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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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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
2.4.1.0a $2$ $4$ $4$ $1$ $0$ $[\ ]$ $[ ]$ $\langle \rangle$ $( )$ $x$ $4$ $1$ $1$ $1$
2.2.2.4a $2$ $4$ $2$ $2$ $4$ $[2]$ $[1]$ $\langle\frac{1}{2}\rangle$ $(1)$ $x^2 + 2 a_{1} x + 4 c_{2} + 2$ $4$ $4$ $3$ $3$
2.2.2.6a $2$ $4$ $2$ $2$ $6$ $[3]$ $[2]$ $\langle1\rangle$ $(2)$ $x^2 + 4 b_{3} x + 8 c_{4} + 2$ $4$ $6$ $4$ $3$
2.1.4.4a $2$ $4$ $1$ $4$ $4$ $[\frac{4}{3}, \frac{4}{3}]$ $[\frac{1}{3}, \frac{1}{3}]$ $\langle\frac{1}{6}, \frac{1}{4}\rangle$ $(\frac{1}{3}, \frac{1}{3})$ $x^4 + 2 a_{1} x + 2$ $1$ $1$ $1$ $1$
2.1.4.6a $2$ $4$ $1$ $4$ $6$ $[2, 2]$ $[1, 1]$ $\langle\frac{1}{2}, \frac{3}{4}\rangle$ $(1, 1)$ $x^4 + 2 a_{3} x^3 + 2 b_{2} x^2 + 4 c_{4} + 2$ $2$ $3$ $2$ $2$
2.1.4.8a $2$ $4$ $1$ $4$ $8$ $[\frac{8}{3}, \frac{8}{3}]$ $[\frac{5}{3}, \frac{5}{3}]$ $\langle\frac{5}{6}, \frac{5}{4}\rangle$ $(\frac{5}{3}, \frac{5}{3})$ $x^4 + 4 b_{6} x^2 + 4 a_{5} x + 2$ $1$ $2$ $2$ $1$
2.1.4.8b $2$ $4$ $1$ $4$ $8$ $[2, 3]$ $[1, 2]$ $\langle\frac{1}{2}, \frac{5}{4}\rangle$ $(1, 3)$ $x^4 + 4 b_{7} x^3 + 2 a_{2} x^2 + 4 a_{5} x + 4 c_{4} + 8 c_{8} + 2$ $4$ $6$ $2$ $2$
2.1.4.9a $2$ $4$ $1$ $4$ $9$ $[2, \frac{7}{2}]$ $[1, \frac{5}{2}]$ $\langle\frac{1}{2}, \frac{3}{2}\rangle$ $(1, 4)$ $x^4 + 4 b_{7} x^3 + (2 a_{2} + 8 c_{10}) x^2 + 8 b_{9} x + 4 c_{4} + 2$ $4$ $8$ $4$ $1$
2.1.4.10a $2$ $4$ $1$ $4$ $10$ $[3, \frac{7}{2}]$ $[2, \frac{5}{2}]$ $\langle1, \frac{7}{4}\rangle$ $(2, 3)$ $x^4 + 4 a_{7} x^3 + (4 b_{6} + 8 c_{10}) x^2 + 8 b_{9} x + 8 c_{8} + 2$ $4$ $8$ $4$ $1$
2.1.4.11a $2$ $4$ $1$ $4$ $11$ $[3, 4]$ $[2, 3]$ $\langle1, 2\rangle$ $(2, 4)$ $x^4 + 8 b_{11} x^3 + 4 b_{6} x^2 + 8 b_{9} x + 8 c_{8} + 16 c_{12} + 2$ $4$ $20$ $8$ $3$
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