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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
5.15.1.0a $5$ $15$ $15$ $1$ $0$ $[\ ]$ $[ ]$ $\langle \rangle$ $( )$ $x$ $15$ $1$ $1$ $1$
5.5.3.10a $5$ $15$ $5$ $3$ $10$ $[\ ]$ $[ ]$ $\langle \rangle$ $( )$ $x^3 + 5$ $5$ $1$ $1$ $1$
5.3.5.15a $5$ $15$ $3$ $5$ $15$ $[\frac{5}{4}]$ $[\frac{1}{4}]$ $\langle\frac{1}{5}\rangle$ $(\frac{1}{4})$ $x^5 + 5 a_{1} x + 5$ $3$ $44$ $124$ $44$
5.3.5.18a $5$ $15$ $3$ $5$ $18$ $[\frac{3}{2}]$ $[\frac{1}{2}]$ $\langle\frac{2}{5}\rangle$ $(\frac{1}{2})$ $x^5 + 5 a_{2} x^2 + 5$ $3$ $44$ $124$ $44$
5.3.5.21a $5$ $15$ $3$ $5$ $21$ $[\frac{7}{4}]$ $[\frac{3}{4}]$ $\langle\frac{3}{5}\rangle$ $(\frac{3}{4})$ $x^5 + 5 a_{3} x^3 + 5$ $3$ $44$ $124$ $44$
5.3.5.24a $5$ $15$ $3$ $5$ $24$ $[2]$ $[1]$ $\langle\frac{4}{5}\rangle$ $(1)$ $x^5 + 5 a_{4} x^4 + 25 c_{5} + 5$ $15$ $88$ $124$ $46$
5.3.5.27a $5$ $15$ $3$ $5$ $27$ $[\frac{9}{4}]$ $[\frac{5}{4}]$ $\langle1\rangle$ $(\frac{5}{4})$ $x^5 + 25 b_{6} x + 5$ $3$ $45$ $125$ $2$
5.1.15.15a $5$ $15$ $1$ $15$ $15$ $[\frac{13}{12}]$ $[\frac{1}{12}]$ $\langle\frac{1}{15}\rangle$ $(\frac{1}{4})$ $x^{15} + 5 a_{1} x + 5$ $1$ $4$ $4$ $1$
5.1.15.16a $5$ $15$ $1$ $15$ $16$ $[\frac{7}{6}]$ $[\frac{1}{6}]$ $\langle\frac{2}{15}\rangle$ $(\frac{1}{2})$ $x^{15} + 5 a_{2} x^2 + 5$ $1$ $4$ $4$ $2$
5.1.15.17a $5$ $15$ $1$ $15$ $17$ $[\frac{5}{4}]$ $[\frac{1}{4}]$ $\langle\frac{1}{5}\rangle$ $(\frac{3}{4})$ $x^{15} + 5 a_{3} x^3 + 5$ $1$ $4$ $4$ $1$
5.1.15.18a $5$ $15$ $1$ $15$ $18$ $[\frac{4}{3}]$ $[\frac{1}{3}]$ $\langle\frac{4}{15}\rangle$ $(1)$ $x^{15} + 5 c_{5} x^5 + 5 a_{4} x^4 + 5$ $5$ $8$ $4$ $5$
5.1.15.20a $5$ $15$ $1$ $15$ $20$ $[\frac{3}{2}]$ $[\frac{1}{2}]$ $\langle\frac{2}{5}\rangle$ $(\frac{3}{2})$ $x^{15} + 5 b_{7} x^7 + 5 a_{6} x^6 + 5$ $1$ $20$ $20$ $4$
5.1.15.21a $5$ $15$ $1$ $15$ $21$ $[\frac{19}{12}]$ $[\frac{7}{12}]$ $\langle\frac{7}{15}\rangle$ $(\frac{7}{4})$ $x^{15} + 5 b_{8} x^8 + 5 a_{7} x^7 + 5$ $1$ $20$ $20$ $2$
5.1.15.22a $5$ $15$ $1$ $15$ $22$ $[\frac{5}{3}]$ $[\frac{2}{3}]$ $\langle\frac{8}{15}\rangle$ $(2)$ $x^{15} + 5 c_{10} x^{10} + 5 b_{9} x^9 + 5 a_{8} x^8 + 5$ $5$ $40$ $20$ $5$
5.1.15.23a $5$ $15$ $1$ $15$ $23$ $[\frac{7}{4}]$ $[\frac{3}{4}]$ $\langle\frac{3}{5}\rangle$ $(\frac{9}{4})$ $x^{15} + 5 b_{11} x^{11} + 5 a_{9} x^9 + 5$ $1$ $20$ $20$ $2$
5.1.15.25a $5$ $15$ $1$ $15$ $25$ $[\frac{23}{12}]$ $[\frac{11}{12}]$ $\langle\frac{11}{15}\rangle$ $(\frac{11}{4})$ $x^{15} + 5 b_{13} x^{13} + 5 b_{12} x^{12} + 5 a_{11} x^{11} + 5$ $1$ $100$ $100$ $2$
5.1.15.26a $5$ $15$ $1$ $15$ $26$ $[2]$ $[1]$ $\langle\frac{4}{5}\rangle$ $(3)$ $x^{15} + 5 b_{14} x^{14} + 5 b_{13} x^{13} + 5 a_{12} x^{12} + 25 c_{15} + 5$ $5$ $200$ $100$ $12$
5.1.15.27a $5$ $15$ $1$ $15$ $27$ $[\frac{25}{12}]$ $[\frac{13}{12}]$ $\langle\frac{13}{15}\rangle$ $(\frac{13}{4})$ $x^{15} + 5 b_{14} x^{14} + 5 a_{13} x^{13} + 25 b_{16} x + 5$ $1$ $100$ $100$ $2$
5.1.15.28a $5$ $15$ $1$ $15$ $28$ $[\frac{13}{6}]$ $[\frac{7}{6}]$ $\langle\frac{14}{15}\rangle$ $(\frac{7}{2})$ $x^{15} + 5 a_{14} x^{14} + 25 b_{17} x^2 + 25 b_{16} x + 5$ $1$ $100$ $100$ $4$
5.1.15.29a $5$ $15$ $1$ $15$ $29$ $[\frac{9}{4}]$ $[\frac{5}{4}]$ $\langle1\rangle$ $(\frac{15}{4})$ $x^{15} + 25 b_{18} x^3 + 25 b_{17} x^2 + 25 b_{16} x + 5$ $1$ $125$ $125$ $3$
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