$p$-adic field search results

The results below are complete, since the LMFDB contains all p-adic fields of degree at most 23 and residue characteristic at most 199

Results (6 matches)

  Download displayed columns for results to

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
2.21.1.0a1.1	$21$	$x^{21} + x^{6} + x^{5} + x^{2} + 1$	$2$	$21$	$1$	$0$	$C_{21}$ (as 21T1)	$21$	$1$	$[\ ]$	$[\ ]$	$[\ ]^{21}$	$[\ ]^{21}$	$[\ ]$	$[\ ]$	$21$	$t^{21} + t^{6} + t^{5} + t^{2} + 1$	$x - 2$	$[0]$	$[\ ]$		$[1]$
2.7.3.14a1.1	$21$	$( x^{7} + x + 1 )^{3} + 2$	$2$	$7$	$3$	$14$	$S_3\times C_7$ (as 21T6)	$14$	$3$	$[\ ]$	$[\ ]$	$[\ ]_{3}^{14}$	$[\ ]_{3}^{14}$	$[\ ]^{2}$	$[\ ]^{2}$	$7$	$t^{7} + t + 1$	$x^{3} + 2$	$[0]$	$[2]$	$z^2 + z + 1$	$[3]$
2.3.7.18a1.1	$21$	$( x^{3} + x + 1 )^{7} + 2 x$	$2$	$3$	$7$	$18$	$C_7:C_{21}$ (as 21T13)	$21$	$7$	$[\ ]$	$[\ ]$	$[\ ]_{7}^{21}$	$[\ ]_{7}^{21}$	$[\ ]^{7}$	$[\ ]^{7}$	$7$	$t^{3} + t + 1$	$x^{7} + 2 t$	$[0]$	$[1]$	$z^6 + z^5 + z^4 + z^3 + z^2 + z + 1$	$[7]$
2.3.7.18a1.2	$21$	$( x^{3} + x + 1 )^{7} + 2$	$2$	$3$	$7$	$18$	$C_7:C_3$ (as 21T2)	$3$	$7$	$[\ ]$	$[\ ]$	$[\ ]_{7}^{3}$	$[\ ]_{7}^{3}$	$[\ ]$	$[\ ]$	$21$	$t^{3} + t + 1$	$x^{7} + 2$	$[0]$	$[1]$	$z^6 + z^5 + z^4 + z^3 + z^2 + z + 1$	$[7]$
2.3.7.18a1.3	$21$	$( x^{3} + x + 1 )^{7} + 2 x + 2$	$2$	$3$	$7$	$18$	$C_7:C_{21}$ (as 21T13)	$21$	$7$	$[\ ]$	$[\ ]$	$[\ ]_{7}^{21}$	$[\ ]_{7}^{21}$	$[\ ]^{7}$	$[\ ]^{7}$	$7$	$t^{3} + t + 1$	$x^{7} + 2 t + 2$	$[0]$	$[1]$	$z^6 + z^5 + z^4 + z^3 + z^2 + z + 1$	$[7]$
2.1.21.20a1.1	$21$	$x^{21} + 2$	$2$	$1$	$21$	$20$	$C_{21}:C_6$ (as 21T11)	$6$	$21$	$[\ ]$	$[\ ]$	$[\ ]_{21}^{6}$	$[\ ]_{21}^{6}$	$[\ ]^{6}$	$[\ ]^{6}$	$1$	$t + 1$	$x^{21} + 2$	$[0]$	$[6]$	$z^{20} + z^{19} + z^{16} + z^{15} + z^4 + z^3 + 1$	$[21]$

  Download displayed columns for results to