Properties

Label 103.3.1.0a1.1-2.1.0a
Base 103.3.1.0a1.1
Degree \(2\)
e \(1\)
f \(2\)
c \(0\)

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Invariants

Residue field characteristic: $103$
Degree: $2$
Base field: 103.3.1.0a1.1
Ramification index $e$: $1$
Residue field degree $f$: $2$
Discriminant exponent $c$: $0$
Absolute Artin slopes: $[\ ]$
Swan slopes: $[\ ]$
Means: $\langle\ \rangle$
Rams: $(\ )$
Field count: $1$ (complete)
Ambiguity: $2$
Mass: $1$
Absolute Mass: $1/6$

Varying

These invariants are all associated to absolute extensions of $\Q_{ 103 }$ within this relative family, not the relative extension.

Galois group: $C_6$
Hidden Artin slopes: $[\ ]$
Indices of inseparability: $[0]$
Associated inertia: $[\ ]$
Jump Set: undefined

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
103.6.1.0a1.1 $x^{6} + 96 x^{3} + 9 x^{2} + 30 x + 5$ $C_6$ (as 6T1) $6$ $6$ $[\ ]^{6}$ $[\ ]^{6}$ $[\ ]$ $[\ ]$ $[0]$ $[\ ]$ undefined
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