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The results below are complete, since the LMFDB contains all families of p-adic fields of degree at most 47 and residue characteristic at most 199

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Residue characteristic $p$ Degree $n$ Ramification index $e$ Residue field degree $f$ Discriminant exponent $c$
Mass Ambiguity Field count Wild segments Herbrand invariant
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Results (6 matches)

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Label $p$ $n$ $f$ $e$ $c$ Abs. Artin slopes Swan slopes Means Rams Generic poly Ambiguity Field count Mass Num. Packets
7.32.1.0a $7$ $32$ $32$ $1$ $0$ $[\ ]$ $[ ]$ $\langle \rangle$ $( )$ $x$ $32$ $0$ $1$ $0$
7.16.2.16a $7$ $32$ $16$ $2$ $16$ $[\ ]$ $[ ]$ $\langle \rangle$ $( )$ $x^2 + 7 d_{0}$ $32$ $0$ $1$ $0$
7.8.4.24a $7$ $32$ $8$ $4$ $24$ $[\ ]$ $[ ]$ $\langle \rangle$ $( )$ $x^4 + 7 d_{0}$ $32$ $0$ $1$ $0$
7.4.8.28a $7$ $32$ $4$ $8$ $28$ $[\ ]$ $[ ]$ $\langle \rangle$ $( )$ $x^8 + 7 d_{0}$ $32$ $0$ $1$ $0$
7.2.16.30a $7$ $32$ $2$ $16$ $30$ $[\ ]$ $[ ]$ $\langle \rangle$ $( )$ $x^{16} + 7 d_{0}$ $32$ $0$ $1$ $0$
7.1.32.31a $7$ $32$ $1$ $32$ $31$ $[\ ]$ $[ ]$ $\langle \rangle$ $( )$ $x^{32} + 7 d_{0}$ $2$ $0$ $1$ $0$
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