pp-adic field search results

Results (16 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
2.16.44.6	$16$	$x^{16} + 4 x^{15} + 20 x^{14} + 32 x^{13} + 36 x^{12} + 96 x^{11} + 164 x^{10} + 104 x^{9} + 256 x^{8} + 264 x^{7} + 288 x^{6} + 112 x^{5} + 392 x^{4} + 112 x^{3} + 232 x^{2} - 112 x + 196$	$2$	$8$	$2$	$44$	$C_4:D_4$ (as 16T34)	$2$	$1$	$[2, 3, 7/2]$	$[2, 3, 3, 7/2]^{2}$	$t^{2} + t + 1$	$x^{8} + \left(4 t + 4\right) x^{7} + \left(4 t + 4\right) x^{6} + \left(8 t + 14\right) x^{4} + \left(8 t + 8\right) x^{3} + \left(4 t + 8\right) x^{2} + 8 t x + 14$	$[15, 10, 4, 0]$	$[1, 1, 1]$
2.16.44.7	$16$	$x^{16} + 4 x^{15} + 12 x^{14} + 16 x^{13} + 10 x^{12} + 48 x^{11} + 60 x^{10} + 40 x^{9} + 224 x^{8} + 88 x^{7} + 192 x^{6} + 144 x^{5} + 108 x^{4} + 192 x^{3} - 8 x^{2} - 48 x + 36$	$2$	$8$	$2$	$44$	$C_4:D_4$ (as 16T34)	$2$	$1$	$[2, 3, 7/2]$	$[2, 2, 3, 7/2]^{2}$	$t^{2} + t + 1$	$x^{8} + \left(4 t + 4\right) x^{7} + 4 t x^{6} + \left(10 t + 2\right) x^{4} + 12 t x^{2} + 8 t x + 6$	$[15, 10, 4, 0]$	$[1, 1, 1]$
2.16.44.8	$16$	$x^{16} + 4 x^{15} + 24 x^{14} + 16 x^{13} + 28 x^{12} + 16 x^{11} + 84 x^{10} + 56 x^{9} + 112 x^{8} + 24 x^{7} + 72 x^{6} + 176 x^{5} + 152 x^{4} + 272 x^{3} + 200 x^{2} + 80 x + 52$	$2$	$8$	$2$	$44$	$C_4:D_4$ (as 16T34)	$2$	$1$	$[2, 3, 7/2]$	$[2, 3, 3, 7/2]^{2}$	$t^{2} + t + 1$	$x^{8} + \left(4 t + 4\right) x^{7} + 4 x^{6} + 6 x^{4} + 8 t x^{3} + \left(12 t + 8\right) x^{2} + \left(8 t + 8\right) x + 8 t + 2$	$[15, 10, 4, 0]$	$[1, 1, 1]$
2.16.46.1	$16$	$x^{16} + 4 x^{15} + 2 x^{12} + 4 x^{10} + 12 x^{6} + 4 x^{4} + 8 x + 14$	$2$	$16$	$1$	$46$	$C_4:D_4$ (as 16T34)	$2$	$1$	$[2, 2, 3, 7/2]$	$[2, 2, 3, 7/2]^{2}$	$t + 1$	$x^{16} + 4 x^{15} + 2 x^{12} + 4 x^{10} + 12 x^{6} + 4 x^{4} + 8 x + 14$	$[31, 22, 12, 12, 0]$	$[1, 1, 2]$
2.16.48.14	$16$	$x^{16} + 4 x^{14} + 4 x^{10} + 2 x^{8} + 8 x^{7} + 8 x^{5} + 8 x^{3} + 8 x^{2} + 8 x + 14$	$2$	$16$	$1$	$48$	$C_4:D_4$ (as 16T34)	$2$	$1$	$[2, 3, 3, 7/2]$	$[2, 3, 3, 7/2]^{2}$	$t + 1$	$x^{16} + 4 x^{14} + 4 x^{10} + 2 x^{8} + 8 x^{7} + 8 x^{5} + 8 x^{3} + 8 x^{2} + 8 x + 14$	$[33, 26, 24, 8, 0]$	$[1, 2, 1]$
2.16.48.15	$16$	$x^{16} + 4 x^{10} + 2 x^{8} + 8 x + 10$	$2$	$16$	$1$	$48$	$C_4:D_4$ (as 16T34)	$2$	$1$	$[2, 3, 3, 7/2]$	$[2, 3, 3, 7/2]^{2}$	$t + 1$	$x^{16} + 4 x^{10} + 2 x^{8} + 8 x + 10$	$[33, 26, 24, 8, 0]$	$[1, 2, 1]$
2.16.50.5	$16$	$x^{16} + 4 x^{14} + 2 x^{12} + 8 x^{11} + 8 x^{9} + 12 x^{6} + 8 x^{3} + 30$	$2$	$16$	$1$	$50$	$C_4:D_4$ (as 16T34)	$2$	$1$	$[2, 2, 3, 4]$	$[2, 2, 3, 4]^{2}$	$t + 1$	$x^{16} + 4 x^{14} + 2 x^{12} + 8 x^{11} + 8 x^{9} + 12 x^{6} + 8 x^{3} + 30$	$[35, 22, 12, 12, 0]$	$[1, 1, 2]$
2.16.50.6	$16$	$x^{16} + 8 x^{15} + 4 x^{14} + 10 x^{12} + 8 x^{9} + 8 x^{8} + 4 x^{6} + 8 x^{3} + 22$	$2$	$16$	$1$	$50$	$C_4:D_4$ (as 16T34)	$2$	$1$	$[2, 2, 3, 4]$	$[2, 2, 3, 4]^{2}$	$t + 1$	$x^{16} + 8 x^{15} + 4 x^{14} + 10 x^{12} + 8 x^{9} + 8 x^{8} + 4 x^{6} + 8 x^{3} + 22$	$[35, 22, 12, 12, 0]$	$[1, 1, 2]$
2.16.52.19	$16$	$x^{16} + 16 x^{15} + 88 x^{14} + 184 x^{13} + 100 x^{12} + 80 x^{11} + 432 x^{10} + 160 x^{9} + 32 x^{8} + 32 x^{7} - 128 x^{6} + 400 x^{5} + 8 x^{4} - 128 x^{3} + 652$	$2$	$8$	$2$	$52$	$C_4:D_4$ (as 16T34)	$2$	$1$	$[3, 7/2, 4]$	$[2, 3, 7/2, 4]^{2}$	$t^{2} + t + 1$	$x^{8} + 8 x^{7} + 12 x^{6} + 8 t x^{5} + \left(4 t + 12\right) x^{4} + 8 x^{3} + 28 t + 6$	$[19, 14, 8, 0]$	$[1, 1, 1]$
2.16.52.20	$16$	$x^{16} + 16 x^{15} + 80 x^{14} + 128 x^{13} + 136 x^{12} + 208 x^{11} + 320 x^{10} + 128 x^{9} + 204 x^{8} + 672 x^{7} + 544 x^{6} + 720 x^{4} + 480 x^{3} + 900$	$2$	$8$	$2$	$52$	$C_4:D_4$ (as 16T34)	$2$	$1$	$[3, 7/2, 4]$	$[2, 3, 7/2, 4]^{2}$	$t^{2} + t + 1$	$x^{8} + 8 x^{7} + \left(8 t + 12\right) x^{6} + 12 x^{4} + 8 x^{3} + 30$	$[19, 14, 8, 0]$	$[1, 1, 1]$
2.16.52.21	$16$	$x^{16} + 16 x^{15} + 80 x^{14} + 128 x^{13} + 108 x^{12} - 16 x^{11} + 136 x^{10} + 64 x^{9} + 96 x^{8} + 352 x^{7} + 560 x^{6} - 64 x^{5} - 8 x^{4} + 384 x^{3} - 144 x^{2} + 588$	$2$	$8$	$2$	$52$	$C_4:D_4$ (as 16T34)	$2$	$1$	$[3, 7/2, 4]$	$[2, 3, 7/2, 4]^{2}$	$t^{2} + t + 1$	$x^{8} + 8 x^{7} + \left(8 t + 12\right) x^{6} + 4 t x^{4} + 8 x^{3} + 8 t x^{2} + 4 t + 26$	$[19, 14, 8, 0]$	$[1, 1, 1]$
2.16.54.27	$16$	$x^{16} + 12 x^{14} + 8 x^{11} + 2 x^{8} + 8 x^{7} + 4 x^{4} + 8 x^{2} + 14$	$2$	$16$	$1$	$54$	$C_4:D_4$ (as 16T34)	$2$	$1$	$[2, 3, 7/2, 4]$	$[2, 3, 7/2, 4]^{2}$	$t + 1$	$x^{16} + 12 x^{14} + 8 x^{11} + 2 x^{8} + 8 x^{7} + 4 x^{4} + 8 x^{2} + 14$	$[39, 30, 20, 8, 0]$	$[1, 1, 1, 1]$
2.16.54.28	$16$	$x^{16} + 4 x^{14} + 8 x^{13} + 12 x^{12} + 8 x^{9} + 14 x^{8} + 8 x^{7} + 4 x^{4} + 14$	$2$	$16$	$1$	$54$	$C_4:D_4$ (as 16T34)	$2$	$1$	$[2, 3, 7/2, 4]$	$[2, 3, 7/2, 4]^{2}$	$t + 1$	$x^{16} + 4 x^{14} + 8 x^{13} + 12 x^{12} + 8 x^{9} + 14 x^{8} + 8 x^{7} + 4 x^{4} + 14$	$[39, 30, 20, 8, 0]$	$[1, 1, 1, 1]$
2.16.54.29	$16$	$x^{16} + 4 x^{14} + 8 x^{13} + 8 x^{11} + 8 x^{9} + 6 x^{8} + 8 x^{7} + 12 x^{4} + 10$	$2$	$16$	$1$	$54$	$C_4:D_4$ (as 16T34)	$2$	$1$	$[2, 3, 7/2, 4]$	$[2, 3, 7/2, 4]^{2}$	$t + 1$	$x^{16} + 4 x^{14} + 8 x^{13} + 8 x^{11} + 8 x^{9} + 6 x^{8} + 8 x^{7} + 12 x^{4} + 10$	$[39, 30, 20, 8, 0]$	$[1, 1, 1, 1]$
2.16.54.30	$16$	$x^{16} + 8 x^{15} + 12 x^{14} + 8 x^{12} + 8 x^{11} + 8 x^{9} + 10 x^{8} + 8 x^{7} + 4 x^{4} + 14$	$2$	$16$	$1$	$54$	$C_4:D_4$ (as 16T34)	$2$	$1$	$[2, 3, 7/2, 4]$	$[2, 3, 7/2, 4]^{2}$	$t + 1$	$x^{16} + 8 x^{15} + 12 x^{14} + 8 x^{12} + 8 x^{11} + 8 x^{9} + 10 x^{8} + 8 x^{7} + 4 x^{4} + 14$	$[39, 30, 20, 8, 0]$	$[1, 1, 1, 1]$
2.16.54.31	$16$	$x^{16} + 12 x^{14} + 8 x^{11} + 8 x^{9} + 2 x^{8} + 8 x^{7} + 4 x^{4} + 6$	$2$	$16$	$1$	$54$	$C_4:D_4$ (as 16T34)	$2$	$1$	$[2, 3, 7/2, 4]$	$[2, 3, 7/2, 4]^{2}$	$t + 1$	$x^{16} + 12 x^{14} + 8 x^{11} + 8 x^{9} + 2 x^{8} + 8 x^{7} + 4 x^{4} + 6$	$[39, 30, 20, 8, 0]$	$[1, 1, 1, 1]$

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