$p$-adic field search results

Results (24 matches)

 

Label	$n$	Polynomial	$p$	$e$	$f$	$c$	Galois group	$u$	$t$	Visible slopes	Slope content	Unram. Ext.	Eisen. Poly.	Ind. of Insep.	Assoc. Inertia
5.15.16.2	$15$	$x^{15} + 10 x^{3} + 10 x^{2} + 5$	$5$	$15$	$1$	$16$	$(C_5^2 : C_3):C_4$ (as 15T17)	$2$	$6$	$[7/6]$	$[7/6, 7/6]_{6}^{2}$	$t + 3$	$x^{15} + 10 x^{3} + 10 x^{2} + 5$	$[2, 0]$	$[2, 2]$
5.15.16.3	$15$	$x^{15} + 20 x^{3} + 15 x^{2} + 5$	$5$	$15$	$1$	$16$	$(C_5^2 : C_3):C_4$ (as 15T17)	$2$	$6$	$[7/6]$	$[7/6, 7/6]_{6}^{2}$	$t + 3$	$x^{15} + 20 x^{3} + 15 x^{2} + 5$	$[2, 0]$	$[2, 2]$
5.15.18.49	$15$	$x^{15} + 10 x^{5} + 20 x^{4} + 5$	$5$	$15$	$1$	$18$	$(C_5^2 : C_3):C_4$ (as 15T17)	$4$	$3$	$[4/3]$	$[4/3, 4/3]_{3}^{4}$	$t + 3$	$x^{15} + 10 x^{5} + 20 x^{4} + 5$	$[4, 0]$	$[4, 2]$
5.15.18.50	$15$	$x^{15} + 10 x^{5} + 5 x^{4} + 5$	$5$	$15$	$1$	$18$	$(C_5^2 : C_3):C_4$ (as 15T17)	$4$	$3$	$[4/3]$	$[4/3, 4/3]_{3}^{4}$	$t + 3$	$x^{15} + 10 x^{5} + 5 x^{4} + 5$	$[4, 0]$	$[4, 2]$
5.15.22.1	$15$	$x^{15} + 5 x^{10} + 10 x^{9} + 10 x^{8} + 10 x^{5} + 5$	$5$	$15$	$1$	$22$	$(C_5^2 : C_3):C_4$ (as 15T17)	$4$	$3$	$[5/3]$	$[5/3, 5/3]_{3}^{4}$	$t + 3$	$x^{15} + 5 x^{10} + 10 x^{9} + 10 x^{8} + 10 x^{5} + 5$	$[8, 0]$	$[4, 2]$
5.15.22.11	$15$	$x^{15} + 5 x^{10} + 20 x^{9} + 15 x^{8} + 20 x^{5} + 5$	$5$	$15$	$1$	$22$	$(C_5^2 : C_3):C_4$ (as 15T17)	$4$	$3$	$[5/3]$	$[5/3, 5/3]_{3}^{4}$	$t + 3$	$x^{15} + 5 x^{10} + 20 x^{9} + 15 x^{8} + 20 x^{5} + 5$	$[8, 0]$	$[4, 2]$
5.15.22.12	$15$	$x^{15} + 15 x^{9} + 10 x^{8} + 10 x^{5} + 5$	$5$	$15$	$1$	$22$	$(C_5^2 : C_3):C_4$ (as 15T17)	$4$	$3$	$[5/3]$	$[5/3, 5/3]_{3}^{4}$	$t + 3$	$x^{15} + 15 x^{9} + 10 x^{8} + 10 x^{5} + 5$	$[8, 0]$	$[4, 2]$
5.15.22.13	$15$	$x^{15} + 5 x^{10} + 15 x^{9} + 10 x^{8} + 5$	$5$	$15$	$1$	$22$	$(C_5^2 : C_3):C_4$ (as 15T17)	$4$	$3$	$[5/3]$	$[5/3, 5/3]_{3}^{4}$	$t + 3$	$x^{15} + 5 x^{10} + 15 x^{9} + 10 x^{8} + 5$	$[8, 0]$	$[4, 2]$
5.15.22.15	$15$	$x^{15} + 15 x^{10} + 15 x^{8} + 5$	$5$	$15$	$1$	$22$	$(C_5^2 : C_3):C_4$ (as 15T17)	$4$	$3$	$[5/3]$	$[5/3, 5/3]_{3}^{4}$	$t + 3$	$x^{15} + 15 x^{10} + 15 x^{8} + 5$	$[8, 0]$	$[4, 2]$
5.15.22.17	$15$	$x^{15} + 10 x^{10} + 20 x^{9} + 10 x^{8} + 15 x^{5} + 5$	$5$	$15$	$1$	$22$	$(C_5^2 : C_3):C_4$ (as 15T17)	$4$	$3$	$[5/3]$	$[5/3, 5/3]_{3}^{4}$	$t + 3$	$x^{15} + 10 x^{10} + 20 x^{9} + 10 x^{8} + 15 x^{5} + 5$	$[8, 0]$	$[4, 2]$
5.15.22.18	$15$	$x^{15} + 15 x^{10} + 5 x^{9} + 10 x^{8} + 20 x^{5} + 5$	$5$	$15$	$1$	$22$	$(C_5^2 : C_3):C_4$ (as 15T17)	$4$	$3$	$[5/3]$	$[5/3, 5/3]_{3}^{4}$	$t + 3$	$x^{15} + 15 x^{10} + 5 x^{9} + 10 x^{8} + 20 x^{5} + 5$	$[8, 0]$	$[4, 2]$
5.15.22.2	$15$	$x^{15} + 5 x^{10} + 20 x^{9} + 15 x^{8} + 15 x^{5} + 5$	$5$	$15$	$1$	$22$	$(C_5^2 : C_3):C_4$ (as 15T17)	$4$	$3$	$[5/3]$	$[5/3, 5/3]_{3}^{4}$	$t + 3$	$x^{15} + 5 x^{10} + 20 x^{9} + 15 x^{8} + 15 x^{5} + 5$	$[8, 0]$	$[4, 2]$
5.15.22.20	$15$	$x^{15} + 20 x^{10} + 20 x^{9} + 15 x^{8} + 5$	$5$	$15$	$1$	$22$	$(C_5^2 : C_3):C_4$ (as 15T17)	$4$	$3$	$[5/3]$	$[5/3, 5/3]_{3}^{4}$	$t + 3$	$x^{15} + 20 x^{10} + 20 x^{9} + 15 x^{8} + 5$	$[8, 0]$	$[4, 2]$
5.15.22.3	$15$	$x^{15} + 5 x^{10} + 10 x^{9} + 15 x^{8} + 5$	$5$	$15$	$1$	$22$	$(C_5^2 : C_3):C_4$ (as 15T17)	$4$	$3$	$[5/3]$	$[5/3, 5/3]_{3}^{4}$	$t + 3$	$x^{15} + 5 x^{10} + 10 x^{9} + 15 x^{8} + 5$	$[8, 0]$	$[4, 2]$
5.15.28.1	$15$	$x^{15} + 5 x^{14} + 5 x^{10} + 50 x^{3} + 75 x^{2} + 75 x + 55$	$5$	$15$	$1$	$28$	$(C_5^2 : C_3):C_4$ (as 15T17)	$2$	$6$	$[13/6]$	$[13/6, 13/6]_{6}^{2}$	$t + 3$	$x^{15} + 5 x^{14} + 5 x^{10} + 50 x^{3} + 75 x^{2} + 75 x + 55$	$[14, 0]$	$[2, 2]$
5.15.28.18	$15$	$x^{15} + 5 x^{14} + 10 x^{10} + 5 x^{5} + 25 x^{2} + 25 x + 30$	$5$	$15$	$1$	$28$	$(C_5^2 : C_3):C_4$ (as 15T17)	$2$	$6$	$[13/6]$	$[13/6, 13/6]_{6}^{2}$	$t + 3$	$x^{15} + 5 x^{14} + 10 x^{10} + 5 x^{5} + 25 x^{2} + 25 x + 30$	$[14, 0]$	$[2, 2]$
5.15.28.34	$15$	$x^{15} + 5 x^{14} + 10 x^{10} + 10 x^{5} + 100 x + 80$	$5$	$15$	$1$	$28$	$(C_5^2 : C_3):C_4$ (as 15T17)	$2$	$6$	$[13/6]$	$[13/6, 13/6]_{6}^{2}$	$t + 3$	$x^{15} + 5 x^{14} + 10 x^{10} + 10 x^{5} + 100 x + 80$	$[14, 0]$	$[2, 2]$
5.15.28.35	$15$	$x^{15} + 5 x^{14} + 5 x^{10} + 20 x^{5} + 100 x^{2} + 25 x + 30$	$5$	$15$	$1$	$28$	$(C_5^2 : C_3):C_4$ (as 15T17)	$2$	$6$	$[13/6]$	$[13/6, 13/6]_{6}^{2}$	$t + 3$	$x^{15} + 5 x^{14} + 5 x^{10} + 20 x^{5} + 100 x^{2} + 25 x + 30$	$[14, 0]$	$[2, 2]$
5.15.28.41	$15$	$x^{15} + 20 x^{14} + 10 x^{10} + 20 x^{5} + 100 x^{3} + 50 x^{2} + 100 x + 105$	$5$	$15$	$1$	$28$	$(C_5^2 : C_3):C_4$ (as 15T17)	$2$	$6$	$[13/6]$	$[13/6, 13/6]_{6}^{2}$	$t + 3$	$x^{15} + 20 x^{14} + 10 x^{10} + 20 x^{5} + 100 x^{3} + 50 x^{2} + 100 x + 105$	$[14, 0]$	$[2, 2]$
5.15.28.44	$15$	$x^{15} + 5 x^{14} + 15 x^{10} + 50 x^{3} + 75 x^{2} + 100 x + 105$	$5$	$15$	$1$	$28$	$(C_5^2 : C_3):C_4$ (as 15T17)	$2$	$6$	$[13/6]$	$[13/6, 13/6]_{6}^{2}$	$t + 3$	$x^{15} + 5 x^{14} + 15 x^{10} + 50 x^{3} + 75 x^{2} + 100 x + 105$	$[14, 0]$	$[2, 2]$
5.15.28.50	$15$	$x^{15} + 20 x^{14} + 10 x^{5} + 25 x^{3} + 75 x^{2} + 25 x + 105$	$5$	$15$	$1$	$28$	$(C_5^2 : C_3):C_4$ (as 15T17)	$2$	$6$	$[13/6]$	$[13/6, 13/6]_{6}^{2}$	$t + 3$	$x^{15} + 20 x^{14} + 10 x^{5} + 25 x^{3} + 75 x^{2} + 25 x + 105$	$[14, 0]$	$[2, 2]$
5.15.28.69	$15$	$x^{15} + 20 x^{14} + 5 x^{10} + 20 x^{5} + 75 x^{2} + 50 x + 30$	$5$	$15$	$1$	$28$	$(C_5^2 : C_3):C_4$ (as 15T17)	$2$	$6$	$[13/6]$	$[13/6, 13/6]_{6}^{2}$	$t + 3$	$x^{15} + 20 x^{14} + 5 x^{10} + 20 x^{5} + 75 x^{2} + 50 x + 30$	$[14, 0]$	$[2, 2]$
5.15.28.72	$15$	$x^{15} + 20 x^{14} + 5 x^{10} + 25 x^{3} + 50 x^{2} + 50 x + 80$	$5$	$15$	$1$	$28$	$(C_5^2 : C_3):C_4$ (as 15T17)	$2$	$6$	$[13/6]$	$[13/6, 13/6]_{6}^{2}$	$t + 3$	$x^{15} + 20 x^{14} + 5 x^{10} + 25 x^{3} + 50 x^{2} + 50 x + 80$	$[14, 0]$	$[2, 2]$
5.15.28.78	$15$	$x^{15} + 20 x^{14} + 15 x^{10} + 20 x^{5} + 25 x^{3} + 25 x^{2} + 25 x + 5$	$5$	$15$	$1$	$28$	$(C_5^2 : C_3):C_4$ (as 15T17)	$2$	$6$	$[13/6]$	$[13/6, 13/6]_{6}^{2}$	$t + 3$	$x^{15} + 20 x^{14} + 15 x^{10} + 20 x^{5} + 25 x^{3} + 25 x^{2} + 25 x + 5$	$[14, 0]$	$[2, 2]$