - 98x³ - 49x² + 98x + 49	$7$	$7$	$2$	$14$	$F_7 \times C_2$ (as 14T7)	$2$	$6$	$[7/6]$	$[7/6]_{6}^{2}$	$[1, 0]$	$[1]$
7.14.14.22	$14$	x¹⁴ + 14x⁹ - 182x⁸ + 14x⁷ + 49x⁴ - 1274x³ - 2205x² - 1274x + 49	$7$	$7$	$2$	$14$	$C_7^2:(C_2\times C_6)$ (as 14T24)	$2$	$6$	$[7/6]$	$[7/6, 7/6]_{6}^{2}$	$[1, 0]$	$[1]$
7.14.14.23	$14$	x¹⁴ - 28x⁹ - 42x⁸ + 14x⁷ - 98x⁴ - 49x² - 294x + 49	$7$	$7$	$2$	$14$	$C_7^2:C_{12}$ (as 14T23)	$2$	$6$	$[7/6]$	$[7/6, 7/6]_{6}^{2}$	$[1, 0]$	$[1]$
7.14.14.24	$14$	x¹⁴ - 14x⁹ + 84x⁸ + 14x⁷ - 245x⁴ - 588x³ + 1666x² + 588x + 49	$7$	$7$	$2$	$14$	$F_7 \times C_2$ (as 14T7)	$2$	$6$	$[7/6]$	$[7/6]_{6}^{2}$	$[1, 0]$	$[1]$
7.14.14.25	$14$	x¹⁴ - 56x⁹ + 70x⁸ + 14x⁷ - 1862x⁴ - 1960x³ + 833x² + 490x + 49	$7$	$7$	$2$	$14$	$F_7 \times C_2$ (as 14T7)	$2$	$6$	$[7/6]$	$[7/6]_{6}^{2}$	$[1, 0]$	$[1]$
7.14.14.26	$14$	x¹⁴ - 154x⁹ - 112x⁸ + 14x⁷ - 1421x⁴ - 196x³ - 588x² - 784x + 49	$7$	$7$	$2$	$14$	$C_7^2:C_{12}$ (as 14T23)	$2$	$6$	$[7/6]$	$[7/6, 7/6]_{6}^{2}$	$[1, 0]$	$[1]$
7.14.14.27	$14$	x¹⁴ - 70x⁹ - 98x⁸ + 14x⁷ + 49x⁴ - 1274x³ - 2793x² - 686x + 49	$7$	$7$	$2$	$14$	$C_7^2:(C_2\times C_6)$ (as 14T24)	$2$	$6$	$[7/6]$	$[7/6, 7/6]_{6}^{2}$	$[1, 0]$	$[1]$
7.14.14.28	$14$	x¹⁴ + 28x² + 14x + 21	$7$	$14$	$1$	$14$	$C_7^2:(C_3\times D_4)$ (as 14T32)	$2$	$12$	$[13/12]$	$[13/12, 13/12]_{12}^{2}$	$[1, 0]$	$[1, 1]$
7.14.14.29	$14$	x¹⁴ + 35x² + 7x + 21	$7$	$14$	$1$	$14$	$C_7^2:(C_3\times D_4)$ (as 14T32)	$2$	$12$	$[13/12]$	$[13/12, 13/12]_{12}^{2}$	$[1, 0]$	$[1, 1]$
7.14.14.3	$14$	x¹⁴ + 42x⁹ + 42x⁸ + 14x⁷ + 441x⁴ + 882x³ + 441x² + 294x + 49	$7$	$7$	$2$	$14$	$C_7^2:C_{12}$ (as 14T23)	$2$	$6$	$[7/6]$	$[7/6, 7/6]_{6}^{2}$	$[1, 0]$	$[1]$
7.14.14.30	$14$	x¹⁴ + 42x² + 21x + 7	$7$	$14$	$1$	$14$	$C_7^2:(C_3\times D_4)$ (as 14T32)	$2$	$12$	$[13/12]$	$[13/12, 13/12]_{12}^{2}$	$[1, 0]$	$[1, 1]$
7.14.14.31	$14$	x¹⁴ + 35x² + 14x + 7	$7$	$14$	$1$	$14$	$C_7^2:(C_3\times D_4)$ (as 14T32)	$2$	$12$	$[13/12]$	$[13/12, 13/12]_{12}^{2}$	$[1, 0]$	$[1, 1]$
7.14.14.32	$14$	x¹⁴ + 7x² + 21x + 21	$7$	$14$	$1$	$14$	$C_7^2:(C_3\times D_4)$ (as 14T32)	$2$	$12$	$[13/12]$	$[13/12, 13/12]_{12}^{2}$	$[1, 0]$	$[1, 1]$
7.14.14.33	$14$	x¹⁴ + 21x² + 7x + 7	$7$	$14$	$1$	$14$	$C_7^2:(C_3\times D_4)$ (as 14T32)	$2$	$12$	$[13/12]$	$[13/12, 13/12]_{12}^{2}$	$[1, 0]$	$[1, 1]$
7.14.14.4	$14$	x¹⁴ - 14x⁹ + 28x⁸ + 14x⁷ - 1127x⁴ - 196x³ + 98x² + 196x + 49	$7$	$7$	$2$	$14$	$F_7 \times C_2$ (as 14T7)	$2$	$6$	$[7/6]$	$[7/6]_{6}^{2}$	$[1, 0]$	$[1]$
7.14.14.5	$14$	x¹⁴ - 56x⁹ + 56x⁸ + 14x⁷ - 392x⁴ - 1568x³ + 392x² + 392x + 49	$7$	$7$	$2$	$14$	$F_7 \times C_2$ (as 14T7)	$2$	$6$	$[7/6]$	$[7/6]_{6}^{2}$	$[1, 0]$	$[1]$
7.14.14.6	$14$	x¹⁴ - 196x⁹ - 210x⁸ + 14x⁷ + 2254x⁴ + 5880x³ + 2303x² - 1470x + 49	$7$	$7$	$2$	$14$	$C_7^2:C_{12}$ (as 14T23)	$2$	$6$	$[7/6]$	$[7/6, 7/6]_{6}^{2}$	$[1, 0]$	$[1]$
7.14.14.7	$14$	x¹⁴ - 238x⁹ - 196x⁸ + 14x⁷ + 3577x⁴ + 2156x³ - 2646x² - 1372x + 49	$7$	$7$	$2$	$14$	$C_7^2:(C_2\times C_6)$ (as 14T24)	$2$	$6$	$[7/6]$	$[7/6, 7/6]_{6}^{2}$	$[1, 0]$	$[1]$
7.14.14.8	$14$	x¹⁴ - 14x⁹ - 84x⁸ + 14x⁷ - 1127x⁴ - 4116x³ - 3038x² - 588x + 49	$7$	$7$	$2$	$14$	$C_7^2:C_{12}$ (as 14T23)	$2$	$6$	$[7/6]$	$[7/6, 7/6]_{6}^{2}$	$[1, 0]$	$[1]$
7.14.14.9	$14$	x¹⁴ + 14x⁹ - 56x⁸ + 14x⁷ + 49x⁴ - 392x³ - 1764x² - 392x + 49	$7$	$7$	$2$	$14$	$C_7^2:(C_2\times C_6)$ (as 14T24)	$2$	$6$	$[7/6]$	$[7/6, 7/6]_{6}^{2}$	$[1, 0]$	$[1]$
7.14.15.1	$14$	x¹⁴ + 14x³ + 7x² + 21	$7$	$14$	$1$	$15$	$F_7 \times C_2$ (as 14T7)	$2$	$6$	$[7/6]$	$[7/6]_{6}^{2}$	$[2, 0]$	$[2, 1]$
7.14.15.10	$14$	x¹⁴ + 21x³ + 35x² + 21	$7$	$14$	$1$	$15$	$F_7$ (as 14T4)	$1$	$6$	$[7/6]$	$[7/6]_{6}$	$[2, 0]$	$[1, 1]$
7.14.15.11	$14$	x¹⁴ + 7x³ + 42x² + 7	$7$	$14$	$1$	$15$	$F_7 \times C_2$ (as 14T7)	$2$	$6$	$[7/6]$	$[7/6]_{6}^{2}$	$[2, 0]$	$[2, 1]$
7.14.15.12	$14$	x¹⁴ + 28x² + 21	$7$	$14$	$1$	$15$	$F_7 \times C_2$ (as 14T7)	$2$	$6$	$[7/6]$	$[7/6]_{6}^{2}$	$[2, 0]$	$[2, 1]$
7.14.15.2	$14$	x¹⁴ + 7x³ + 35x² + 7	$7$	$14$	$1$	$15$	$F_7 \times C_2$ (as 14T7)	$2$	$6$	$[7/6]$	$[7/6]_{6}^{2}$	$[2, 0]$	$[2, 1]$
7.14.15.3	$14$	x¹⁴ + 14x³ + 21x² + 7	$7$	$14$	$1$	$15$	$F_7 \times C_2$ (as 14T7)	$2$	$6$	$[7/6]$	$[7/6]_{6}^{2}$	$[2, 0]$	$[2, 1]$
7.14.15.4	$14$	x¹⁴ + 14x³ + 14x² + 21	$7$	$14$	$1$	$15$	$F_7 \times C_2$ (as 14T7)	$2$	$6$	$[7/6]$	$[7/6]_{6}^{2}$	$[2, 0]$	$[2, 1]$
7.14.15.5	$14$	x¹⁴ + 7x³ + 7x² + 7	$7$	$14$	$1$	$15$	$F_7$ (as 14T4)	$1$	$6$	$[7/6]$	$[7/6]_{6}$	$[2, 0]$	$[1, 1]$
7.14.15.6	$14$	x¹⁴ + 7x³ + 21x² + 21	$7$	$14$	$1$	$15$	$F_7$ (as 14T4)	$1$	$6$	$[7/6]$	$[7/6]_{6}$	$[2, 0]$	$[1, 1]$
7.14.15.7	$14$	x¹⁴ + 21x³ + 28x² + 7	$7$	$14$	$1$	$15$	$F_7$ (as 14T4)	$1$	$6$	$[7/6]$	$[7/6]_{6}$	$[2, 0]$	$[1, 1]$
7.14.15.8	$14$	x¹⁴ + 14x³ + 42x² + 21	$7$	$14$	$1$	$15$	$F_7$ (as 14T4)	$1$	$6$	$[7/6]$	$[7/6]_{6}$	$[2, 0]$	$[1, 1]$
7.14.15.9	$14$	x¹⁴ + 21x³ + 14x² + 7	$7$	$14$	$1$	$15$	$F_7$ (as 14T4)	$1$	$6$	$[7/6]$	$[7/6]_{6}$	$[2, 0]$	$[1, 1]$
7.14.16.1	$14$	x¹⁴ - 182x¹⁰ - 210x⁹ + 14x⁷ - 2303x⁶ - 2058x⁵ + 441x⁴ - 1274x³ - 1470x² + 49	$7$	$7$	$2$	$16$	$C_7^2:C_6$ (as 14T14)	$2$	$3$	$[4/3]$	$[4/3, 4/3]_{3}^{2}$	$[2, 0]$	$[1]$
7.14.16.10	$14$	x¹⁴ - 238x¹⁰ - 28x⁹ + 14x⁷ + 3577x⁶ - 196x⁵ - 98x⁴ - 1666x³ - 196x² + 49	$7$	$7$	$2$	$16$	$C_7^2:C_{12}$ (as 14T23)	$4$	$3$	$[4/3]$	$[4/3, 4/3]_{3}^{4}$	$[2, 0]$	$[2]$

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