$p$-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
5.1.15.27a1.1	$15$	$x^{15} + 5 x^{13} + 5$	$5$	$1$	$15$	$27$	$C_5^2:(C_4\times S_3)$ (as 15T27)	$2$	$12$	$[\frac{25}{12}]$	$[\frac{13}{12}]$	$[\frac{25}{12}, \frac{25}{12}]_{12}^{2}$	$[\frac{13}{12},\frac{13}{12}]_{12}^{2}$	$[\frac{25}{12}]^{2}_{4}$	$[\frac{13}{12}]^{2}_{4}$	$1$	$t + 3$	$x^{15} + 5 x^{13} + 5$	$[13, 0]$	$[2, 1]$	$z^{10} + 3 z^5 + 3,3 z + 2$	undefined
5.1.15.27a1.2	$15$	$x^{15} + 5 x^{13} + 25 x + 5$	$5$	$1$	$15$	$27$	$C_5^2:(C_4\times S_3)$ (as 15T27)	$2$	$12$	$[\frac{25}{12}]$	$[\frac{13}{12}]$	$[\frac{25}{12}, \frac{25}{12}]_{12}^{2}$	$[\frac{13}{12},\frac{13}{12}]_{12}^{2}$	$[\frac{25}{12}]^{2}_{4}$	$[\frac{13}{12}]^{2}_{4}$	$1$	$t + 3$	$x^{15} + 5 x^{13} + 25 x + 5$	$[13, 0]$	$[2, 1]$	$z^{10} + 3 z^5 + 3,3 z + 2$	undefined
5.1.15.27a1.3	$15$	$x^{15} + 5 x^{13} + 50 x + 5$	$5$	$1$	$15$	$27$	$C_5^2:(C_4\times S_3)$ (as 15T27)	$2$	$12$	$[\frac{25}{12}]$	$[\frac{13}{12}]$	$[\frac{25}{12}, \frac{25}{12}]_{12}^{2}$	$[\frac{13}{12},\frac{13}{12}]_{12}^{2}$	$[\frac{25}{12}]^{2}_{4}$	$[\frac{13}{12}]^{2}_{4}$	$1$	$t + 3$	$x^{15} + 5 x^{13} + 50 x + 5$	$[13, 0]$	$[2, 1]$	$z^{10} + 3 z^5 + 3,3 z + 2$	undefined
5.1.15.27a1.4	$15$	$x^{15} + 5 x^{13} + 75 x + 5$	$5$	$1$	$15$	$27$	$C_5^2:(C_4\times S_3)$ (as 15T27)	$2$	$12$	$[\frac{25}{12}]$	$[\frac{13}{12}]$	$[\frac{25}{12}, \frac{25}{12}]_{12}^{2}$	$[\frac{13}{12},\frac{13}{12}]_{12}^{2}$	$[\frac{25}{12}]^{2}_{4}$	$[\frac{13}{12}]^{2}_{4}$	$1$	$t + 3$	$x^{15} + 5 x^{13} + 75 x + 5$	$[13, 0]$	$[2, 1]$	$z^{10} + 3 z^5 + 3,3 z + 2$	undefined
5.1.15.27a1.5	$15$	$x^{15} + 5 x^{13} + 100 x + 5$	$5$	$1$	$15$	$27$	$C_5^2:(C_4\times S_3)$ (as 15T27)	$2$	$12$	$[\frac{25}{12}]$	$[\frac{13}{12}]$	$[\frac{25}{12}, \frac{25}{12}]_{12}^{2}$	$[\frac{13}{12},\frac{13}{12}]_{12}^{2}$	$[\frac{25}{12}]^{2}_{4}$	$[\frac{13}{12}]^{2}_{4}$	$1$	$t + 3$	$x^{15} + 5 x^{13} + 100 x + 5$	$[13, 0]$	$[2, 1]$	$z^{10} + 3 z^5 + 3,3 z + 2$	undefined
5.1.15.27a1.26	$15$	$x^{15} + 10 x^{13} + 5$	$5$	$1$	$15$	$27$	$C_5^2:(C_4\times S_3)$ (as 15T27)	$2$	$12$	$[\frac{25}{12}]$	$[\frac{13}{12}]$	$[\frac{25}{12}, \frac{25}{12}]_{12}^{2}$	$[\frac{13}{12},\frac{13}{12}]_{12}^{2}$	$[\frac{25}{12}]^{2}_{4}$	$[\frac{13}{12}]^{2}_{4}$	$1$	$t + 3$	$x^{15} + 10 x^{13} + 5$	$[13, 0]$	$[2, 1]$	$z^{10} + 3 z^5 + 3,3 z + 4$	undefined
5.1.15.27a1.27	$15$	$x^{15} + 10 x^{13} + 25 x + 5$	$5$	$1$	$15$	$27$	$C_5^2:(C_4\times S_3)$ (as 15T27)	$2$	$12$	$[\frac{25}{12}]$	$[\frac{13}{12}]$	$[\frac{25}{12}, \frac{25}{12}]_{12}^{2}$	$[\frac{13}{12},\frac{13}{12}]_{12}^{2}$	$[\frac{25}{12}]^{2}_{4}$	$[\frac{13}{12}]^{2}_{4}$	$1$	$t + 3$	$x^{15} + 10 x^{13} + 25 x + 5$	$[13, 0]$	$[2, 1]$	$z^{10} + 3 z^5 + 3,3 z + 4$	undefined
5.1.15.27a1.28	$15$	$x^{15} + 10 x^{13} + 50 x + 5$	$5$	$1$	$15$	$27$	$C_5^2:(C_4\times S_3)$ (as 15T27)	$2$	$12$	$[\frac{25}{12}]$	$[\frac{13}{12}]$	$[\frac{25}{12}, \frac{25}{12}]_{12}^{2}$	$[\frac{13}{12},\frac{13}{12}]_{12}^{2}$	$[\frac{25}{12}]^{2}_{4}$	$[\frac{13}{12}]^{2}_{4}$	$1$	$t + 3$	$x^{15} + 10 x^{13} + 50 x + 5$	$[13, 0]$	$[2, 1]$	$z^{10} + 3 z^5 + 3,3 z + 4$	undefined
5.1.15.27a1.29	$15$	$x^{15} + 10 x^{13} + 75 x + 5$	$5$	$1$	$15$	$27$	$C_5^2:(C_4\times S_3)$ (as 15T27)	$2$	$12$	$[\frac{25}{12}]$	$[\frac{13}{12}]$	$[\frac{25}{12}, \frac{25}{12}]_{12}^{2}$	$[\frac{13}{12},\frac{13}{12}]_{12}^{2}$	$[\frac{25}{12}]^{2}_{4}$	$[\frac{13}{12}]^{2}_{4}$	$1$	$t + 3$	$x^{15} + 10 x^{13} + 75 x + 5$	$[13, 0]$	$[2, 1]$	$z^{10} + 3 z^5 + 3,3 z + 4$	undefined
5.1.15.27a1.30	$15$	$x^{15} + 10 x^{13} + 100 x + 5$	$5$	$1$	$15$	$27$	$C_5^2:(C_4\times S_3)$ (as 15T27)	$2$	$12$	$[\frac{25}{12}]$	$[\frac{13}{12}]$	$[\frac{25}{12}, \frac{25}{12}]_{12}^{2}$	$[\frac{13}{12},\frac{13}{12}]_{12}^{2}$	$[\frac{25}{12}]^{2}_{4}$	$[\frac{13}{12}]^{2}_{4}$	$1$	$t + 3$	$x^{15} + 10 x^{13} + 100 x + 5$	$[13, 0]$	$[2, 1]$	$z^{10} + 3 z^5 + 3,3 z + 4$	undefined
5.1.15.27a1.51	$15$	$x^{15} + 15 x^{13} + 5$	$5$	$1$	$15$	$27$	$C_5^2:(C_4\times S_3)$ (as 15T27)	$2$	$12$	$[\frac{25}{12}]$	$[\frac{13}{12}]$	$[\frac{25}{12}, \frac{25}{12}]_{12}^{2}$	$[\frac{13}{12},\frac{13}{12}]_{12}^{2}$	$[\frac{25}{12}]^{2}_{4}$	$[\frac{13}{12}]^{2}_{4}$	$1$	$t + 3$	$x^{15} + 15 x^{13} + 5$	$[13, 0]$	$[2, 1]$	$z^{10} + 3 z^5 + 3,3 z + 1$	undefined
5.1.15.27a1.52	$15$	$x^{15} + 15 x^{13} + 25 x + 5$	$5$	$1$	$15$	$27$	$C_5^2:(C_4\times S_3)$ (as 15T27)	$2$	$12$	$[\frac{25}{12}]$	$[\frac{13}{12}]$	$[\frac{25}{12}, \frac{25}{12}]_{12}^{2}$	$[\frac{13}{12},\frac{13}{12}]_{12}^{2}$	$[\frac{25}{12}]^{2}_{4}$	$[\frac{13}{12}]^{2}_{4}$	$1$	$t + 3$	$x^{15} + 15 x^{13} + 25 x + 5$	$[13, 0]$	$[2, 1]$	$z^{10} + 3 z^5 + 3,3 z + 1$	undefined
5.1.15.27a1.53	$15$	$x^{15} + 15 x^{13} + 50 x + 5$	$5$	$1$	$15$	$27$	$C_5^2:(C_4\times S_3)$ (as 15T27)	$2$	$12$	$[\frac{25}{12}]$	$[\frac{13}{12}]$	$[\frac{25}{12}, \frac{25}{12}]_{12}^{2}$	$[\frac{13}{12},\frac{13}{12}]_{12}^{2}$	$[\frac{25}{12}]^{2}_{4}$	$[\frac{13}{12}]^{2}_{4}$	$1$	$t + 3$	$x^{15} + 15 x^{13} + 50 x + 5$	$[13, 0]$	$[2, 1]$	$z^{10} + 3 z^5 + 3,3 z + 1$	undefined
5.1.15.27a1.54	$15$	$x^{15} + 15 x^{13} + 75 x + 5$	$5$	$1$	$15$	$27$	$C_5^2:(C_4\times S_3)$ (as 15T27)	$2$	$12$	$[\frac{25}{12}]$	$[\frac{13}{12}]$	$[\frac{25}{12}, \frac{25}{12}]_{12}^{2}$	$[\frac{13}{12},\frac{13}{12}]_{12}^{2}$	$[\frac{25}{12}]^{2}_{4}$	$[\frac{13}{12}]^{2}_{4}$	$1$	$t + 3$	$x^{15} + 15 x^{13} + 75 x + 5$	$[13, 0]$	$[2, 1]$	$z^{10} + 3 z^5 + 3,3 z + 1$	undefined
5.1.15.27a1.55	$15$	$x^{15} + 15 x^{13} + 100 x + 5$	$5$	$1$	$15$	$27$	$C_5^2:(C_4\times S_3)$ (as 15T27)	$2$	$12$	$[\frac{25}{12}]$	$[\frac{13}{12}]$	$[\frac{25}{12}, \frac{25}{12}]_{12}^{2}$	$[\frac{13}{12},\frac{13}{12}]_{12}^{2}$	$[\frac{25}{12}]^{2}_{4}$	$[\frac{13}{12}]^{2}_{4}$	$1$	$t + 3$	$x^{15} + 15 x^{13} + 100 x + 5$	$[13, 0]$	$[2, 1]$	$z^{10} + 3 z^5 + 3,3 z + 1$	undefined
5.1.15.27a1.76	$15$	$x^{15} + 20 x^{13} + 5$	$5$	$1$	$15$	$27$	$C_5^2:(C_4\times S_3)$ (as 15T27)	$2$	$12$	$[\frac{25}{12}]$	$[\frac{13}{12}]$	$[\frac{25}{12}, \frac{25}{12}]_{12}^{2}$	$[\frac{13}{12},\frac{13}{12}]_{12}^{2}$	$[\frac{25}{12}]^{2}_{4}$	$[\frac{13}{12}]^{2}_{4}$	$1$	$t + 3$	$x^{15} + 20 x^{13} + 5$	$[13, 0]$	$[2, 1]$	$z^{10} + 3 z^5 + 3,3 z + 3$	undefined
5.1.15.27a1.77	$15$	$x^{15} + 20 x^{13} + 25 x + 5$	$5$	$1$	$15$	$27$	$C_5^2:(C_4\times S_3)$ (as 15T27)	$2$	$12$	$[\frac{25}{12}]$	$[\frac{13}{12}]$	$[\frac{25}{12}, \frac{25}{12}]_{12}^{2}$	$[\frac{13}{12},\frac{13}{12}]_{12}^{2}$	$[\frac{25}{12}]^{2}_{4}$	$[\frac{13}{12}]^{2}_{4}$	$1$	$t + 3$	$x^{15} + 20 x^{13} + 25 x + 5$	$[13, 0]$	$[2, 1]$	$z^{10} + 3 z^5 + 3,3 z + 3$	undefined
5.1.15.27a1.78	$15$	$x^{15} + 20 x^{13} + 50 x + 5$	$5$	$1$	$15$	$27$	$C_5^2:(C_4\times S_3)$ (as 15T27)	$2$	$12$	$[\frac{25}{12}]$	$[\frac{13}{12}]$	$[\frac{25}{12}, \frac{25}{12}]_{12}^{2}$	$[\frac{13}{12},\frac{13}{12}]_{12}^{2}$	$[\frac{25}{12}]^{2}_{4}$	$[\frac{13}{12}]^{2}_{4}$	$1$	$t + 3$	$x^{15} + 20 x^{13} + 50 x + 5$	$[13, 0]$	$[2, 1]$	$z^{10} + 3 z^5 + 3,3 z + 3$	undefined
5.1.15.27a1.79	$15$	$x^{15} + 20 x^{13} + 75 x + 5$	$5$	$1$	$15$	$27$	$C_5^2:(C_4\times S_3)$ (as 15T27)	$2$	$12$	$[\frac{25}{12}]$	$[\frac{13}{12}]$	$[\frac{25}{12}, \frac{25}{12}]_{12}^{2}$	$[\frac{13}{12},\frac{13}{12}]_{12}^{2}$	$[\frac{25}{12}]^{2}_{4}$	$[\frac{13}{12}]^{2}_{4}$	$1$	$t + 3$	$x^{15} + 20 x^{13} + 75 x + 5$	$[13, 0]$	$[2, 1]$	$z^{10} + 3 z^5 + 3,3 z + 3$	undefined
5.1.15.27a1.80	$15$	$x^{15} + 20 x^{13} + 100 x + 5$	$5$	$1$	$15$	$27$	$C_5^2:(C_4\times S_3)$ (as 15T27)	$2$	$12$	$[\frac{25}{12}]$	$[\frac{13}{12}]$	$[\frac{25}{12}, \frac{25}{12}]_{12}^{2}$	$[\frac{13}{12},\frac{13}{12}]_{12}^{2}$	$[\frac{25}{12}]^{2}_{4}$	$[\frac{13}{12}]^{2}_{4}$	$1$	$t + 3$	$x^{15} + 20 x^{13} + 100 x + 5$	$[13, 0]$	$[2, 1]$	$z^{10} + 3 z^5 + 3,3 z + 3$	undefined

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