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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 (34 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
5.10.10.10	$10$	$x^{10} + 40 x^{6} + 10 x^{5} - 200 x^{4} + 400 x^{2} + 200 x + 25$	$5$	$5$	$2$	$10$	$F_{5}\times C_2$ (as 10T5)	$2$	$4$	$[5/4]$	$[5/4]_{4}^{2}$	$t^{2} + 4 t + 2$	$x^{5} + \left(10 t + 20\right) x^{2} + 20 x + 5$	$[1, 0]$	$[1]$
5.10.10.7	$10$	$x^{10} - 50 x^{7} + 10 x^{6} + 10 x^{5} + 175 x^{4} - 250 x^{3} - 225 x^{2} + 50 x + 25$	$5$	$5$	$2$	$10$	$F_{5}\times C_2$ (as 10T5)	$2$	$4$	$[5/4]$	$[5/4]_{4}^{2}$	$t^{2} + 4 t + 2$	$x^{5} + \left(15 t + 5\right) x^{2} + 5 x + 5$	$[1, 0]$	$[1]$
5.10.10.8	$10$	$x^{10} - 50 x^{7} + 30 x^{6} + 10 x^{5} - 175 x^{4} - 750 x^{3} - 25 x^{2} + 150 x + 25$	$5$	$5$	$2$	$10$	$F_{5}\times C_2$ (as 10T5)	$2$	$4$	$[5/4]$	$[5/4]_{4}^{2}$	$t^{2} + 4 t + 2$	$x^{5} + \left(20 t + 15\right) x^{2} + 15 x + 5$	$[1, 0]$	$[1]$
5.10.10.9	$10$	$x^{10} + 20 x^{6} + 10 x^{5} - 50 x^{4} + 100 x^{2} + 100 x + 25$	$5$	$5$	$2$	$10$	$F_{5}\times C_2$ (as 10T5)	$2$	$4$	$[5/4]$	$[5/4]_{4}^{2}$	$t^{2} + 4 t + 2$	$x^{5} + \left(5 t + 10\right) x^{2} + 10 x + 5$	$[1, 0]$	$[1]$
5.10.11.3	$10$	$x^{10} + 10 x^{2} + 5$	$5$	$10$	$1$	$11$	$F_{5}\times C_2$ (as 10T5)	$2$	$4$	$[5/4]$	$[5/4]_{4}^{2}$	$t + 3$	$x^{10} + 10 x^{2} + 5$	$[2, 0]$	$[2, 1]$
5.10.11.4	$10$	$x^{10} + 15 x^{2} + 5$	$5$	$10$	$1$	$11$	$F_{5}\times C_2$ (as 10T5)	$2$	$4$	$[5/4]$	$[5/4]_{4}^{2}$	$t + 3$	$x^{10} + 15 x^{2} + 5$	$[2, 0]$	$[2, 1]$
5.10.11.7	$10$	$x^{10} + 5 x^{2} + 10$	$5$	$10$	$1$	$11$	$F_{5}\times C_2$ (as 10T5)	$2$	$4$	$[5/4]$	$[5/4]_{4}^{2}$	$t + 3$	$x^{10} + 5 x^{2} + 10$	$[2, 0]$	$[2, 1]$
5.10.11.8	$10$	$x^{10} + 20 x^{2} + 10$	$5$	$10$	$1$	$11$	$F_{5}\times C_2$ (as 10T5)	$2$	$4$	$[5/4]$	$[5/4]_{4}^{2}$	$t + 3$	$x^{10} + 20 x^{2} + 10$	$[2, 0]$	$[2, 1]$
5.10.13.10	$10$	$x^{10} + 10 x^{4} + 10$	$5$	$10$	$1$	$13$	$F_{5}\times C_2$ (as 10T5)	$4$	$2$	$[3/2]$	$[3/2]_{2}^{4}$	$t + 3$	$x^{10} + 10 x^{4} + 10$	$[4, 0]$	$[4, 1]$
5.10.13.3	$10$	$x^{10} + 20 x^{4} + 5$	$5$	$10$	$1$	$13$	$F_{5}\times C_2$ (as 10T5)	$4$	$2$	$[3/2]$	$[3/2]_{2}^{4}$	$t + 3$	$x^{10} + 20 x^{4} + 5$	$[4, 0]$	$[4, 1]$
5.10.13.4	$10$	$x^{10} + 5 x^{4} + 5$	$5$	$10$	$1$	$13$	$F_{5}\times C_2$ (as 10T5)	$4$	$2$	$[3/2]$	$[3/2]_{2}^{4}$	$t + 3$	$x^{10} + 5 x^{4} + 5$	$[4, 0]$	$[4, 1]$
5.10.13.9	$10$	$x^{10} + 15 x^{4} + 10$	$5$	$10$	$1$	$13$	$F_{5}\times C_2$ (as 10T5)	$4$	$2$	$[3/2]$	$[3/2]_{2}^{4}$	$t + 3$	$x^{10} + 15 x^{4} + 10$	$[4, 0]$	$[4, 1]$
5.10.14.10	$10$	$x^{10} - 10 x^{8} + 400 x^{6} + 10 x^{5} + 200 x^{3} + 25$	$5$	$5$	$2$	$14$	$F_{5}\times C_2$ (as 10T5)	$2$	$4$	$[7/4]$	$[7/4]_{4}^{2}$	$t^{2} + 4 t + 2$	$x^{5} + \left(5 t + 10\right) x^{4} + 20 x^{3} + 5$	$[3, 0]$	$[1]$
5.10.14.7	$10$	$x^{10} - 50 x^{9} - 165 x^{8} - 250 x^{7} + 25 x^{6} + 10 x^{5} - 250 x^{4} + 50 x^{3} + 25$	$5$	$5$	$2$	$14$	$F_{5}\times C_2$ (as 10T5)	$2$	$4$	$[7/4]$	$[7/4]_{4}^{2}$	$t^{2} + 4 t + 2$	$x^{5} + \left(20 t + 15\right) x^{4} + 5 x^{3} + 5$	$[3, 0]$	$[1]$
5.10.14.8	$10$	$x^{10} - 50 x^{9} + 195 x^{8} - 500 x^{7} + 100 x^{6} + 10 x^{5} - 250 x^{4} + 100 x^{3} + 25$	$5$	$5$	$2$	$14$	$F_{5}\times C_2$ (as 10T5)	$2$	$4$	$[7/4]$	$[7/4]_{4}^{2}$	$t^{2} + 4 t + 2$	$x^{5} + \left(15 t + 5\right) x^{4} + 10 x^{3} + 5$	$[3, 0]$	$[1]$
5.10.14.9	$10$	$x^{10} - 170 x^{8} + 225 x^{6} + 10 x^{5} + 150 x^{3} + 25$	$5$	$5$	$2$	$14$	$F_{5}\times C_2$ (as 10T5)	$2$	$4$	$[7/4]$	$[7/4]_{4}^{2}$	$t^{2} + 4 t + 2$	$x^{5} + \left(10 t + 20\right) x^{4} + 15 x^{3} + 5$	$[3, 0]$	$[1]$
5.10.15.15	$10$	$x^{10} + 10 x^{6} + 10$	$5$	$10$	$1$	$15$	$F_{5}\times C_2$ (as 10T5)	$2$	$4$	$[7/4]$	$[7/4]_{4}^{2}$	$t + 3$	$x^{10} + 10 x^{6} + 10$	$[6, 0]$	$[2, 1]$
5.10.15.16	$10$	$x^{10} + 15 x^{6} + 10$	$5$	$10$	$1$	$15$	$F_{5}\times C_2$ (as 10T5)	$2$	$4$	$[7/4]$	$[7/4]_{4}^{2}$	$t + 3$	$x^{10} + 15 x^{6} + 10$	$[6, 0]$	$[2, 1]$
5.10.15.3	$10$	$x^{10} + 5 x^{6} + 5$	$5$	$10$	$1$	$15$	$F_{5}\times C_2$ (as 10T5)	$2$	$4$	$[7/4]$	$[7/4]_{4}^{2}$	$t + 3$	$x^{10} + 5 x^{6} + 5$	$[6, 0]$	$[2, 1]$
5.10.15.4	$10$	$x^{10} + 20 x^{6} + 5$	$5$	$10$	$1$	$15$	$F_{5}\times C_2$ (as 10T5)	$2$	$4$	$[7/4]$	$[7/4]_{4}^{2}$	$t + 3$	$x^{10} + 20 x^{6} + 5$	$[6, 0]$	$[2, 1]$
5.10.17.31	$10$	$x^{10} + 5 x^{8} + 10$	$5$	$10$	$1$	$17$	$F_{5}\times C_2$ (as 10T5)	$4$	$2$	$[2]$	$[2]_{2}^{4}$	$t + 3$	$x^{10} + 5 x^{8} + 10$	$[8, 0]$	$[4, 1]$
5.10.17.32	$10$	$x^{10} + 20 x^{8} + 10$	$5$	$10$	$1$	$17$	$F_{5}\times C_2$ (as 10T5)	$4$	$2$	$[2]$	$[2]_{2}^{4}$	$t + 3$	$x^{10} + 20 x^{8} + 10$	$[8, 0]$	$[4, 1]$
5.10.17.7	$10$	$x^{10} + 10 x^{8} + 5$	$5$	$10$	$1$	$17$	$F_{5}\times C_2$ (as 10T5)	$4$	$2$	$[2]$	$[2]_{2}^{4}$	$t + 3$	$x^{10} + 10 x^{8} + 5$	$[8, 0]$	$[4, 1]$
5.10.17.8	$10$	$x^{10} + 15 x^{8} + 5$	$5$	$10$	$1$	$17$	$F_{5}\times C_2$ (as 10T5)	$4$	$2$	$[2]$	$[2]_{2}^{4}$	$t + 3$	$x^{10} + 15 x^{8} + 5$	$[8, 0]$	$[4, 1]$
5.10.18.1	$10$	$x^{10} + 200 x^{6} + 60 x^{5} - 1250 x^{4} + 10000 x^{2} + 6000 x + 900$	$5$	$5$	$2$	$18$	$F_{5}\times C_2$ (as 10T5)	$2$	$4$	$[9/4]$	$[9/4]_{4}^{2}$	$t^{2} + 4 t + 2$	$x^{5} + \left(25 t + 50\right) x^{2} + 100 x + 30$	$[5, 0]$	$[1]$
5.10.18.2	$10$	$x^{10} - 50 x^{7} - 50 x^{6} - 140 x^{5} - 4375 x^{4} - 8750 x^{3} - 10875 x^{2} - 6500 x - 100$	$5$	$5$	$2$	$18$	$F_{5}\times C_2$ (as 10T5)	$2$	$4$	$[9/4]$	$[9/4]_{4}^{2}$	$t^{2} + 4 t + 2$	$x^{5} + \left(50 t + 75\right) x^{2} + \left(50 t + 75\right) x + 50 t + 30$	$[5, 0]$	$[1]$
5.10.18.3	$10$	$x^{10} - 300 x^{7} - 300 x^{6} - 340 x^{5} + 11250 x^{4} + 15000 x^{3} + 23500 x^{2} + 11000 x + 8900$	$5$	$5$	$2$	$18$	$F_{5}\times C_2$ (as 10T5)	$2$	$4$	$[9/4]$	$[9/4]_{4}^{2}$	$t^{2} + 4 t + 2$	$x^{5} + 75 t x^{2} + \left(100 t + 50\right) x + 100 t + 30$	$[5, 0]$	$[1]$
5.10.18.4	$10$	$x^{10} - 250 x^{7} - 50 x^{6} - 40 x^{5} - 4375 x^{4} - 3750 x^{3} - 5625 x^{2} - 1500 x - 850$	$5$	$5$	$2$	$18$	$F_{5}\times C_2$ (as 10T5)	$2$	$4$	$[9/4]$	$[9/4]_{4}^{2}$	$t^{2} + 4 t + 2$	$x^{5} + \left(100 t + 75\right) x^{2} + \left(25 t + 25\right) x + 25 t + 30$	$[5, 0]$	$[1]$
5.10.18.5	$10$	$x^{10} + 100 x^{7} - 300 x^{6} - 240 x^{5} + 2500 x^{4} - 15000 x^{3} - 750 x^{2} + 13500 x + 3150$	$5$	$5$	$2$	$18$	$F_{5}\times C_2$ (as 10T5)	$2$	$4$	$[9/4]$	$[9/4]_{4}^{2}$	$t^{2} + 4 t + 2$	$x^{5} + 50 x^{2} + 75 t x + 75 t + 30$	$[5, 0]$	$[1]$
5.10.19.16	$10$	$x^{10} + 75 x^{2} + 60$	$5$	$10$	$1$	$19$	$F_{5}\times C_2$ (as 10T5)	$2$	$4$	$[9/4]$	$[9/4]_{4}^{2}$	$t + 3$	$x^{10} + 75 x^{2} + 60$	$[10, 0]$	$[2, 1]$
5.10.19.17	$10$	$x^{10} + 10$	$5$	$10$	$1$	$19$	$F_{5}\times C_2$ (as 10T5)	$2$	$4$	$[9/4]$	$[9/4]_{4}^{2}$	$t + 3$	$x^{10} + 10$	$[10, 0]$	$[2, 1]$
5.10.19.18	$10$	$x^{10} + 50 x^{2} + 85$	$5$	$10$	$1$	$19$	$F_{5}\times C_2$ (as 10T5)	$2$	$4$	$[9/4]$	$[9/4]_{4}^{2}$	$t + 3$	$x^{10} + 50 x^{2} + 85$	$[10, 0]$	$[2, 1]$
5.10.19.19	$10$	$x^{10} + 100 x^{2} + 35$	$5$	$10$	$1$	$19$	$F_{5}\times C_2$ (as 10T5)	$2$	$4$	$[9/4]$	$[9/4]_{4}^{2}$	$t + 3$	$x^{10} + 100 x^{2} + 35$	$[10, 0]$	$[2, 1]$
5.10.19.20	$10$	$x^{10} + 25 x^{2} + 110$	$5$	$10$	$1$	$19$	$F_{5}\times C_2$ (as 10T5)	$2$	$4$	$[9/4]$	$[9/4]_{4}^{2}$	$t + 3$	$x^{10} + 25 x^{2} + 110$	$[10, 0]$	$[2, 1]$

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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.