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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 (36 matches)

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Label	$n$	Polynomial	$p$	$e$	$f$	$c$	Galois group	$u$	$t$	Visible slopes	Slope content	Unram. Ext.	Eisen. Poly.	Ind. of Insep.	Assoc. Inertia
2.4.4.3	$4$	$x^{4} + 2 x^{3} + 4 x^{2} + 12 x + 12$	$2$	$2$	$2$	$4$	$D_{4}$ (as 4T3)	$2$	$1$	$[2]$	$[2, 2]^{2}$	$t^{2} + t + 1$	$x^{2} + \left(2 t + 2\right) x + 4 t + 2$	$[1, 0]$	$[1]$
2.4.4.4	$4$	$x^{4} - 2 x^{3} + 4 x^{2} + 12 x + 12$	$2$	$2$	$2$	$4$	$D_{4}$ (as 4T3)	$2$	$1$	$[2]$	$[2, 2]^{2}$	$t^{2} + t + 1$	$x^{2} + 2 t x + 4 t + 2$	$[1, 0]$	$[1]$
2.4.6.5	$4$	$x^{4} - 4 x^{3} + 36 x^{2} + 8 x + 148$	$2$	$2$	$2$	$6$	$D_{4}$ (as 4T3)	$2$	$1$	$[3]$	$[2, 3]^{2}$	$t^{2} + t + 1$	$x^{2} + 4 t x + 8 t + 14$	$[2, 0]$	$[1]$
2.4.6.6	$4$	$x^{4} - 4 x^{3} + 28 x^{2} - 24 x + 36$	$2$	$2$	$2$	$6$	$D_{4}$ (as 4T3)	$2$	$1$	$[3]$	$[2, 3]^{2}$	$t^{2} + t + 1$	$x^{2} + 4 t x + 6$	$[2, 0]$	$[1]$
2.4.6.8	$4$	$x^{4} + 2 x^{3} + 2$	$2$	$4$	$1$	$6$	$D_{4}$ (as 4T3)	$2$	$1$	$[2, 2]$	$[2, 2]^{2}$	$t + 1$	$x^{4} + 2 x^{3} + 2$	$[3, 3, 0]$	$[2]$
2.4.6.9	$4$	$x^{4} + 2 x^{3} + 6$	$2$	$4$	$1$	$6$	$D_{4}$ (as 4T3)	$2$	$1$	$[2, 2]$	$[2, 2]^{2}$	$t + 1$	$x^{4} + 2 x^{3} + 6$	$[3, 3, 0]$	$[2]$
2.4.8.5	$4$	$x^{4} + 2 x^{2} + 4 x + 6$	$2$	$4$	$1$	$8$	$D_{4}$ (as 4T3)	$2$	$1$	$[2, 3]$	$[2, 3]^{2}$	$t + 1$	$x^{4} + 2 x^{2} + 4 x + 6$	$[5, 2, 0]$	$[1, 1]$
2.4.8.6	$4$	$x^{4} + 6 x^{2} + 4 x + 10$	$2$	$4$	$1$	$8$	$D_{4}$ (as 4T3)	$2$	$1$	$[2, 3]$	$[2, 3]^{2}$	$t + 1$	$x^{4} + 6 x^{2} + 4 x + 10$	$[5, 2, 0]$	$[1, 1]$
2.4.9.1	$4$	$x^{4} + 10 x^{2} + 2$	$2$	$4$	$1$	$9$	$D_{4}$ (as 4T3)	$1$	$1$	$[2, 7/2]$	$[2, 3, 7/2]$	$t + 1$	$x^{4} + 10 x^{2} + 2$	$[6, 2, 0]$	$[1, 1]$
2.4.9.2	$4$	$x^{4} + 2 x^{2} + 2$	$2$	$4$	$1$	$9$	$D_{4}$ (as 4T3)	$1$	$1$	$[2, 7/2]$	$[2, 3, 7/2]$	$t + 1$	$x^{4} + 2 x^{2} + 2$	$[6, 2, 0]$	$[1, 1]$
2.4.9.3	$4$	$x^{4} + 4 x^{3} + 2 x^{2} + 2$	$2$	$4$	$1$	$9$	$D_{4}$ (as 4T3)	$1$	$1$	$[2, 7/2]$	$[2, 3, 7/2]$	$t + 1$	$x^{4} + 4 x^{3} + 2 x^{2} + 2$	$[6, 2, 0]$	$[1, 1]$
2.4.9.4	$4$	$x^{4} + 10 x^{2} + 8 x + 2$	$2$	$4$	$1$	$9$	$D_{4}$ (as 4T3)	$1$	$1$	$[2, 7/2]$	$[2, 3, 7/2]$	$t + 1$	$x^{4} + 10 x^{2} + 8 x + 2$	$[6, 2, 0]$	$[1, 1]$
2.4.9.5	$4$	$x^{4} + 10 x^{2} + 8 x + 6$	$2$	$4$	$1$	$9$	$D_{4}$ (as 4T3)	$1$	$1$	$[2, 7/2]$	$[2, 3, 7/2]$	$t + 1$	$x^{4} + 10 x^{2} + 8 x + 6$	$[6, 2, 0]$	$[1, 1]$
2.4.9.6	$4$	$x^{4} + 4 x^{3} + 10 x^{2} + 14$	$2$	$4$	$1$	$9$	$D_{4}$ (as 4T3)	$1$	$1$	$[2, 7/2]$	$[2, 3, 7/2]$	$t + 1$	$x^{4} + 4 x^{3} + 10 x^{2} + 14$	$[6, 2, 0]$	$[1, 1]$
2.4.9.7	$4$	$x^{4} + 2 x^{2} + 6$	$2$	$4$	$1$	$9$	$D_{4}$ (as 4T3)	$1$	$1$	$[2, 7/2]$	$[2, 3, 7/2]$	$t + 1$	$x^{4} + 2 x^{2} + 6$	$[6, 2, 0]$	$[1, 1]$
2.4.9.8	$4$	$x^{4} + 10 x^{2} + 6$	$2$	$4$	$1$	$9$	$D_{4}$ (as 4T3)	$1$	$1$	$[2, 7/2]$	$[2, 3, 7/2]$	$t + 1$	$x^{4} + 10 x^{2} + 6$	$[6, 2, 0]$	$[1, 1]$
2.4.10.1	$4$	$x^{4} + 4 x^{3} + 10$	$2$	$4$	$1$	$10$	$D_{4}$ (as 4T3)	$1$	$1$	$[3, 7/2]$	$[2, 3, 7/2]$	$t + 1$	$x^{4} + 4 x^{3} + 10$	$[7, 4, 0]$	$[1, 1]$
2.4.10.2	$4$	$x^{4} + 4 x^{3} + 2$	$2$	$4$	$1$	$10$	$D_{4}$ (as 4T3)	$1$	$1$	$[3, 7/2]$	$[2, 3, 7/2]$	$t + 1$	$x^{4} + 4 x^{3} + 2$	$[7, 4, 0]$	$[1, 1]$
2.4.10.3	$4$	$x^{4} + 4 x^{3} + 8 x^{2} + 2$	$2$	$4$	$1$	$10$	$D_{4}$ (as 4T3)	$1$	$1$	$[3, 7/2]$	$[2, 3, 7/2]$	$t + 1$	$x^{4} + 4 x^{3} + 8 x^{2} + 2$	$[7, 4, 0]$	$[1, 1]$
2.4.10.4	$4$	$x^{4} + 4 x^{3} + 8 x^{2} + 10$	$2$	$4$	$1$	$10$	$D_{4}$ (as 4T3)	$1$	$1$	$[3, 7/2]$	$[2, 3, 7/2]$	$t + 1$	$x^{4} + 4 x^{3} + 8 x^{2} + 10$	$[7, 4, 0]$	$[1, 1]$
2.4.10.5	$4$	$x^{4} + 4 x^{3} + 4 x^{2} + 10$	$2$	$4$	$1$	$10$	$D_{4}$ (as 4T3)	$1$	$1$	$[3, 7/2]$	$[2, 3, 7/2]$	$t + 1$	$x^{4} + 4 x^{3} + 4 x^{2} + 10$	$[7, 4, 0]$	$[1, 1]$
2.4.10.6	$4$	$x^{4} + 4 x^{3} + 12 x^{2} + 10$	$2$	$4$	$1$	$10$	$D_{4}$ (as 4T3)	$1$	$1$	$[3, 7/2]$	$[2, 3, 7/2]$	$t + 1$	$x^{4} + 4 x^{3} + 12 x^{2} + 10$	$[7, 4, 0]$	$[1, 1]$
2.4.10.7	$4$	$x^{4} + 4 x^{3} + 4 x^{2} + 2$	$2$	$4$	$1$	$10$	$D_{4}$ (as 4T3)	$1$	$1$	$[3, 7/2]$	$[2, 3, 7/2]$	$t + 1$	$x^{4} + 4 x^{3} + 4 x^{2} + 2$	$[7, 4, 0]$	$[1, 1]$
2.4.10.8	$4$	$x^{4} + 4 x^{3} + 12 x^{2} + 2$	$2$	$4$	$1$	$10$	$D_{4}$ (as 4T3)	$1$	$1$	$[3, 7/2]$	$[2, 3, 7/2]$	$t + 1$	$x^{4} + 4 x^{3} + 12 x^{2} + 2$	$[7, 4, 0]$	$[1, 1]$
2.4.11.11	$4$	$x^{4} + 10$	$2$	$4$	$1$	$11$	$D_{4}$ (as 4T3)	$1$	$1$	$[3, 4]$	$[2, 3, 4]$	$t + 1$	$x^{4} + 10$	$[8, 4, 0]$	$[1, 1]$
2.4.11.12	$4$	$x^{4} + 26$	$2$	$4$	$1$	$11$	$D_{4}$ (as 4T3)	$1$	$1$	$[3, 4]$	$[2, 3, 4]$	$t + 1$	$x^{4} + 26$	$[8, 4, 0]$	$[1, 1]$
2.4.11.13	$4$	$x^{4} + 8 x^{3} + 8 x + 10$	$2$	$4$	$1$	$11$	$D_{4}$ (as 4T3)	$2$	$1$	$[3, 4]$	$[3, 4]^{2}$	$t + 1$	$x^{4} + 8 x^{3} + 8 x + 10$	$[8, 4, 0]$	$[1, 1]$
2.4.11.14	$4$	$x^{4} + 8 x + 10$	$2$	$4$	$1$	$11$	$D_{4}$ (as 4T3)	$2$	$1$	$[3, 4]$	$[3, 4]^{2}$	$t + 1$	$x^{4} + 8 x + 10$	$[8, 4, 0]$	$[1, 1]$
2.4.11.15	$4$	$x^{4} + 12 x^{2} + 8 x + 2$	$2$	$4$	$1$	$11$	$D_{4}$ (as 4T3)	$1$	$1$	$[3, 4]$	$[2, 3, 4]$	$t + 1$	$x^{4} + 12 x^{2} + 8 x + 2$	$[8, 4, 0]$	$[1, 1]$
2.4.11.16	$4$	$x^{4} + 12 x^{2} + 8 x + 18$	$2$	$4$	$1$	$11$	$D_{4}$ (as 4T3)	$1$	$1$	$[3, 4]$	$[2, 3, 4]$	$t + 1$	$x^{4} + 12 x^{2} + 8 x + 18$	$[8, 4, 0]$	$[1, 1]$
2.4.11.17	$4$	$x^{4} + 8 x^{3} + 8 x + 2$	$2$	$4$	$1$	$11$	$D_{4}$ (as 4T3)	$2$	$1$	$[3, 4]$	$[3, 4]^{2}$	$t + 1$	$x^{4} + 8 x^{3} + 8 x + 2$	$[8, 4, 0]$	$[1, 1]$
2.4.11.18	$4$	$x^{4} + 8 x + 18$	$2$	$4$	$1$	$11$	$D_{4}$ (as 4T3)	$2$	$1$	$[3, 4]$	$[3, 4]^{2}$	$t + 1$	$x^{4} + 8 x + 18$	$[8, 4, 0]$	$[1, 1]$
2.4.11.19	$4$	$x^{4} + 12 x^{2} + 8 x + 26$	$2$	$4$	$1$	$11$	$D_{4}$ (as 4T3)	$1$	$1$	$[3, 4]$	$[2, 3, 4]$	$t + 1$	$x^{4} + 12 x^{2} + 8 x + 26$	$[8, 4, 0]$	$[1, 1]$
2.4.11.20	$4$	$x^{4} + 12 x^{2} + 8 x + 10$	$2$	$4$	$1$	$11$	$D_{4}$ (as 4T3)	$1$	$1$	$[3, 4]$	$[2, 3, 4]$	$t + 1$	$x^{4} + 12 x^{2} + 8 x + 10$	$[8, 4, 0]$	$[1, 1]$
2.4.11.5	$4$	$x^{4} + 2$	$2$	$4$	$1$	$11$	$D_{4}$ (as 4T3)	$1$	$1$	$[3, 4]$	$[2, 3, 4]$	$t + 1$	$x^{4} + 2$	$[8, 4, 0]$	$[1, 1]$
2.4.11.6	$4$	$x^{4} + 18$	$2$	$4$	$1$	$11$	$D_{4}$ (as 4T3)	$1$	$1$	$[3, 4]$	$[2, 3, 4]$	$t + 1$	$x^{4} + 18$	$[8, 4, 0]$	$[1, 1]$

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Elliptic curves over $\Q$
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This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.