$p$-adic family 197.1.2.1a

• Label: 197.1.2.1a
• Base: 197.1.1.0a1.1
• Degree: \(2\)
• e: \(2\)
• f: \(1\)
• c: \(1\)

Defining polynomial

$x^{2} + 197d_{0}$

Invariants

Residue field characteristic:	$197$
Degree:	$2$
Base field:	$\Q_{197}$
Ramification index $e$:	$2$
Residue field degree $f$:	$1$
Discriminant exponent $c$:	$1$
Artin slopes:	$[\ ]$
Swan slopes:	$[\ ]$
Means:	$\langle\ \rangle$
Rams:	$(\ )$
Field count:	$2$ (complete)
Ambiguity:	$2$
Mass:	$1$
Absolute Mass:	$1$

Varying

Indices of inseparability:	$[0]$
Associated inertia:	$[1]$
Jump Set:	undefined

Galois groups and Hidden Artin slopes

		Galois groups
		$C_2$ (as 2T1)
hidden slopes	$[\ ]$	2

Fields

Showing all 2

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Label	Packet size	Polynomial	Galois group	Galois degree	$\#\Aut(K/\Q_p)$	Artin slope content	Swan slope content	Hidden Artin slopes	Hidden Swan slopes	Ind. of Insep.	Assoc. Inertia	Resid. Poly	Jump Set
197.1.2.1a1.1	2	$x^{2} + 197$	$C_2$ (as 2T1)	$2$	$2$	$[\ ]_{2}$	$[\ ]_{2}$	$[\ ]$	$[\ ]$	$[0]$	$[1]$	$z + 2$	undefined
197.1.2.1a1.2	2	$x^{2} + 394$	$C_2$ (as 2T1)	$2$	$2$	$[\ ]_{2}$	$[\ ]_{2}$	$[\ ]$	$[\ ]$	$[0]$	$[1]$	$z + 2$	undefined

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