$p$-adic family 149.1.10.9a

• Label: 149.1.10.9a
• Base: 149.1.1.0a1.1
• Degree: \(10\)
• e: \(10\)
• f: \(1\)
• c: \(9\)

Defining polynomial

$x^{10} + 149d_{0}$

Invariants

Residue field characteristic:	$149$
Degree:	$10$
Base field:	$\Q_{149}$
Ramification index $e$:	$10$
Residue field degree $f$:	$1$
Discriminant exponent $c$:	$9$
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:	$[2]$
Jump Set:	undefined

Galois groups and Hidden Artin slopes

		Galois groups
		$D_{10}$ (as 10T3)
hidden slopes	$[\ ]^{2}$	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
149.1.10.9a1.1	2	$x^{10} + 149$	$D_{10}$ (as 10T3)	$20$	$2$	$[\ ]_{10}^{2}$	$[\ ]_{10}^{2}$	$[\ ]^{2}$	$[\ ]^{2}$	$[0]$	$[2]$	$z^9 + 10 z^8 + 45 z^7 + 120 z^6 + 61 z^5 + 103 z^4 + 61 z^3 + 120 z^2 + 45 z + 10$	undefined
149.1.10.9a1.2	2	$x^{10} + 298$	$D_{10}$ (as 10T3)	$20$	$2$	$[\ ]_{10}^{2}$	$[\ ]_{10}^{2}$	$[\ ]^{2}$	$[\ ]^{2}$	$[0]$	$[2]$	$z^9 + 10 z^8 + 45 z^7 + 120 z^6 + 61 z^5 + 103 z^4 + 61 z^3 + 120 z^2 + 45 z + 10$	undefined

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