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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 785 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
3.12.0.1	$12$	x¹² + x⁶ + x⁵ + x⁴ + x² + 2	$3$	$1$	$12$	$0$	$C_{12}$ (as 12T1)	$12$	$1$	$[\ ]$	$[\ ]^{12}$	$[0]$	$[]$
3.12.6.1	$12$	x¹² + 18x⁸ + 81x⁴ - 486x² + 1458	$3$	$2$	$6$	$6$	$C_{12}$ (as 12T1)	$6$	$2$	$[\ ]$	$[\ ]_{2}^{6}$	$[0]$	$[1]$
3.12.6.2	$12$	x¹² + 22x¹⁰ + 177x⁸ + 4x⁷ + 644x⁶ - 100x⁵ + 876x⁴ - 224x³ + 1076x² + 344x + 112	$3$	$2$	$6$	$6$	$C_6\times C_2$ (as 12T2)	$6$	$2$	$[\ ]$	$[\ ]_{2}^{6}$	$[0]$	$[1]$
3.12.9.1	$12$	x¹² + 18x⁴ - 27	$3$	$4$	$3$	$9$	$D_4 \times C_3$ (as 12T14)	$6$	$4$	$[\ ]$	$[\ ]_{4}^{6}$	$[0]$	$[2]$
3.12.9.2	$12$	x¹² + 8x¹⁰ + 4x⁹ + 33x⁸ + 24x⁷ - 10x⁶ - 96x⁵ + 163x⁴ + 12x³ - 6x² + 68x + 172	$3$	$4$	$3$	$9$	$D_4 \times C_3$ (as 12T14)	$6$	$4$	$[\ ]$	$[\ ]_{4}^{6}$	$[0]$	$[2]$
3.12.12.1	$12$	x¹² - 36x¹⁰ + 12x⁹ + 540x⁸ - 324x⁷ - 3402x⁶ + 3240x⁵ + 8424x⁴ - 10260x³ + 4860x² - 972x + 81	$3$	$3$	$4$	$12$	$C_3^2:F_9$ (as 12T173)	$4$	$2$	$[3/2]$	$[3/2, 3/2, 3/2, 3/2]_{2}^{4}$	$[1, 0]$	$[1]$
3.12.12.10	$12$	x¹² - 24x¹¹ + 306x¹⁰ - 2004x⁹ + 7236x⁸ - 4374x⁷ - 1458x⁶ + 5832x⁵ - 1836x³ + 324x² + 486x + 81	$3$	$3$	$4$	$12$	$C_3^2:F_9$ (as 12T173)	$4$	$2$	$[3/2]$	$[3/2, 3/2, 3/2, 3/2]_{2}^{4}$	$[1, 0]$	$[1]$
3.12.12.11	$12$	x¹² - 48x¹¹ + 846x¹⁰ - 5820x⁹ + 38376x⁸ + 37098x⁷ - 36666x⁶ - 17928x⁵ + 11340x⁴ - 1188x³ + 486x + 81	$3$	$3$	$4$	$12$	$C_3^3:(C_4\times S_3)$ (as 12T170)	$4$	$2$	$[3/2]$	$[3/2, 3/2, 3/2, 3/2]_{2}^{4}$	$[1, 0]$	$[1]$
3.12.12.12	$12$	x¹² - 12x¹¹ + 156x¹⁰ - 1104x⁹ + 3420x⁸ + 972x⁷ - 1890x⁶ + 1404x⁵ + 1944x⁴ + 432x³ + 324x² + 324x + 81	$3$	$3$	$4$	$12$	$C_2\times C_3^2:C_4$ (as 12T41)	$4$	$2$	$[3/2]$	$[3/2, 3/2]_{2}^{4}$	$[1, 0]$	$[1]$
3.12.12.13	$12$	x¹² - 36x¹¹ + 324x¹⁰ + 588x⁹ + 9414x⁸ + 56376x⁷ + 114642x⁶ + 92448x⁵ + 23409x⁴ + 2376x³ + 3078x² - 972x + 81	$3$	$3$	$4$	$12$	$C_3^2:F_9$ (as 12T173)	$4$	$2$	$[3/2]$	$[3/2, 3/2, 3/2, 3/2]_{2}^{4}$	$[1, 0]$	$[1]$
3.12.12.14	$12$	x¹² + 54x¹⁰ - 240x⁹ - 1935x⁸ + 7236x⁷ + 45198x⁶ + 60156x⁵ + 16686x⁴ - 13824x³ + 5184x² - 972x + 81	$3$	$3$	$4$	$12$	$C_3^2:F_9$ (as 12T173)	$4$	$2$	$[3/2]$	$[3/2, 3/2, 3/2, 3/2]_{2}^{4}$	$[1, 0]$	$[1]$
3.12.12.15	$12$	x¹² - 18x¹¹ + 186x¹⁰ - 798x⁹ + 2817x⁸ + 30456x⁷ + 55404x⁶ + 28404x⁵ - 2511x⁴ + 918x³ + 2754x² - 810x + 81	$3$	$3$	$4$	$12$	$C_3^2:F_9$ (as 12T173)	$4$	$2$	$[3/2]$	$[3/2, 3/2, 3/2, 3/2]_{2}^{4}$	$[1, 0]$	$[1]$
3.12.12.16	$12$	x¹² - 18x¹¹ + 30x¹⁰ + 1020x⁹ + 3249x⁸ + 6480x⁷ + 21924x⁶ + 35208x⁵ + 7452x⁴ - 8478x³ + 5670x² - 1134x + 81	$3$	$3$	$4$	$12$	$C_3^3:(C_4\times S_3)$ (as 12T170)	$4$	$2$	$[3/2]$	$[3/2, 3/2, 3/2, 3/2]_{2}^{4}$	$[1, 0]$	$[1]$
3.12.12.17	$12$	x¹² + 36x¹¹ + 540x¹⁰ + 3900x⁹ + 8028x⁸ - 44388x⁷ + 21870x⁶ + 7020x⁵ + 20412x⁴ - 8316x³ + 4212x² - 972x + 81	$3$	$3$	$4$	$12$	$C_3^3:(C_4\times S_3)$ (as 12T170)	$4$	$2$	$[3/2]$	$[3/2, 3/2, 3/2, 3/2]_{2}^{4}$	$[1, 0]$	$[1]$
3.12.12.18	$12$	x¹² - 36x¹¹ + 438x¹⁰ + 120x⁹ - 4563x⁸ + 1188x⁷ + 22410x⁶ + 10692x⁵ - 17658x⁴ - 3780x³ + 6804x² - 1296x + 81	$3$	$3$	$4$	$12$	$F_9$ (as 12T46)	$4$	$2$	$[3/2]$	$[3/2, 3/2]_{2}^{4}$	$[1, 0]$	$[1]$
3.12.12.19	$12$	x¹² - 12x¹¹ + 78x¹⁰ - 564x⁹ + 5913x⁸ - 7182x⁶ + 972x⁵ + 7614x⁴ + 3024x³ + 1620x² + 648x + 81	$3$	$3$	$4$	$12$	$C_3^2:C_4\times S_3$ (as 12T119)	$4$	$2$	$[3/2]$	$[3/2, 3/2, 3/2]_{2}^{4}$	$[1, 0]$	$[1]$
3.12.12.2	$12$	x¹² - 48x¹¹ + 606x¹⁰ + 2856x⁹ + 29529x⁸ + 112428x⁷ + 183222x⁶ + 125172x⁵ + 19926x⁴ + 3024x³ + 9072x² - 1620x + 81	$3$	$3$	$4$	$12$	$C_3^2:F_9$ (as 12T173)	$4$	$2$	$[3/2]$	$[3/2, 3/2, 3/2, 3/2]_{2}^{4}$	$[1, 0]$	$[1]$
3.12.12.20	$12$	x¹² + 30x¹⁰ + 228x⁹ + 1872x⁸ + 5778x⁷ + 15336x⁶ + 18036x⁵ + 12879x⁴ + 7074x³ + 3240x² + 810x + 81	$3$	$3$	$4$	$12$	$C_3^2:F_9$ (as 12T173)	$4$	$2$	$[3/2]$	$[3/2, 3/2, 3/2, 3/2]_{2}^{4}$	$[1, 0]$	$[1]$
3.12.12.21	$12$	x¹² - 6x¹¹ + 60x¹⁰ - 114x⁹ + 2286x⁸ + 33750x⁷ + 101790x⁶ + 91152x⁵ + 24867x⁴ + 6102x³ + 5832x² - 1296x + 81	$3$	$3$	$4$	$12$	$C_3^2:F_9$ (as 12T173)	$4$	$2$	$[3/2]$	$[3/2, 3/2, 3/2, 3/2]_{2}^{4}$	$[1, 0]$	$[1]$
3.12.12.22	$12$	x¹² + 36x¹¹ + 426x¹⁰ + 2172x⁹ + 14769x⁸ + 20628x⁷ + 31050x⁶ + 11016x⁵ + 7938x⁴ + 3672x³ + 972x² + 324x + 81	$3$	$3$	$4$	$12$	$C_3^2:C_4\times S_3$ (as 12T119)	$4$	$2$	$[3/2]$	$[3/2, 3/2, 3/2]_{2}^{4}$	$[1, 0]$	$[1]$
3.12.12.23	$12$	x¹² + 6x¹¹ + 12x¹⁰ + 12x⁹ + 189x⁸ + 108x⁷ + 324x⁶ + 648x⁵ + 891x⁴ + 918x³ + 648x² + 324x + 81	$3$	$3$	$4$	$12$	$S_3 \times C_4$ (as 12T11)	$4$	$2$	$[3/2]$	$[3/2]_{2}^{4}$	$[1, 0]$	$[1]$
3.12.12.24	$12$	x¹² - 12x⁷ - 6x⁶ + 72x² + 72x + 18	$3$	$6$	$2$	$12$	$C_3^4:\OD_{16}$ (as 12T215)	$4$	$4$	$[5/4]$	$[5/4, 5/4, 5/4, 5/4]_{4}^{4}$	$[1, 0]$	$[1, 1]$
3.12.12.25	$12$	x¹² - 6x⁷ - 6x⁶ + 9x⁴ + 36x³ + 63x² + 54x + 18	$3$	$6$	$2$	$12$	$C_3^4:\OD_{16}$ (as 12T215)	$4$	$4$	$[5/4]$	$[5/4, 5/4, 5/4, 5/4]_{4}^{4}$	$[1, 0]$	$[1, 1]$
3.12.12.26	$12$	x¹² - 12x⁸ + 6x⁷ + 6x⁶ + 72x⁴ - 36x³ - 27x² + 18x + 9	$3$	$6$	$2$	$12$	$\SOPlus(4,2)$ (as 12T34)	$2$	$4$	$[5/4]$	$[5/4, 5/4]_{4}^{2}$	$[1, 0]$	$[1, 1]$
3.12.12.27	$12$	x¹² - 12x⁷ + 6x⁶ + 9x⁴ + 36x³ + 72x² - 36x + 9	$3$	$6$	$2$	$12$	$\PSU(3,2)$ (as 12T47)	$2$	$4$	$[5/4]$	$[5/4, 5/4]_{4}^{2}$	$[1, 0]$	$[1, 1]$
3.12.12.28	$12$	x¹² + 6x⁶ + 36x⁴ + 36x³ + 9x² + 9	$3$	$6$	$2$	$12$	$\SOPlus(4,2)$ (as 12T34)	$2$	$4$	$[5/4]$	$[5/4, 5/4]_{4}^{2}$	$[1, 0]$	$[1, 1]$
3.12.12.29	$12$	x¹² + 3x + 3	$3$	$12$	$1$	$12$	$F_9:C_2$ (as 12T84)	$2$	$8$	$[9/8]$	$[9/8, 9/8]_{8}^{2}$	$[1, 0]$	$[1, 2]$
3.12.12.3	$12$	x¹² + 6x¹¹ + 60x¹⁰ + 210x⁹ + 1170x⁸ + 2322x⁷ + 1782x⁶ + 6048x⁵ + 13527x⁴ + 8370x³ + 2916x² + 648x + 81	$3$	$3$	$4$	$12$	$C_3^3:(C_4\times S_3)$ (as 12T170)	$4$	$2$	$[3/2]$	$[3/2, 3/2, 3/2, 3/2]_{2}^{4}$	$[1, 0]$	$[1]$
3.12.12.30	$12$	x¹² + 3x² + 3x + 6	$3$	$12$	$1$	$12$	$F_9:C_2$ (as 12T84)	$2$	$8$	$[9/8]$	$[9/8, 9/8]_{8}^{2}$	$[1, 0]$	$[1, 2]$
3.12.12.4	$12$	x¹² - 24x¹¹ + 192x¹⁰ + 1236x⁹ + 2160x⁸ + 7560x⁷ + 29430x⁶ + 30456x⁵ + 6804x⁴ - 540x³ + 1296x² - 648x + 81	$3$	$3$	$4$	$12$	$F_9$ (as 12T46)	$4$	$2$	$[3/2]$	$[3/2, 3/2]_{2}^{4}$	$[1, 0]$	$[1]$
3.12.12.5	$12$	x¹² - 12x¹¹ + 132x¹⁰ - 204x⁹ + 3024x⁸ - 432x⁷ + 3510x⁶ + 2268x⁵ - 972x⁴ + 756x³ + 1620x² + 648x + 81	$3$	$3$	$4$	$12$	$S_3 \times C_4$ (as 12T11)	$4$	$2$	$[3/2]$	$[3/2]_{2}^{4}$	$[1, 0]$	$[1]$
3.12.12.6	$12$	x¹² - 24x¹¹ + 270x¹⁰ - 924x⁹ + 1557x⁸ + 9828x⁷ + 8694x⁶ + 1080x⁵ + 1134x⁴ + 1404x³ + 81	$3$	$3$	$4$	$12$	$C_6.D_6$ (as 12T39)	$4$	$2$	$[3/2]$	$[3/2, 3/2]_{2}^{4}$	$[1, 0]$	$[1]$
3.12.12.7	$12$	x¹² + 6x¹¹ + 24x¹⁰ + 48x⁹ + 576x⁸ + 5508x⁷ + 19710x⁶ + 29538x⁵ + 13608x⁴ - 3456x³ + 1458x² - 324x + 81	$3$	$3$	$4$	$12$	$C_3^2:C_4\times S_3$ (as 12T119)	$4$	$2$	$[3/2]$	$[3/2, 3/2, 3/2]_{2}^{4}$	$[1, 0]$	$[1]$
3.12.12.8	$12$	x¹² + 42x¹¹ + 732x¹⁰ + 6888x⁹ + 37836x⁸ + 101736x⁷ + 148230x⁶ + 129006x⁵ + 72900x⁴ + 28944x³ + 8262x² + 1296x + 81	$3$	$3$	$4$	$12$	$C_3^2:C_4\times S_3$ (as 12T119)	$4$	$2$	$[3/2]$	$[3/2, 3/2, 3/2]_{2}^{4}$	$[1, 0]$	$[1]$
3.12.12.9	$12$	x¹² + 6x¹¹ - 12x¹⁰ - 60x⁹ + 261x⁸ + 540x⁷ + 540x⁶ + 1728x⁵ + 2187x⁴ - 1674x³ + 1296x² - 324x + 81	$3$	$3$	$4$	$12$	$C_2\times C_3^2:C_4$ (as 12T41)	$4$	$2$	$[3/2]$	$[3/2, 3/2]_{2}^{4}$	$[1, 0]$	$[1]$
3.12.13.1	$12$	x¹² + 3x² + 3	$3$	$12$	$1$	$13$	$\SOPlus(4,2)$ (as 12T36)	$2$	$4$	$[5/4]$	$[5/4, 5/4]_{4}^{2}$	$[2, 0]$	$[2, 2]$
3.12.13.2	$12$	x¹² + 3x³ + 6x² + 3	$3$	$12$	$1$	$13$	$S_3^2:C_6$ (as 12T121)	$6$	$4$	$[5/4]$	$[5/4, 5/4]_{4}^{6}$	$[2, 0]$	$[1, 2]$
3.12.13.3	$12$	x¹² + 3x³ + 3x² + 6	$3$	$12$	$1$	$13$	$S_3^2:C_6$ (as 12T121)	$6$	$4$	$[5/4]$	$[5/4, 5/4]_{4}^{6}$	$[2, 0]$	$[1, 2]$
3.12.13.4	$12$	x¹² + 6x² + 6	$3$	$12$	$1$	$13$	$\SOPlus(4,2)$ (as 12T36)	$2$	$4$	$[5/4]$	$[5/4, 5/4]_{4}^{2}$	$[2, 0]$	$[2, 2]$
3.12.13.5	$12$	x¹² + 6x² + 3	$3$	$12$	$1$	$13$	$\SOPlus(4,2)$ (as 12T35)	$2$	$4$	$[5/4]$	$[5/4, 5/4]_{4}^{2}$	$[2, 0]$	$[1, 2]$
3.12.13.6	$12$	x¹² + 3x² + 6	$3$	$12$	$1$	$13$	$\SOPlus(4,2)$ (as 12T35)	$2$	$4$	$[5/4]$	$[5/4, 5/4]_{4}^{2}$	$[2, 0]$	$[1, 2]$
3.12.14.1	$12$	x¹² - 6x⁸ - 6x⁶ + 18x⁴ + 36x² + 18	$3$	$6$	$2$	$14$	$(C_3\times C_3):C_4$ (as 12T17)	$2$	$2$	$[3/2]$	$[3/2, 3/2]_{2}^{2}$	$[2, 0]$	$[1, 1]$
3.12.14.10	$12$	x¹² - 6x⁹ + 12x⁸ + 51x⁶ - 36x⁵ + 36x⁴ - 18x³ + 36x² + 9	$3$	$6$	$2$	$14$	$C_6\times S_3$ (as 12T18)	$6$	$2$	$[3/2]$	$[3/2]_{2}^{6}$	$[2, 0]$	$[1, 1]$
3.12.14.11	$12$	x¹² + 12x¹¹ + 72x¹⁰ + 280x⁹ + 792x⁸ + 1728x⁷ + 2918x⁶ + 3684x⁵ + 3156x⁴ + 1376x³ - 36x² - 168x + 25	$3$	$6$	$2$	$14$	$D_6$ (as 12T3)	$2$	$2$	$[3/2]$	$[3/2]_{2}^{2}$	$[2, 0]$	$[1, 1]$
3.12.14.12	$12$	x¹² + 12x⁸ - 6x⁶ + 36x⁴ - 36x² + 18	$3$	$6$	$2$	$14$	$C_6.D_6$ (as 12T39)	$4$	$2$	$[3/2]$	$[3/2, 3/2]_{2}^{4}$	$[2, 0]$	$[2, 1]$
3.12.14.13	$12$	x¹² + 12x⁹ - 6x⁸ + 30x⁶ - 36x⁵ + 45x⁴ - 36x³ + 54x² + 18	$3$	$6$	$2$	$14$	$C_3^2:C_{12}$ (as 12T73)	$6$	$2$	$[3/2]$	$[3/2, 3/2]_{2}^{6}$	$[2, 0]$	$[1, 1]$
3.12.14.14	$12$	x¹² - 6x⁸ - 6x⁶ + 45x⁴ + 54x² + 18	$3$	$6$	$2$	$14$	$(C_3\times C_3):C_4$ (as 12T17)	$2$	$2$	$[3/2]$	$[3/2, 3/2]_{2}^{2}$	$[2, 0]$	$[1, 1]$
3.12.14.15	$12$	x¹² - 6x⁹ + 6x⁸ + 24x⁶ - 18x⁵ + 9x⁴ - 18x³ + 18x² + 9	$3$	$6$	$2$	$14$	$C_6\times S_3$ (as 12T18)	$6$	$2$	$[3/2]$	$[3/2]_{2}^{6}$	$[2, 0]$	$[1, 1]$
3.12.14.2	$12$	x¹² - 6x⁹ + 6x⁸ + 39x⁶ + 18x⁵ + 18x⁴ + 54x³ + 18	$3$	$6$	$2$	$14$	$C_3^2:C_{12}$ (as 12T73)	$6$	$2$	$[3/2]$	$[3/2, 3/2]_{2}^{6}$	$[2, 0]$	$[1, 1]$
3.12.14.3	$12$	x¹² + 30x⁶ + 72x⁵ + 36x⁴ + 36x³ + 36x² + 18	$3$	$6$	$2$	$14$	$S_3 \times C_4$ (as 12T11)	$4$	$2$	$[3/2]$	$[3/2]_{2}^{4}$	$[2, 0]$	$[2, 1]$

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Elliptic curves over $\Q$
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