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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 (10 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
3.6.1.0a $3$ $6$ $6$ $1$ $0$ $[\ ]$ $[ ]$ $\langle \rangle$ $( )$ $x$ $6$ $1$ $1$ $1$
3.3.2.3a $3$ $6$ $3$ $2$ $3$ $[\ ]$ $[ ]$ $\langle \rangle$ $( )$ $x^2 + 3 d_{0}$ $6$ $2$ $1$ $1$
3.2.3.6a $3$ $6$ $2$ $3$ $6$ $[\frac{3}{2}]$ $[\frac{1}{2}]$ $\langle\frac{1}{3}\rangle$ $(\frac{1}{2})$ $x^3 + 3 a_{1} x + 3$ $2$ $5$ $8$ $5$
3.2.3.8a $3$ $6$ $2$ $3$ $8$ $[2]$ $[1]$ $\langle\frac{2}{3}\rangle$ $(1)$ $x^3 + 3 a_{2} x^2 + 9 c_{3} + 3$ $6$ $10$ $8$ $6$
3.2.3.10a $3$ $6$ $2$ $3$ $10$ $[\frac{5}{2}]$ $[\frac{3}{2}]$ $\langle1\rangle$ $(\frac{3}{2})$ $x^3 + 9 b_{4} x + 3$ $2$ $6$ $9$ $2$
3.1.6.6a $3$ $6$ $1$ $6$ $6$ $[\frac{5}{4}]$ $[\frac{1}{4}]$ $\langle\frac{1}{6}\rangle$ $(\frac{1}{2})$ $x^6 + 3 a_{1} x + 3 d_{0}$ $2$ $2$ $2$ $1$
3.1.6.7a $3$ $6$ $1$ $6$ $7$ $[\frac{3}{2}]$ $[\frac{1}{2}]$ $\langle\frac{1}{3}\rangle$ $(1)$ $x^6 + 3 c_{3} x^3 + 3 a_{2} x^2 + 3 d_{0}$ $6$ $6$ $2$ $3$
3.1.6.9a $3$ $6$ $1$ $6$ $9$ $[2]$ $[1]$ $\langle\frac{2}{3}\rangle$ $(2)$ $x^6 + 3 b_{5} x^5 + 3 a_{4} x^4 + 3 d_{0} + 9 c_{6}$ $6$ $16$ $6$ $4$
3.1.6.10a $3$ $6$ $1$ $6$ $10$ $[\frac{9}{4}]$ $[\frac{5}{4}]$ $\langle\frac{5}{6}\rangle$ $(\frac{5}{2})$ $x^6 + 3 a_{5} x^5 + 9 b_{7} x + 3 d_{0}$ $2$ $6$ $6$ $1$
3.1.6.11a $3$ $6$ $1$ $6$ $11$ $[\frac{5}{2}]$ $[\frac{3}{2}]$ $\langle1\rangle$ $(3)$ $x^6 + 9 c_{9} x^3 + 9 b_{8} x^2 + 9 b_{7} x + 3 d_{0}$ $6$ $21$ $9$ $5$
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