$p$-adic family 2.1.4.11a1.5-3.1.0a

• Label: 2.1.4.11a1.5-3.1.0a
• Base: 2.1.4.11a1.5
• Degree: \(3\)
• e: \(1\)
• f: \(3\)
• c: \(0\)

Invariants

Residue field characteristic:	$2$
Degree:	$3$
Base field:	2.1.4.11a1.5
Ramification index $e$:	$1$
Residue field degree $f$:	$3$
Discriminant exponent $c$:	$0$
Absolute Artin slopes:	$[3,4]$
Swan slopes:	$[\ ]$
Means:	$\langle\ \rangle$
Rams:	$(\ )$
Field count:	$1$ (complete)
Ambiguity:	$3$
Mass:	$1$
Absolute Mass:	$1/6$

Varying

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

Galois group:	$D_4 \times C_3$
Hidden Artin slopes:	$[2]$
Indices of inseparability:	$[8,4,0]$
Associated inertia:	$[1,1]$
Jump Set:	$[1,3,7]$

Fields

Showing all 1

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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
2.3.4.33a1.25	$( x^{3} + x + 1 )^{4} + 10$	$D_4 \times C_3$ (as 12T14)	$24$	$6$	$[2, 3, 4]^{3}$	$[1,2,3]^{3}$	$[2]$	$[1]$	$[8, 4, 0]$	$[1, 1]$	$z^2 + (t + 1),(t + 1) z + (t^2 + 1)$	$[1, 3, 7]$

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