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 $c$
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Results (1-50 of 121 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
5.25.1.0a $5$ $25$ $25$ $1$ $0$ $[\ ]$ $[ ]$ $\langle \rangle$ $( )$ $x$ $25$ $0$ $1$ $0$
5.5.5.25a $5$ $25$ $5$ $5$ $25$ $[\frac{5}{4}]$ $[\frac{1}{4}]$ $\langle\frac{1}{5}\rangle$ $(\frac{1}{4})$ $x^5 + 5 a_{1} x + 5$ $5$ $0$ $3124$ $0$
5.5.5.30a $5$ $25$ $5$ $5$ $30$ $[\frac{3}{2}]$ $[\frac{1}{2}]$ $\langle\frac{2}{5}\rangle$ $(\frac{1}{2})$ $x^5 + 5 a_{2} x^2 + 5$ $5$ $0$ $3124$ $0$
5.5.5.35a $5$ $25$ $5$ $5$ $35$ $[\frac{7}{4}]$ $[\frac{3}{4}]$ $\langle\frac{3}{5}\rangle$ $(\frac{3}{4})$ $x^5 + 5 a_{3} x^3 + 5$ $5$ $0$ $3124$ $0$
5.5.5.40a $5$ $25$ $5$ $5$ $40$ $[2]$ $[1]$ $\langle\frac{4}{5}\rangle$ $(1)$ $x^5 + 5 a_{4} x^4 + 25 c_{5} + 5$ $25$ $0$ $3124$ $0$
5.5.5.45a $5$ $25$ $5$ $5$ $45$ $[\frac{9}{4}]$ $[\frac{5}{4}]$ $\langle1\rangle$ $(\frac{5}{4})$ $x^5 + 25 b_{6} x + 5$ $5$ $0$ $3125$ $0$
5.1.25.25a $5$ $25$ $1$ $25$ $25$ $[\frac{25}{24}, \frac{25}{24}]$ $[\frac{1}{24}, \frac{1}{24}]$ $\langle\frac{1}{30}, \frac{1}{25}\rangle$ $(\frac{1}{24}, \frac{1}{24})$ $x^{25} + 5 a_{1} x + 5$ $1$ $0$ $4$ $0$
5.1.25.26a $5$ $25$ $1$ $25$ $26$ $[\frac{13}{12}, \frac{13}{12}]$ $[\frac{1}{12}, \frac{1}{12}]$ $\langle\frac{1}{15}, \frac{2}{25}\rangle$ $(\frac{1}{12}, \frac{1}{12})$ $x^{25} + 5 a_{2} x^2 + 5$ $1$ $0$ $4$ $0$
5.1.25.27a $5$ $25$ $1$ $25$ $27$ $[\frac{9}{8}, \frac{9}{8}]$ $[\frac{1}{8}, \frac{1}{8}]$ $\langle\frac{1}{10}, \frac{3}{25}\rangle$ $(\frac{1}{8}, \frac{1}{8})$ $x^{25} + 5 a_{3} x^3 + 5$ $1$ $0$ $4$ $0$
5.1.25.28a $5$ $25$ $1$ $25$ $28$ $[\frac{7}{6}, \frac{7}{6}]$ $[\frac{1}{6}, \frac{1}{6}]$ $\langle\frac{2}{15}, \frac{4}{25}\rangle$ $(\frac{1}{6}, \frac{1}{6})$ $x^{25} + 5 a_{4} x^4 + 5$ $1$ $0$ $4$ $0$
5.1.25.30a $5$ $25$ $1$ $25$ $30$ $[\frac{5}{4}, \frac{5}{4}]$ $[\frac{1}{4}, \frac{1}{4}]$ $\langle\frac{1}{5}, \frac{6}{25}\rangle$ $(\frac{1}{4}, \frac{1}{4})$ $x^{25} + 5 a_{6} x^6 + 5 b_{5} x^5 + 5$ $1$ $0$ $20$ $0$
5.1.25.31a $5$ $25$ $1$ $25$ $31$ $[\frac{31}{24}, \frac{31}{24}]$ $[\frac{7}{24}, \frac{7}{24}]$ $\langle\frac{7}{30}, \frac{7}{25}\rangle$ $(\frac{7}{24}, \frac{7}{24})$ $x^{25} + 5 a_{7} x^7 + 5$ $1$ $0$ $4$ $0$
5.1.25.31b $5$ $25$ $1$ $25$ $31$ $[\frac{5}{4}, \frac{13}{10}]$ $[\frac{1}{4}, \frac{3}{10}]$ $\langle\frac{1}{5}, \frac{7}{25}\rangle$ $(\frac{1}{4}, \frac{1}{2})$ $x^{25} + 5 a_{7} x^7 + 5 a_{5} x^5 + 5$ $1$ $0$ $16$ $0$
5.1.25.32a $5$ $25$ $1$ $25$ $32$ $[\frac{4}{3}, \frac{4}{3}]$ $[\frac{1}{3}, \frac{1}{3}]$ $\langle\frac{4}{15}, \frac{8}{25}\rangle$ $(\frac{1}{3}, \frac{1}{3})$ $x^{25} + 5 a_{8} x^8 + 5$ $1$ $0$ $4$ $0$
5.1.25.32b $5$ $25$ $1$ $25$ $32$ $[\frac{5}{4}, \frac{27}{20}]$ $[\frac{1}{4}, \frac{7}{20}]$ $\langle\frac{1}{5}, \frac{8}{25}\rangle$ $(\frac{1}{4}, \frac{3}{4})$ $x^{25} + 5 a_{8} x^8 + 5 a_{5} x^5 + 5$ $1$ $0$ $16$ $0$
5.1.25.33a $5$ $25$ $1$ $25$ $33$ $[\frac{11}{8}, \frac{11}{8}]$ $[\frac{3}{8}, \frac{3}{8}]$ $\langle\frac{3}{10}, \frac{9}{25}\rangle$ $(\frac{3}{8}, \frac{3}{8})$ $x^{25} + 5 a_{9} x^9 + 5$ $1$ $0$ $4$ $0$
5.1.25.33b $5$ $25$ $1$ $25$ $33$ $[\frac{5}{4}, \frac{7}{5}]$ $[\frac{1}{4}, \frac{2}{5}]$ $\langle\frac{1}{5}, \frac{9}{25}\rangle$ $(\frac{1}{4}, 1)$ $x^{25} + 5 c_{10} x^{10} + 5 a_{9} x^9 + 5 a_{5} x^5 + 5$ $5$ $0$ $16$ $0$
5.1.25.35a $5$ $25$ $1$ $25$ $35$ $[\frac{35}{24}, \frac{35}{24}]$ $[\frac{11}{24}, \frac{11}{24}]$ $\langle\frac{11}{30}, \frac{11}{25}\rangle$ $(\frac{11}{24}, \frac{11}{24})$ $x^{25} + 5 a_{11} x^{11} + 5 b_{10} x^{10} + 5$ $1$ $0$ $20$ $0$
5.1.25.35b $5$ $25$ $1$ $25$ $35$ $[\frac{5}{4}, \frac{3}{2}]$ $[\frac{1}{4}, \frac{1}{2}]$ $\langle\frac{1}{5}, \frac{11}{25}\rangle$ $(\frac{1}{4}, \frac{3}{2})$ $x^{25} + 5 b_{12} x^{12} + 5 a_{11} x^{11} + 5 a_{5} x^5 + 5$ $1$ $0$ $80$ $0$
5.1.25.36a $5$ $25$ $1$ $25$ $36$ $[\frac{3}{2}, \frac{3}{2}]$ $[\frac{1}{2}, \frac{1}{2}]$ $\langle\frac{2}{5}, \frac{12}{25}\rangle$ $(\frac{1}{2}, \frac{1}{2})$ $x^{25} + 5 a_{12} x^{12} + 5 b_{10} x^{10} + 5$ $1$ $0$ $20$ $0$
5.1.25.36b $5$ $25$ $1$ $25$ $36$ $[\frac{5}{4}, \frac{31}{20}]$ $[\frac{1}{4}, \frac{11}{20}]$ $\langle\frac{1}{5}, \frac{12}{25}\rangle$ $(\frac{1}{4}, \frac{7}{4})$ $x^{25} + 5 b_{13} x^{13} + 5 a_{12} x^{12} + 5 a_{5} x^5 + 5$ $1$ $0$ $80$ $0$
5.1.25.37a $5$ $25$ $1$ $25$ $37$ $[\frac{37}{24}, \frac{37}{24}]$ $[\frac{13}{24}, \frac{13}{24}]$ $\langle\frac{13}{30}, \frac{13}{25}\rangle$ $(\frac{13}{24}, \frac{13}{24})$ $x^{25} + 5 a_{13} x^{13} + 5$ $1$ $0$ $4$ $0$
5.1.25.37b $5$ $25$ $1$ $25$ $37$ $[\frac{5}{4}, \frac{8}{5}]$ $[\frac{1}{4}, \frac{3}{5}]$ $\langle\frac{1}{5}, \frac{13}{25}\rangle$ $(\frac{1}{4}, 2)$ $x^{25} + 5 c_{15} x^{15} + 5 b_{14} x^{14} + 5 a_{13} x^{13} + 5 a_{5} x^5 + 5$ $5$ $0$ $80$ $0$
5.1.25.37c $5$ $25$ $1$ $25$ $37$ $[\frac{3}{2}, \frac{31}{20}]$ $[\frac{1}{2}, \frac{11}{20}]$ $\langle\frac{2}{5}, \frac{13}{25}\rangle$ $(\frac{1}{2}, \frac{3}{4})$ $x^{25} + 5 a_{13} x^{13} + 5 a_{10} x^{10} + 5$ $1$ $0$ $16$ $0$
5.1.25.38a $5$ $25$ $1$ $25$ $38$ $[\frac{19}{12}, \frac{19}{12}]$ $[\frac{7}{12}, \frac{7}{12}]$ $\langle\frac{7}{15}, \frac{14}{25}\rangle$ $(\frac{7}{12}, \frac{7}{12})$ $x^{25} + 5 a_{14} x^{14} + 5$ $1$ $0$ $4$ $0$
5.1.25.38b $5$ $25$ $1$ $25$ $38$ $[\frac{5}{4}, \frac{33}{20}]$ $[\frac{1}{4}, \frac{13}{20}]$ $\langle\frac{1}{5}, \frac{14}{25}\rangle$ $(\frac{1}{4}, \frac{9}{4})$ $x^{25} + 5 b_{16} x^{16} + 5 a_{14} x^{14} + 5 a_{5} x^5 + 5$ $1$ $0$ $80$ $0$
5.1.25.38c $5$ $25$ $1$ $25$ $38$ $[\frac{3}{2}, \frac{8}{5}]$ $[\frac{1}{2}, \frac{3}{5}]$ $\langle\frac{2}{5}, \frac{14}{25}\rangle$ $(\frac{1}{2}, 1)$ $x^{25} + 5 c_{15} x^{15} + 5 a_{14} x^{14} + 5 a_{10} x^{10} + 5$ $5$ $0$ $16$ $0$
5.1.25.40a $5$ $25$ $1$ $25$ $40$ $[\frac{5}{3}, \frac{5}{3}]$ $[\frac{2}{3}, \frac{2}{3}]$ $\langle\frac{8}{15}, \frac{16}{25}\rangle$ $(\frac{2}{3}, \frac{2}{3})$ $x^{25} + 5 a_{16} x^{16} + 5 b_{15} x^{15} + 5$ $1$ $0$ $20$ $0$
5.1.25.40b $5$ $25$ $1$ $25$ $40$ $[\frac{5}{4}, \frac{7}{4}]$ $[\frac{1}{4}, \frac{3}{4}]$ $\langle\frac{1}{5}, \frac{16}{25}\rangle$ $(\frac{1}{4}, \frac{11}{4})$ $x^{25} + 5 b_{18} x^{18} + 5 b_{17} x^{17} + 5 a_{16} x^{16} + 5 a_{5} x^5 + 5$ $1$ $0$ $400$ $0$
5.1.25.40c $5$ $25$ $1$ $25$ $40$ $[\frac{3}{2}, \frac{17}{10}]$ $[\frac{1}{2}, \frac{7}{10}]$ $\langle\frac{2}{5}, \frac{16}{25}\rangle$ $(\frac{1}{2}, \frac{3}{2})$ $x^{25} + 5 b_{17} x^{17} + 5 a_{16} x^{16} + 5 a_{10} x^{10} + 5$ $1$ $0$ $80$ $0$
5.1.25.41a $5$ $25$ $1$ $25$ $41$ $[\frac{41}{24}, \frac{41}{24}]$ $[\frac{17}{24}, \frac{17}{24}]$ $\langle\frac{17}{30}, \frac{17}{25}\rangle$ $(\frac{17}{24}, \frac{17}{24})$ $x^{25} + 5 a_{17} x^{17} + 5 b_{15} x^{15} + 5$ $1$ $0$ $20$ $0$
5.1.25.41b $5$ $25$ $1$ $25$ $41$ $[\frac{5}{4}, \frac{9}{5}]$ $[\frac{1}{4}, \frac{4}{5}]$ $\langle\frac{1}{5}, \frac{17}{25}\rangle$ $(\frac{1}{4}, 3)$ $x^{25} + 5 c_{20} x^{20} + 5 b_{19} x^{19} + 5 b_{18} x^{18} + 5 a_{17} x^{17} + 5 a_{5} x^5 + 5$ $5$ $0$ $400$ $0$
5.1.25.41c $5$ $25$ $1$ $25$ $41$ $[\frac{3}{2}, \frac{7}{4}]$ $[\frac{1}{2}, \frac{3}{4}]$ $\langle\frac{2}{5}, \frac{17}{25}\rangle$ $(\frac{1}{2}, \frac{7}{4})$ $x^{25} + 5 b_{18} x^{18} + 5 a_{17} x^{17} + 5 a_{10} x^{10} + 5$ $1$ $0$ $80$ $0$
5.1.25.42a $5$ $25$ $1$ $25$ $42$ $[\frac{7}{4}, \frac{7}{4}]$ $[\frac{3}{4}, \frac{3}{4}]$ $\langle\frac{3}{5}, \frac{18}{25}\rangle$ $(\frac{3}{4}, \frac{3}{4})$ $x^{25} + 5 a_{18} x^{18} + 5 b_{15} x^{15} + 5$ $1$ $0$ $20$ $0$
5.1.25.42b $5$ $25$ $1$ $25$ $42$ $[\frac{5}{4}, \frac{37}{20}]$ $[\frac{1}{4}, \frac{17}{20}]$ $\langle\frac{1}{5}, \frac{18}{25}\rangle$ $(\frac{1}{4}, \frac{13}{4})$ $x^{25} + 5 b_{21} x^{21} + 5 b_{19} x^{19} + 5 a_{18} x^{18} + 5 a_{5} x^5 + 5$ $1$ $0$ $400$ $0$
5.1.25.42c $5$ $25$ $1$ $25$ $42$ $[\frac{3}{2}, \frac{9}{5}]$ $[\frac{1}{2}, \frac{4}{5}]$ $\langle\frac{2}{5}, \frac{18}{25}\rangle$ $(\frac{1}{2}, 2)$ $x^{25} + 5 c_{20} x^{20} + 5 b_{19} x^{19} + 5 a_{18} x^{18} + 5 a_{10} x^{10} + 5$ $5$ $0$ $80$ $0$
5.1.25.43a $5$ $25$ $1$ $25$ $43$ $[\frac{43}{24}, \frac{43}{24}]$ $[\frac{19}{24}, \frac{19}{24}]$ $\langle\frac{19}{30}, \frac{19}{25}\rangle$ $(\frac{19}{24}, \frac{19}{24})$ $x^{25} + 5 a_{19} x^{19} + 5$ $1$ $0$ $4$ $0$
5.1.25.43b $5$ $25$ $1$ $25$ $43$ $[\frac{5}{4}, \frac{19}{10}]$ $[\frac{1}{4}, \frac{9}{10}]$ $\langle\frac{1}{5}, \frac{19}{25}\rangle$ $(\frac{1}{4}, \frac{7}{2})$ $x^{25} + 5 b_{22} x^{22} + 5 b_{21} x^{21} + 5 a_{19} x^{19} + 5 a_{5} x^5 + 5$ $1$ $0$ $400$ $0$
5.1.25.43c $5$ $25$ $1$ $25$ $43$ $[\frac{3}{2}, \frac{37}{20}]$ $[\frac{1}{2}, \frac{17}{20}]$ $\langle\frac{2}{5}, \frac{19}{25}\rangle$ $(\frac{1}{2}, \frac{9}{4})$ $x^{25} + 5 b_{21} x^{21} + 5 a_{19} x^{19} + 5 a_{10} x^{10} + 5$ $1$ $0$ $80$ $0$
5.1.25.43d $5$ $25$ $1$ $25$ $43$ $[\frac{7}{4}, \frac{9}{5}]$ $[\frac{3}{4}, \frac{4}{5}]$ $\langle\frac{3}{5}, \frac{19}{25}\rangle$ $(\frac{3}{4}, 1)$ $x^{25} + 5 c_{20} x^{20} + 5 a_{19} x^{19} + 5 a_{15} x^{15} + 5$ $5$ $0$ $16$ $0$
5.1.25.45a $5$ $25$ $1$ $25$ $45$ $[\frac{15}{8}, \frac{15}{8}]$ $[\frac{7}{8}, \frac{7}{8}]$ $\langle\frac{7}{10}, \frac{21}{25}\rangle$ $(\frac{7}{8}, \frac{7}{8})$ $x^{25} + 5 a_{21} x^{21} + 5 b_{20} x^{20} + 5$ $1$ $0$ $20$ $0$
5.1.25.45b $5$ $25$ $1$ $25$ $45$ $[\frac{5}{4}, 2]$ $[\frac{1}{4}, 1]$ $\langle\frac{1}{5}, \frac{21}{25}\rangle$ $(\frac{1}{4}, 4)$ $x^{25} + 5 b_{24} x^{24} + 5 b_{23} x^{23} + 5 b_{22} x^{22} + 5 a_{21} x^{21} + 5 a_{5} x^5 + 25 c_{25} + 5$ $5$ $0$ $2000$ $0$
5.1.25.45c $5$ $25$ $1$ $25$ $45$ $[\frac{3}{2}, \frac{39}{20}]$ $[\frac{1}{2}, \frac{19}{20}]$ $\langle\frac{2}{5}, \frac{21}{25}\rangle$ $(\frac{1}{2}, \frac{11}{4})$ $x^{25} + 5 b_{23} x^{23} + 5 b_{22} x^{22} + 5 a_{21} x^{21} + 5 a_{10} x^{10} + 5$ $1$ $0$ $400$ $0$
5.1.25.45d $5$ $25$ $1$ $25$ $45$ $[\frac{7}{4}, \frac{19}{10}]$ $[\frac{3}{4}, \frac{9}{10}]$ $\langle\frac{3}{5}, \frac{21}{25}\rangle$ $(\frac{3}{4}, \frac{3}{2})$ $x^{25} + 5 b_{22} x^{22} + 5 a_{21} x^{21} + 5 a_{15} x^{15} + 5$ $1$ $0$ $80$ $0$
5.1.25.46a $5$ $25$ $1$ $25$ $46$ $[\frac{23}{12}, \frac{23}{12}]$ $[\frac{11}{12}, \frac{11}{12}]$ $\langle\frac{11}{15}, \frac{22}{25}\rangle$ $(\frac{11}{12}, \frac{11}{12})$ $x^{25} + 5 a_{22} x^{22} + 5 b_{20} x^{20} + 5$ $1$ $0$ $20$ $0$
5.1.25.46b $5$ $25$ $1$ $25$ $46$ $[\frac{5}{4}, \frac{41}{20}]$ $[\frac{1}{4}, \frac{21}{20}]$ $\langle\frac{1}{5}, \frac{22}{25}\rangle$ $(\frac{1}{4}, \frac{17}{4})$ $x^{25} + 5 b_{24} x^{24} + 5 b_{23} x^{23} + 5 a_{22} x^{22} + 5 a_{5} x^5 + 25 b_{26} x + 5$ $1$ $0$ $2000$ $0$
5.1.25.46c $5$ $25$ $1$ $25$ $46$ $[\frac{3}{2}, 2]$ $[\frac{1}{2}, 1]$ $\langle\frac{2}{5}, \frac{22}{25}\rangle$ $(\frac{1}{2}, 3)$ $x^{25} + 5 b_{24} x^{24} + 5 b_{23} x^{23} + 5 a_{22} x^{22} + 5 a_{10} x^{10} + 25 c_{25} + 5$ $5$ $0$ $400$ $0$
5.1.25.46d $5$ $25$ $1$ $25$ $46$ $[\frac{7}{4}, \frac{39}{20}]$ $[\frac{3}{4}, \frac{19}{20}]$ $\langle\frac{3}{5}, \frac{22}{25}\rangle$ $(\frac{3}{4}, \frac{7}{4})$ $x^{25} + 5 b_{23} x^{23} + 5 a_{22} x^{22} + 5 a_{15} x^{15} + 5$ $1$ $0$ $80$ $0$
5.1.25.47a $5$ $25$ $1$ $25$ $47$ $[\frac{47}{24}, \frac{47}{24}]$ $[\frac{23}{24}, \frac{23}{24}]$ $\langle\frac{23}{30}, \frac{23}{25}\rangle$ $(\frac{23}{24}, \frac{23}{24})$ $x^{25} + 5 a_{23} x^{23} + 5 b_{20} x^{20} + 5$ $1$ $0$ $20$ $0$
5.1.25.47b $5$ $25$ $1$ $25$ $47$ $[\frac{5}{4}, \frac{21}{10}]$ $[\frac{1}{4}, \frac{11}{10}]$ $\langle\frac{1}{5}, \frac{23}{25}\rangle$ $(\frac{1}{4}, \frac{9}{2})$ $x^{25} + 5 b_{24} x^{24} + 5 a_{23} x^{23} + 5 a_{5} x^5 + 25 b_{27} x^2 + 25 b_{26} x + 5$ $1$ $0$ $2000$ $0$
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