$p$-adic family 2.1.6.11a1.15-1.3.2a

• Label: 2.1.6.11a1.15-1.3.2a
• Base: 2.1.6.11a1.15
• Degree: \(3\)
• e: \(3\)
• f: \(1\)
• c: \(2\)

Defining polynomial

$x^{3} + \pi$

Invariants

Residue field characteristic:	$2$
Degree:	$3$
Base field:	2.1.6.11a1.15
Ramification index $e$:	$3$
Residue field degree $f$:	$1$
Discriminant exponent $c$:	$2$
Absolute Artin slopes:	$[3]$
Swan slopes:	$[\ ]$
Means:	$\langle\ \rangle$
Rams:	$(\ )$
Field count:	$1$ (complete)
Ambiguity:	$1$
Mass:	$1$
Absolute Mass:	$1/2$

Varying

These invariants are all associated to absolute extensions of $\Q_{ 2 }$ within this relative family, not the relative extension.

Galois group:	$C_6^2.D_6$
Hidden Artin slopes:	$[\frac{8}{3},\frac{8}{3}]^{6}$
Indices of inseparability:	$[18,0]$
Associated inertia:	$[6,1]$
Jump Set:	$[9,27]$

Fields

Showing all 1

  Download displayed columns for results to

Label	Polynomial $/ \Q_p$	Galois group $/ \Q_p$	Galois degree $/ \Q_p$	$\#\Aut(K/\Q_p)$	Artin slope content $/ \Q_p$	Swan slope content $/ \Q_p$	Hidden Artin slopes $/ \Q_p$	Hidden Swan slopes $/ \Q_p$	Ind. of Insep. $/ \Q_p$	Assoc. Inertia $/ \Q_p$	Resid. Poly	Jump Set
2.1.18.35a1.293	$x^{18} + 4 x^{15} + 4 x^{9} + 4 x^{3} + 2$	$C_6^2.D_6$ (as 18T147)	$432$	$2$	$[\frac{8}{3}, \frac{8}{3}, 3]_{9}^{6}$	$[\frac{5}{3},\frac{5}{3},2]_{9}^{6}$	$[\frac{8}{3},\frac{8}{3}]^{6}$	$[\frac{5}{3},\frac{5}{3}]^{6}$	$[18, 0]$	$[6, 1]$	$z^{16} + z^{14} + 1,z + 1$	$[9, 27]$

  Download displayed columns for results to