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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 (20 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
3.12.1.0a $3$ $12$ $12$ $1$ $0$ $[\ ]$ $[ ]$ $\langle \rangle$ $( )$ $x$ $12$ $1$ $1$ $1$
3.6.2.6a $3$ $12$ $6$ $2$ $6$ $[\ ]$ $[ ]$ $\langle \rangle$ $( )$ $x^2 + 3 d_{0}$ $12$ $2$ $1$ $2$
3.4.3.12a $3$ $12$ $4$ $3$ $12$ $[\frac{3}{2}]$ $[\frac{1}{2}]$ $\langle\frac{1}{3}\rangle$ $(\frac{1}{2})$ $x^3 + 3 a_{1} x + 3$ $4$ $23$ $80$ $23$
3.4.3.16a $3$ $12$ $4$ $3$ $16$ $[2]$ $[1]$ $\langle\frac{2}{3}\rangle$ $(1)$ $x^3 + 3 a_{2} x^2 + 9 c_{3} + 3$ $12$ $46$ $80$ $28$
3.4.3.20a $3$ $12$ $4$ $3$ $20$ $[\frac{5}{2}]$ $[\frac{3}{2}]$ $\langle1\rangle$ $(\frac{3}{2})$ $x^3 + 9 b_{4} x + 3$ $4$ $24$ $81$ $4$
3.3.4.9a $3$ $12$ $3$ $4$ $9$ $[\ ]$ $[ ]$ $\langle \rangle$ $( )$ $x^4 + 3 d_{0}$ $6$ $2$ $1$ $1$
3.2.6.12a $3$ $12$ $2$ $6$ $12$ $[\frac{5}{4}]$ $[\frac{1}{4}]$ $\langle\frac{1}{6}\rangle$ $(\frac{1}{2})$ $x^6 + 3 a_{1} x + 3 d_{0}$ $4$ $5$ $8$ $5$
3.2.6.14a $3$ $12$ $2$ $6$ $14$ $[\frac{3}{2}]$ $[\frac{1}{2}]$ $\langle\frac{1}{3}\rangle$ $(1)$ $x^6 + 3 c_{3} x^3 + 3 a_{2} x^2 + 3 d_{0}$ $12$ $15$ $8$ $15$
3.2.6.18a $3$ $12$ $2$ $6$ $18$ $[2]$ $[1]$ $\langle\frac{2}{3}\rangle$ $(2)$ $x^6 + 3 b_{5} x^5 + 3 a_{4} x^4 + 3 d_{0} + 9 c_{6}$ $12$ $88$ $72$ $30$
3.2.6.20a $3$ $12$ $2$ $6$ $20$ $[\frac{9}{4}]$ $[\frac{5}{4}]$ $\langle\frac{5}{6}\rangle$ $(\frac{5}{2})$ $x^6 + 3 a_{5} x^5 + 9 b_{7} x + 3 d_{0}$ $4$ $39$ $72$ $8$
3.2.6.22a $3$ $12$ $2$ $6$ $22$ $[\frac{5}{2}]$ $[\frac{3}{2}]$ $\langle1\rangle$ $(3)$ $x^6 + 9 c_{9} x^3 + 9 b_{8} x^2 + 9 b_{7} x + 3 d_{0}$ $12$ $96$ $81$ $16$
3.1.12.12a $3$ $12$ $1$ $12$ $12$ $[\frac{9}{8}]$ $[\frac{1}{8}]$ $\langle\frac{1}{12}\rangle$ $(\frac{1}{2})$ $x^{12} + 3 a_{1} x + 3 d_{0}$ $2$ $2$ $2$ $1$
3.1.12.13a $3$ $12$ $1$ $12$ $13$ $[\frac{5}{4}]$ $[\frac{1}{4}]$ $\langle\frac{1}{6}\rangle$ $(1)$ $x^{12} + 3 c_{3} x^3 + 3 a_{2} x^2 + 3 d_{0}$ $6$ $6$ $2$ $3$
3.1.12.15a $3$ $12$ $1$ $12$ $15$ $[\frac{3}{2}]$ $[\frac{1}{2}]$ $\langle\frac{1}{3}\rangle$ $(2)$ $x^{12} + 3 c_{6} x^6 + 3 b_{5} x^5 + 3 a_{4} x^4 + 3 d_{0}$ $6$ $16$ $6$ $6$
3.1.12.16a $3$ $12$ $1$ $12$ $16$ $[\frac{13}{8}]$ $[\frac{5}{8}]$ $\langle\frac{5}{12}\rangle$ $(\frac{5}{2})$ $x^{12} + 3 b_{7} x^7 + 3 a_{5} x^5 + 3 d_{0}$ $2$ $6$ $6$ $2$
3.1.12.18a $3$ $12$ $1$ $12$ $18$ $[\frac{15}{8}]$ $[\frac{7}{8}]$ $\langle\frac{7}{12}\rangle$ $(\frac{7}{2})$ $x^{12} + 3 b_{10} x^{10} + 3 b_{8} x^8 + 3 a_{7} x^7 + 3 d_{0}$ $2$ $18$ $18$ $2$
3.1.12.19a $3$ $12$ $1$ $12$ $19$ $[2]$ $[1]$ $\langle\frac{2}{3}\rangle$ $(4)$ $x^{12} + 3 b_{11} x^{11} + 3 b_{10} x^{10} + 3 a_{8} x^8 + 3 d_{0} + 9 c_{12}$ $6$ $48$ $18$ $8$
3.1.12.21a $3$ $12$ $1$ $12$ $21$ $[\frac{9}{4}]$ $[\frac{5}{4}]$ $\langle\frac{5}{6}\rangle$ $(5)$ $x^{12} + 3 b_{11} x^{11} + 3 a_{10} x^{10} + 9 c_{15} x^3 + 9 b_{14} x^2 + 9 b_{13} x + 3 d_{0}$ $6$ $114$ $54$ $10$
3.1.12.22a $3$ $12$ $1$ $12$ $22$ $[\frac{19}{8}]$ $[\frac{11}{8}]$ $\langle\frac{11}{12}\rangle$ $(\frac{11}{2})$ $x^{12} + 3 a_{11} x^{11} + 9 b_{16} x^4 + 9 b_{14} x^2 + 9 b_{13} x + 3 d_{0}$ $2$ $54$ $54$ $3$
3.1.12.23a $3$ $12$ $1$ $12$ $23$ $[\frac{5}{2}]$ $[\frac{3}{2}]$ $\langle1\rangle$ $(6)$ $x^{12} + 9 c_{18} x^6 + 9 b_{17} x^5 + 9 b_{16} x^4 + 9 b_{14} x^2 + 9 b_{13} x + 3 d_{0}$ $6$ $180$ $81$ $15$
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