$p$-adic family 2.1.8.20a1.2-2.1.0a

• Label: 2.1.8.20a1.2-2.1.0a
• Base: 2.1.8.20a1.2
• Degree: \(2\)
• e: \(1\)
• f: \(2\)
• c: \(0\)

Invariants

Residue field characteristic:	$2$
Degree:	$2$
Base field:	2.1.8.20a1.2
Ramification index $e$:	$1$
Residue field degree $f$:	$2$
Discriminant exponent $c$:	$0$
Absolute Artin slopes:	$[\frac{20}{7},\frac{20}{7},\frac{20}{7}]$
Swan slopes:	$[\ ]$
Means:	$\langle\ \rangle$
Rams:	$(\ )$
Field count:	$1$ (complete)
Ambiguity:	$2$
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:	$F_8:C_6$
Hidden Artin slopes:	$[\ ]^{3}_{7}$
Indices of inseparability:	$[13,13,8,0]$
Associated inertia:	$[1]$
Jump Set:	$[1,3,7,15]$

Fields

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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
2.2.8.40a1.3	$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{6} + 4 ( x^{2} + x + 1 )^{5} + 2$	$F_8:C_6$ (as 16T712)	$336$	$2$	$[\frac{20}{7}, \frac{20}{7}, \frac{20}{7}]_{7}^{6}$	$[\frac{13}{7},\frac{13}{7},\frac{13}{7}]_{7}^{6}$	$[\ ]^{3}_{7}$	$[\ ]^{3}_{7}$	$[13, 13, 8, 0]$	$[1]$	$z + 1$	$[1, 3, 7, 15]$

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