$p$-adic field search results

Results (20 matches)

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Label	$n$	Polynomial	$p$	$f$	$e$	$c$	Galois group	$u$	$t$	Visible Artin slopes	Visible Swan slopes	Artin slope content	Swan slope content	Hidden Artin slopes	Hidden Swan slopes	$\#\Aut(K/\Q_p)$	Unram. Ext.	Eisen. Poly.	Ind. of Insep.	Assoc. Inertia	Resid. Poly	Jump Set
5.1.15.26a2.6	$15$	$x^{15} + 5 x^{14} + 20 x^{12} + 5$	$5$	$1$	$15$	$26$	$C_5\wr S_3$ (as 15T32)	$2$	$3$	$[2]$	$[1]$	$[\frac{4}{3}, \frac{4}{3}, 2]_{3}^{2}$	$[\frac{1}{3},\frac{1}{3},1]_{3}^{2}$	$[\frac{4}{3},\frac{4}{3}]^{2}$	$[\frac{1}{3},\frac{1}{3}]^{2}$	$5$	$t + 3$	$x^{15} + 5 x^{14} + 20 x^{12} + 5$	$[12, 0]$	$[2, 1]$	$z^{10} + 3 z^5 + 3,3 z^4 + 2$	undefined
5.1.15.26a2.7	$15$	$x^{15} + 5 x^{14} + 20 x^{12} + 30$	$5$	$1$	$15$	$26$	$C_5\wr S_3$ (as 15T32)	$2$	$3$	$[2]$	$[1]$	$[\frac{4}{3}, \frac{4}{3}, 2]_{3}^{2}$	$[\frac{1}{3},\frac{1}{3},1]_{3}^{2}$	$[\frac{4}{3},\frac{4}{3}]^{2}$	$[\frac{1}{3},\frac{1}{3}]^{2}$	$5$	$t + 3$	$x^{15} + 5 x^{14} + 20 x^{12} + 30$	$[12, 0]$	$[2, 1]$	$z^{10} + 3 z^5 + 3,3 z^4 + 2$	undefined
5.1.15.26a2.8	$15$	$x^{15} + 5 x^{14} + 20 x^{12} + 55$	$5$	$1$	$15$	$26$	$C_5\wr S_3$ (as 15T32)	$2$	$3$	$[2]$	$[1]$	$[\frac{4}{3}, \frac{4}{3}, 2]_{3}^{2}$	$[\frac{1}{3},\frac{1}{3},1]_{3}^{2}$	$[\frac{4}{3},\frac{4}{3}]^{2}$	$[\frac{1}{3},\frac{1}{3}]^{2}$	$5$	$t + 3$	$x^{15} + 5 x^{14} + 20 x^{12} + 55$	$[12, 0]$	$[2, 1]$	$z^{10} + 3 z^5 + 3,3 z^4 + 2$	undefined
5.1.15.26a2.9	$15$	$x^{15} + 5 x^{14} + 20 x^{12} + 80$	$5$	$1$	$15$	$26$	$C_5\wr S_3$ (as 15T32)	$2$	$3$	$[2]$	$[1]$	$[\frac{4}{3}, \frac{4}{3}, 2]_{3}^{2}$	$[\frac{1}{3},\frac{1}{3},1]_{3}^{2}$	$[\frac{4}{3},\frac{4}{3}]^{2}$	$[\frac{1}{3},\frac{1}{3}]^{2}$	$5$	$t + 3$	$x^{15} + 5 x^{14} + 20 x^{12} + 80$	$[12, 0]$	$[2, 1]$	$z^{10} + 3 z^5 + 3,3 z^4 + 2$	undefined
5.1.15.26a2.10	$15$	$x^{15} + 5 x^{14} + 20 x^{12} + 105$	$5$	$1$	$15$	$26$	$C_5\wr S_3$ (as 15T32)	$2$	$3$	$[2]$	$[1]$	$[\frac{4}{3}, \frac{4}{3}, 2]_{3}^{2}$	$[\frac{1}{3},\frac{1}{3},1]_{3}^{2}$	$[\frac{4}{3},\frac{4}{3}]^{2}$	$[\frac{1}{3},\frac{1}{3}]^{2}$	$5$	$t + 3$	$x^{15} + 5 x^{14} + 20 x^{12} + 105$	$[12, 0]$	$[2, 1]$	$z^{10} + 3 z^5 + 3,3 z^4 + 2$	undefined
5.1.15.26a2.11	$15$	$x^{15} + 10 x^{14} + 20 x^{12} + 5$	$5$	$1$	$15$	$26$	$C_5\wr S_3$ (as 15T32)	$2$	$3$	$[2]$	$[1]$	$[\frac{4}{3}, \frac{4}{3}, 2]_{3}^{2}$	$[\frac{1}{3},\frac{1}{3},1]_{3}^{2}$	$[\frac{4}{3},\frac{4}{3}]^{2}$	$[\frac{1}{3},\frac{1}{3}]^{2}$	$5$	$t + 3$	$x^{15} + 10 x^{14} + 20 x^{12} + 5$	$[12, 0]$	$[2, 1]$	$z^{10} + 3 z^5 + 3,3 z^4 + 2$	undefined
5.1.15.26a2.12	$15$	$x^{15} + 10 x^{14} + 20 x^{12} + 30$	$5$	$1$	$15$	$26$	$C_5\wr S_3$ (as 15T32)	$2$	$3$	$[2]$	$[1]$	$[\frac{4}{3}, \frac{4}{3}, 2]_{3}^{2}$	$[\frac{1}{3},\frac{1}{3},1]_{3}^{2}$	$[\frac{4}{3},\frac{4}{3}]^{2}$	$[\frac{1}{3},\frac{1}{3}]^{2}$	$5$	$t + 3$	$x^{15} + 10 x^{14} + 20 x^{12} + 30$	$[12, 0]$	$[2, 1]$	$z^{10} + 3 z^5 + 3,3 z^4 + 2$	undefined
5.1.15.26a2.13	$15$	$x^{15} + 10 x^{14} + 20 x^{12} + 55$	$5$	$1$	$15$	$26$	$C_5\wr S_3$ (as 15T32)	$2$	$3$	$[2]$	$[1]$	$[\frac{4}{3}, \frac{4}{3}, 2]_{3}^{2}$	$[\frac{1}{3},\frac{1}{3},1]_{3}^{2}$	$[\frac{4}{3},\frac{4}{3}]^{2}$	$[\frac{1}{3},\frac{1}{3}]^{2}$	$5$	$t + 3$	$x^{15} + 10 x^{14} + 20 x^{12} + 55$	$[12, 0]$	$[2, 1]$	$z^{10} + 3 z^5 + 3,3 z^4 + 2$	undefined
5.1.15.26a2.14	$15$	$x^{15} + 10 x^{14} + 20 x^{12} + 80$	$5$	$1$	$15$	$26$	$C_5\wr S_3$ (as 15T32)	$2$	$3$	$[2]$	$[1]$	$[\frac{4}{3}, \frac{4}{3}, 2]_{3}^{2}$	$[\frac{1}{3},\frac{1}{3},1]_{3}^{2}$	$[\frac{4}{3},\frac{4}{3}]^{2}$	$[\frac{1}{3},\frac{1}{3}]^{2}$	$5$	$t + 3$	$x^{15} + 10 x^{14} + 20 x^{12} + 80$	$[12, 0]$	$[2, 1]$	$z^{10} + 3 z^5 + 3,3 z^4 + 2$	undefined
5.1.15.26a2.15	$15$	$x^{15} + 10 x^{14} + 20 x^{12} + 105$	$5$	$1$	$15$	$26$	$C_5\wr S_3$ (as 15T32)	$2$	$3$	$[2]$	$[1]$	$[\frac{4}{3}, \frac{4}{3}, 2]_{3}^{2}$	$[\frac{1}{3},\frac{1}{3},1]_{3}^{2}$	$[\frac{4}{3},\frac{4}{3}]^{2}$	$[\frac{1}{3},\frac{1}{3}]^{2}$	$5$	$t + 3$	$x^{15} + 10 x^{14} + 20 x^{12} + 105$	$[12, 0]$	$[2, 1]$	$z^{10} + 3 z^5 + 3,3 z^4 + 2$	undefined
5.1.15.26a2.16	$15$	$x^{15} + 15 x^{14} + 20 x^{12} + 5$	$5$	$1$	$15$	$26$	$C_5\wr S_3$ (as 15T32)	$2$	$3$	$[2]$	$[1]$	$[\frac{4}{3}, \frac{4}{3}, 2]_{3}^{2}$	$[\frac{1}{3},\frac{1}{3},1]_{3}^{2}$	$[\frac{4}{3},\frac{4}{3}]^{2}$	$[\frac{1}{3},\frac{1}{3}]^{2}$	$5$	$t + 3$	$x^{15} + 15 x^{14} + 20 x^{12} + 5$	$[12, 0]$	$[2, 1]$	$z^{10} + 3 z^5 + 3,3 z^4 + 2$	undefined
5.1.15.26a2.17	$15$	$x^{15} + 15 x^{14} + 20 x^{12} + 30$	$5$	$1$	$15$	$26$	$C_5\wr S_3$ (as 15T32)	$2$	$3$	$[2]$	$[1]$	$[\frac{4}{3}, \frac{4}{3}, 2]_{3}^{2}$	$[\frac{1}{3},\frac{1}{3},1]_{3}^{2}$	$[\frac{4}{3},\frac{4}{3}]^{2}$	$[\frac{1}{3},\frac{1}{3}]^{2}$	$5$	$t + 3$	$x^{15} + 15 x^{14} + 20 x^{12} + 30$	$[12, 0]$	$[2, 1]$	$z^{10} + 3 z^5 + 3,3 z^4 + 2$	undefined
5.1.15.26a2.18	$15$	$x^{15} + 15 x^{14} + 20 x^{12} + 55$	$5$	$1$	$15$	$26$	$C_5\wr S_3$ (as 15T32)	$2$	$3$	$[2]$	$[1]$	$[\frac{4}{3}, \frac{4}{3}, 2]_{3}^{2}$	$[\frac{1}{3},\frac{1}{3},1]_{3}^{2}$	$[\frac{4}{3},\frac{4}{3}]^{2}$	$[\frac{1}{3},\frac{1}{3}]^{2}$	$5$	$t + 3$	$x^{15} + 15 x^{14} + 20 x^{12} + 55$	$[12, 0]$	$[2, 1]$	$z^{10} + 3 z^5 + 3,3 z^4 + 2$	undefined
5.1.15.26a2.19	$15$	$x^{15} + 15 x^{14} + 20 x^{12} + 80$	$5$	$1$	$15$	$26$	$C_5\wr S_3$ (as 15T32)	$2$	$3$	$[2]$	$[1]$	$[\frac{4}{3}, \frac{4}{3}, 2]_{3}^{2}$	$[\frac{1}{3},\frac{1}{3},1]_{3}^{2}$	$[\frac{4}{3},\frac{4}{3}]^{2}$	$[\frac{1}{3},\frac{1}{3}]^{2}$	$5$	$t + 3$	$x^{15} + 15 x^{14} + 20 x^{12} + 80$	$[12, 0]$	$[2, 1]$	$z^{10} + 3 z^5 + 3,3 z^4 + 2$	undefined
5.1.15.26a2.20	$15$	$x^{15} + 15 x^{14} + 20 x^{12} + 105$	$5$	$1$	$15$	$26$	$C_5\wr S_3$ (as 15T32)	$2$	$3$	$[2]$	$[1]$	$[\frac{4}{3}, \frac{4}{3}, 2]_{3}^{2}$	$[\frac{1}{3},\frac{1}{3},1]_{3}^{2}$	$[\frac{4}{3},\frac{4}{3}]^{2}$	$[\frac{1}{3},\frac{1}{3}]^{2}$	$5$	$t + 3$	$x^{15} + 15 x^{14} + 20 x^{12} + 105$	$[12, 0]$	$[2, 1]$	$z^{10} + 3 z^5 + 3,3 z^4 + 2$	undefined
5.1.15.26a2.21	$15$	$x^{15} + 20 x^{14} + 20 x^{12} + 5$	$5$	$1$	$15$	$26$	$C_5\wr S_3$ (as 15T32)	$2$	$3$	$[2]$	$[1]$	$[\frac{4}{3}, \frac{4}{3}, 2]_{3}^{2}$	$[\frac{1}{3},\frac{1}{3},1]_{3}^{2}$	$[\frac{4}{3},\frac{4}{3}]^{2}$	$[\frac{1}{3},\frac{1}{3}]^{2}$	$5$	$t + 3$	$x^{15} + 20 x^{14} + 20 x^{12} + 5$	$[12, 0]$	$[2, 1]$	$z^{10} + 3 z^5 + 3,3 z^4 + 2$	undefined
5.1.15.26a2.22	$15$	$x^{15} + 20 x^{14} + 20 x^{12} + 30$	$5$	$1$	$15$	$26$	$C_5\wr S_3$ (as 15T32)	$2$	$3$	$[2]$	$[1]$	$[\frac{4}{3}, \frac{4}{3}, 2]_{3}^{2}$	$[\frac{1}{3},\frac{1}{3},1]_{3}^{2}$	$[\frac{4}{3},\frac{4}{3}]^{2}$	$[\frac{1}{3},\frac{1}{3}]^{2}$	$5$	$t + 3$	$x^{15} + 20 x^{14} + 20 x^{12} + 30$	$[12, 0]$	$[2, 1]$	$z^{10} + 3 z^5 + 3,3 z^4 + 2$	undefined
5.1.15.26a2.23	$15$	$x^{15} + 20 x^{14} + 20 x^{12} + 55$	$5$	$1$	$15$	$26$	$C_5\wr S_3$ (as 15T32)	$2$	$3$	$[2]$	$[1]$	$[\frac{4}{3}, \frac{4}{3}, 2]_{3}^{2}$	$[\frac{1}{3},\frac{1}{3},1]_{3}^{2}$	$[\frac{4}{3},\frac{4}{3}]^{2}$	$[\frac{1}{3},\frac{1}{3}]^{2}$	$5$	$t + 3$	$x^{15} + 20 x^{14} + 20 x^{12} + 55$	$[12, 0]$	$[2, 1]$	$z^{10} + 3 z^5 + 3,3 z^4 + 2$	undefined
5.1.15.26a2.24	$15$	$x^{15} + 20 x^{14} + 20 x^{12} + 80$	$5$	$1$	$15$	$26$	$C_5\wr S_3$ (as 15T32)	$2$	$3$	$[2]$	$[1]$	$[\frac{4}{3}, \frac{4}{3}, 2]_{3}^{2}$	$[\frac{1}{3},\frac{1}{3},1]_{3}^{2}$	$[\frac{4}{3},\frac{4}{3}]^{2}$	$[\frac{1}{3},\frac{1}{3}]^{2}$	$5$	$t + 3$	$x^{15} + 20 x^{14} + 20 x^{12} + 80$	$[12, 0]$	$[2, 1]$	$z^{10} + 3 z^5 + 3,3 z^4 + 2$	undefined
5.1.15.26a2.25	$15$	$x^{15} + 20 x^{14} + 20 x^{12} + 105$	$5$	$1$	$15$	$26$	$C_5\wr S_3$ (as 15T32)	$2$	$3$	$[2]$	$[1]$	$[\frac{4}{3}, \frac{4}{3}, 2]_{3}^{2}$	$[\frac{1}{3},\frac{1}{3},1]_{3}^{2}$	$[\frac{4}{3},\frac{4}{3}]^{2}$	$[\frac{1}{3},\frac{1}{3}]^{2}$	$5$	$t + 3$	$x^{15} + 20 x^{14} + 20 x^{12} + 105$	$[12, 0]$	$[2, 1]$	$z^{10} + 3 z^5 + 3,3 z^4 + 2$	undefined

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