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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 (49 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
2.8.1.0a $2$ $8$ $8$ $1$ $0$ $[\ ]$ $[ ]$ $\langle \rangle$ $( )$ $x$ $8$ $1$ $1$ $1$
2.4.2.8a $2$ $8$ $4$ $2$ $8$ $[2]$ $[1]$ $\langle\frac{1}{2}\rangle$ $(1)$ $x^2 + 2 a_{1} x + 4 c_{2} + 2$ $8$ $10$ $15$ $8$
2.4.2.12a $2$ $8$ $4$ $2$ $12$ $[3]$ $[2]$ $\langle1\rangle$ $(2)$ $x^2 + 4 b_{3} x + 8 c_{4} + 2$ $8$ $12$ $16$ $7$
2.2.4.8a $2$ $8$ $2$ $4$ $8$ $[\frac{4}{3}, \frac{4}{3}]$ $[\frac{1}{3}, \frac{1}{3}]$ $\langle\frac{1}{6}, \frac{1}{4}\rangle$ $(\frac{1}{3}, \frac{1}{3})$ $x^4 + 2 a_{1} x + 2$ $2$ $2$ $3$ $2$
2.2.4.12a $2$ $8$ $2$ $4$ $12$ $[2, 2]$ $[1, 1]$ $\langle\frac{1}{2}, \frac{3}{4}\rangle$ $(1, 1)$ $x^4 + 2 a_{3} x^3 + 2 b_{2} x^2 + 4 c_{4} + 2$ $8$ $12$ $12$ $9$
2.2.4.16a $2$ $8$ $2$ $4$ $16$ $[\frac{8}{3}, \frac{8}{3}]$ $[\frac{5}{3}, \frac{5}{3}]$ $\langle\frac{5}{6}, \frac{5}{4}\rangle$ $(\frac{5}{3}, \frac{5}{3})$ $x^4 + 4 b_{6} x^2 + 4 a_{5} x + 2$ $2$ $7$ $12$ $3$
2.2.4.16b $2$ $8$ $2$ $4$ $16$ $[2, 3]$ $[1, 2]$ $\langle\frac{1}{2}, \frac{5}{4}\rangle$ $(1, 3)$ $x^4 + 4 b_{7} x^3 + 2 a_{2} x^2 + 4 a_{5} x + 4 c_{4} + 8 c_{8} + 2$ $8$ $49$ $36$ $17$
2.2.4.18a $2$ $8$ $2$ $4$ $18$ $[2, \frac{7}{2}]$ $[1, \frac{5}{2}]$ $\langle\frac{1}{2}, \frac{3}{2}\rangle$ $(1, 4)$ $x^4 + 4 b_{7} x^3 + (2 a_{2} + 8 c_{10}) x^2 + 8 b_{9} x + 4 c_{4} + 2$ $8$ $52$ $48$ $8$
2.2.4.20a $2$ $8$ $2$ $4$ $20$ $[3, \frac{7}{2}]$ $[2, \frac{5}{2}]$ $\langle1, \frac{7}{4}\rangle$ $(2, 3)$ $x^4 + 4 a_{7} x^3 + (4 b_{6} + 8 c_{10}) x^2 + 8 b_{9} x + 8 c_{8} + 2$ $8$ $52$ $48$ $8$
2.2.4.22a $2$ $8$ $2$ $4$ $22$ $[3, 4]$ $[2, 3]$ $\langle1, 2\rangle$ $(2, 4)$ $x^4 + 8 b_{11} x^3 + 4 b_{6} x^2 + 8 b_{9} x + 8 c_{8} + 16 c_{12} + 2$ $8$ $82$ $64$ $17$
2.1.8.8a $2$ $8$ $1$ $8$ $8$ $[\frac{8}{7}, \frac{8}{7}, \frac{8}{7}]$ $[\frac{1}{7}, \frac{1}{7}, \frac{1}{7}]$ $\langle\frac{1}{14}, \frac{3}{28}, \frac{1}{8}\rangle$ $(\frac{1}{7}, \frac{1}{7}, \frac{1}{7})$ $x^8 + 2 a_{1} x + 2$ $1$ $1$ $1$ $1$
2.1.8.10a $2$ $8$ $1$ $8$ $10$ $[\frac{10}{7}, \frac{10}{7}, \frac{10}{7}]$ $[\frac{3}{7}, \frac{3}{7}, \frac{3}{7}]$ $\langle\frac{3}{14}, \frac{9}{28}, \frac{3}{8}\rangle$ $(\frac{3}{7}, \frac{3}{7}, \frac{3}{7})$ $x^8 + 2 a_{3} x^3 + 2$ $1$ $1$ $1$ $1$
2.1.8.10b $2$ $8$ $1$ $8$ $10$ $[\frac{4}{3}, \frac{4}{3}, \frac{3}{2}]$ $[\frac{1}{3}, \frac{1}{3}, \frac{1}{2}]$ $\langle\frac{1}{6}, \frac{1}{4}, \frac{3}{8}\rangle$ $(\frac{1}{3}, \frac{1}{3}, 1)$ $x^8 + 2 c_{4} x^4 + 2 a_{3} x^3 + 2 a_{2} x^2 + 2$ $2$ $2$ $1$ $1$
2.1.8.12a $2$ $8$ $1$ $8$ $12$ $[\frac{12}{7}, \frac{12}{7}, \frac{12}{7}]$ $[\frac{5}{7}, \frac{5}{7}, \frac{5}{7}]$ $\langle\frac{5}{14}, \frac{15}{28}, \frac{5}{8}\rangle$ $(\frac{5}{7}, \frac{5}{7}, \frac{5}{7})$ $x^8 + 2 a_{5} x^5 + 2 b_{4} x^4 + 2$ $1$ $2$ $2$ $1$
2.1.8.12b $2$ $8$ $1$ $8$ $12$ $[\frac{4}{3}, \frac{4}{3}, 2]$ $[\frac{1}{3}, \frac{1}{3}, 1]$ $\langle\frac{1}{6}, \frac{1}{4}, \frac{5}{8}\rangle$ $(\frac{1}{3}, \frac{1}{3}, 3)$ $x^8 + 2 b_{7} x^7 + 2 a_{5} x^5 + 2 a_{2} x^2 + 4 c_{8} + 2$ $2$ $4$ $2$ $2$
2.1.8.14a $2$ $8$ $1$ $8$ $14$ $[2, 2, 2]$ $[1, 1, 1]$ $\langle\frac{1}{2}, \frac{3}{4}, \frac{7}{8}\rangle$ $(1, 1, 1)$ $x^8 + 2 a_{7} x^7 + 2 b_{6} x^6 + 2 b_{4} x^4 + 4 c_{8} + 2$ $2$ $6$ $4$ $4$
2.1.8.14b $2$ $8$ $1$ $8$ $14$ $[\frac{4}{3}, \frac{4}{3}, \frac{5}{2}]$ $[\frac{1}{3}, \frac{1}{3}, \frac{3}{2}]$ $\langle\frac{1}{6}, \frac{1}{4}, \frac{7}{8}\rangle$ $(\frac{1}{3}, \frac{1}{3}, 5)$ $x^8 + 2 a_{7} x^7 + 4 c_{12} x^4 + 4 b_{11} x^3 + 2 a_{2} x^2 + 4 b_{9} x + 2$ $2$ $8$ $4$ $1$
2.1.8.16a $2$ $8$ $1$ $8$ $16$ $[\frac{16}{7}, \frac{16}{7}, \frac{16}{7}]$ $[\frac{9}{7}, \frac{9}{7}, \frac{9}{7}]$ $\langle\frac{9}{14}, \frac{27}{28}, \frac{9}{8}\rangle$ $(\frac{9}{7}, \frac{9}{7}, \frac{9}{7})$ $x^8 + 4 b_{10} x^2 + 4 a_{9} x + 2$ $1$ $2$ $2$ $1$
2.1.8.16b $2$ $8$ $1$ $8$ $16$ $[\frac{4}{3}, \frac{4}{3}, 3]$ $[\frac{1}{3}, \frac{1}{3}, 2]$ $\langle\frac{1}{6}, \frac{1}{4}, \frac{9}{8}\rangle$ $(\frac{1}{3}, \frac{1}{3}, 7)$ $x^8 + 4 b_{15} x^7 + 4 b_{13} x^5 + 4 b_{11} x^3 + 2 a_{2} x^2 + 4 a_{9} x + 8 c_{16} + 2$ $2$ $16$ $8$ $3$
2.1.8.16c $2$ $8$ $1$ $8$ $16$ $[2, 2, \frac{5}{2}]$ $[1, 1, \frac{3}{2}]$ $\langle\frac{1}{2}, \frac{3}{4}, \frac{9}{8}\rangle$ $(1, 1, 3)$ $x^8 + 2 a_{6} x^6 + (2 b_{4} + 4 c_{12}) x^4 + 4 b_{11} x^3 + 4 a_{9} x + 4 c_{8} + 2$ $4$ $10$ $4$ $3$
2.1.8.16d $2$ $8$ $1$ $8$ $16$ $[2, \frac{7}{3}, \frac{7}{3}]$ $[1, \frac{4}{3}, \frac{4}{3}]$ $\langle\frac{1}{2}, \frac{11}{12}, \frac{9}{8}\rangle$ $(1, \frac{5}{3}, \frac{5}{3})$ $x^8 + 2 a_{4} x^4 + 4 b_{10} x^2 + 4 a_{9} x + 4 c_{8} + 2$ $2$ $2$ $2$ $1$
2.1.8.17a $2$ $8$ $1$ $8$ $17$ $[\frac{4}{3}, \frac{4}{3}, \frac{13}{4}]$ $[\frac{1}{3}, \frac{1}{3}, \frac{9}{4}]$ $\langle\frac{1}{6}, \frac{1}{4}, \frac{5}{4}\rangle$ $(\frac{1}{3}, \frac{1}{3}, 8)$ $x^8 + 4 b_{15} x^7 + 4 b_{13} x^5 + 4 b_{11} x^3 + (2 a_{2} + 8 c_{18}) x^2 + 8 b_{17} x + 2$ $2$ $32$ $16$ $1$
2.1.8.18a $2$ $8$ $1$ $8$ $18$ $[\frac{18}{7}, \frac{18}{7}, \frac{18}{7}]$ $[\frac{11}{7}, \frac{11}{7}, \frac{11}{7}]$ $\langle\frac{11}{14}, \frac{33}{28}, \frac{11}{8}\rangle$ $(\frac{11}{7}, \frac{11}{7}, \frac{11}{7})$ $x^8 + 4 b_{12} x^4 + 4 a_{11} x^3 + 4 b_{10} x^2 + 2$ $1$ $4$ $4$ $1$
2.1.8.18b $2$ $8$ $1$ $8$ $18$ $[2, 2, 3]$ $[1, 1, 2]$ $\langle\frac{1}{2}, \frac{3}{4}, \frac{11}{8}\rangle$ $(1, 1, 5)$ $x^8 + 4 b_{15} x^7 + 2 a_{6} x^6 + 4 b_{13} x^5 + 2 b_{4} x^4 + 4 a_{11} x^3 + 4 c_{8} + 8 c_{16} + 2$ $4$ $20$ $8$ $6$
2.1.8.18c $2$ $8$ $1$ $8$ $18$ $[2, \frac{8}{3}, \frac{8}{3}]$ $[1, \frac{5}{3}, \frac{5}{3}]$ $\langle\frac{1}{2}, \frac{13}{12}, \frac{11}{8}\rangle$ $(1, \frac{7}{3}, \frac{7}{3})$ $x^8 + 4 b_{13} x^5 + 2 a_{4} x^4 + 4 a_{11} x^3 + 4 b_{10} x^2 + 4 c_{8} + 2$ $2$ $6$ $4$ $2$
2.1.8.20a $2$ $8$ $1$ $8$ $20$ $[\frac{20}{7}, \frac{20}{7}, \frac{20}{7}]$ $[\frac{13}{7}, \frac{13}{7}, \frac{13}{7}]$ $\langle\frac{13}{14}, \frac{39}{28}, \frac{13}{8}\rangle$ $(\frac{13}{7}, \frac{13}{7}, \frac{13}{7})$ $x^8 + 4 b_{14} x^6 + 4 a_{13} x^5 + 4 b_{12} x^4 + 2$ $1$ $4$ $4$ $1$
2.1.8.20b $2$ $8$ $1$ $8$ $20$ $[2, 2, \frac{7}{2}]$ $[1, 1, \frac{5}{2}]$ $\langle\frac{1}{2}, \frac{3}{4}, \frac{13}{8}\rangle$ $(1, 1, 7)$ $x^8 + 4 b_{15} x^7 + 2 a_{6} x^6 + 4 a_{13} x^5 + (2 b_{4} + 8 c_{20}) x^4 + 8 b_{19} x^3 + 8 b_{17} x + 4 c_{8} + 2$ $4$ $40$ $16$ $5$
2.1.8.20c $2$ $8$ $1$ $8$ $20$ $[\frac{8}{3}, \frac{8}{3}, 3]$ $[\frac{5}{3}, \frac{5}{3}, 2]$ $\langle\frac{5}{6}, \frac{5}{4}, \frac{13}{8}\rangle$ $(\frac{5}{3}, \frac{5}{3}, 3)$ $x^8 + 4 b_{15} x^7 + 4 a_{13} x^5 + 4 b_{12} x^4 + 4 a_{10} x^2 + 8 c_{16} + 2$ $2$ $8$ $4$ $1$
2.1.8.20d $2$ $8$ $1$ $8$ $20$ $[2, 3, 3]$ $[1, 2, 2]$ $\langle\frac{1}{2}, \frac{5}{4}, \frac{13}{8}\rangle$ $(1, 3, 3)$ $x^8 + 4 b_{15} x^7 + 4 b_{14} x^6 + 4 a_{13} x^5 + 2 a_{4} x^4 + 4 b_{10} x^2 + 4 c_{8} + 8 c_{16} + 2$ $4$ $16$ $8$ $3$
2.1.8.21a $2$ $8$ $1$ $8$ $21$ $[2, 2, \frac{15}{4}]$ $[1, 1, \frac{11}{4}]$ $\langle\frac{1}{2}, \frac{3}{4}, \frac{7}{4}\rangle$ $(1, 1, 8)$ $x^8 + 4 b_{15} x^7 + (2 a_{6} + 8 c_{22}) x^6 + 8 b_{21} x^5 + 2 b_{4} x^4 + 8 b_{19} x^3 + 8 b_{17} x + 4 c_{8} + 2$ $4$ $64$ $32$ $2$
2.1.8.22a $2$ $8$ $1$ $8$ $22$ $[\frac{8}{3}, \frac{8}{3}, \frac{7}{2}]$ $[\frac{5}{3}, \frac{5}{3}, \frac{5}{2}]$ $\langle\frac{5}{6}, \frac{5}{4}, \frac{15}{8}\rangle$ $(\frac{5}{3}, \frac{5}{3}, 5)$ $x^8 + 4 a_{15} x^7 + (4 b_{12} + 8 c_{20}) x^4 + 8 b_{19} x^3 + 4 a_{10} x^2 + 8 b_{17} x + 2$ $2$ $16$ $8$ $2$
2.1.8.22b $2$ $8$ $1$ $8$ $22$ $[2, \frac{10}{3}, \frac{10}{3}]$ $[1, \frac{7}{3}, \frac{7}{3}]$ $\langle\frac{1}{2}, \frac{17}{12}, \frac{15}{8}\rangle$ $(1, \frac{11}{3}, \frac{11}{3})$ $x^8 + 4 a_{15} x^7 + 4 b_{14} x^6 + 2 a_{4} x^4 + 8 b_{18} x^2 + 8 b_{17} x + 4 c_{8} + 2$ $2$ $8$ $8$ $1$
2.1.8.22c $2$ $8$ $1$ $8$ $22$ $[3, \frac{19}{6}, \frac{19}{6}]$ $[2, \frac{13}{6}, \frac{13}{6}]$ $\langle1, \frac{19}{12}, \frac{15}{8}\rangle$ $(2, \frac{7}{3}, \frac{7}{3})$ $x^8 + 4 a_{15} x^7 + 4 b_{14} x^6 + 4 b_{12} x^4 + 8 b_{17} x + 8 c_{16} + 2$ $2$ $8$ $8$ $1$
2.1.8.22d $2$ $8$ $1$ $8$ $22$ $[2, 3, \frac{7}{2}]$ $[1, 2, \frac{5}{2}]$ $\langle\frac{1}{2}, \frac{5}{4}, \frac{15}{8}\rangle$ $(1, 3, 5)$ $x^8 + 4 a_{15} x^7 + 4 b_{14} x^6 + (2 a_{4} + 8 c_{20}) x^4 + 8 b_{19} x^3 + 4 a_{10} x^2 + 8 b_{17} x + 4 c_{8} + 8 c_{16} + 2$ $8$ $32$ $8$ $5$
2.1.8.24a $2$ $8$ $1$ $8$ $24$ $[\frac{8}{3}, \frac{8}{3}, 4]$ $[\frac{5}{3}, \frac{5}{3}, 3]$ $\langle\frac{5}{6}, \frac{5}{4}, \frac{17}{8}\rangle$ $(\frac{5}{3}, \frac{5}{3}, 7)$ $x^8 + 8 b_{23} x^7 + 8 b_{21} x^5 + 4 b_{12} x^4 + 8 b_{19} x^3 + 4 a_{10} x^2 + 8 a_{17} x + 16 c_{24} + 2$ $2$ $32$ $16$ $1$
2.1.8.24b $2$ $8$ $1$ $8$ $24$ $[3, \frac{7}{2}, \frac{7}{2}]$ $[2, \frac{5}{2}, \frac{5}{2}]$ $\langle1, \frac{7}{4}, \frac{17}{8}\rangle$ $(2, 3, 3)$ $x^8 + 4 b_{14} x^6 + (4 b_{12} + 8 c_{20}) x^4 + 8 b_{19} x^3 + 8 b_{18} x^2 + 8 a_{17} x + 8 c_{16} + 2$ $4$ $24$ $16$ $2$
2.1.8.24c $2$ $8$ $1$ $8$ $24$ $[2, 3, 4]$ $[1, 2, 3]$ $\langle\frac{1}{2}, \frac{5}{4}, \frac{17}{8}\rangle$ $(1, 3, 7)$ $x^8 + 8 b_{23} x^7 + 4 b_{14} x^6 + 8 b_{21} x^5 + 2 a_{4} x^4 + 8 b_{19} x^3 + 4 a_{10} x^2 + 8 a_{17} x + 4 c_{8} + 8 c_{16} + 16 c_{24} + 2$ $8$ $64$ $16$ $10$
2.1.8.24d $2$ $8$ $1$ $8$ $24$ $[2, \frac{7}{2}, \frac{15}{4}]$ $[1, \frac{5}{2}, \frac{11}{4}]$ $\langle\frac{1}{2}, \frac{3}{2}, \frac{17}{8}\rangle$ $(1, 4, 5)$ $x^8 + (4 b_{14} + 8 c_{22}) x^6 + 8 b_{21} x^5 + (2 a_{4} + 8 c_{20}) x^4 + 8 b_{19} x^3 + 8 b_{18} x^2 + 8 a_{17} x + 4 c_{8} + 2$ $8$ $32$ $16$ $1$
2.1.8.25a $2$ $8$ $1$ $8$ $25$ $[\frac{8}{3}, \frac{8}{3}, \frac{17}{4}]$ $[\frac{5}{3}, \frac{5}{3}, \frac{13}{4}]$ $\langle\frac{5}{6}, \frac{5}{4}, \frac{9}{4}\rangle$ $(\frac{5}{3}, \frac{5}{3}, 8)$ $x^8 + 8 b_{23} x^7 + 8 b_{21} x^5 + 4 b_{12} x^4 + 8 b_{19} x^3 + (4 a_{10} + 16 c_{26}) x^2 + 16 b_{25} x + 2$ $2$ $64$ $32$ $1$
2.1.8.25b $2$ $8$ $1$ $8$ $25$ $[2, 3, \frac{17}{4}]$ $[1, 2, \frac{13}{4}]$ $\langle\frac{1}{2}, \frac{5}{4}, \frac{9}{4}\rangle$ $(1, 3, 8)$ $x^8 + 8 b_{23} x^7 + 4 b_{14} x^6 + 8 b_{21} x^5 + 2 a_{4} x^4 + 8 b_{19} x^3 + (4 a_{10} + 16 c_{26}) x^2 + 16 b_{25} x + 4 c_{8} + 8 c_{16} + 2$ $8$ $64$ $32$ $3$
2.1.8.26a $2$ $8$ $1$ $8$ $26$ $[3, \frac{23}{6}, \frac{23}{6}]$ $[2, \frac{17}{6}, \frac{17}{6}]$ $\langle1, \frac{23}{12}, \frac{19}{8}\rangle$ $(2, \frac{11}{3}, \frac{11}{3})$ $x^8 + 8 b_{22} x^6 + 8 b_{21} x^5 + 4 b_{12} x^4 + 8 a_{19} x^3 + 8 b_{18} x^2 + 8 c_{16} + 2$ $2$ $16$ $16$ $1$
2.1.8.26b $2$ $8$ $1$ $8$ $26$ $[2, \frac{7}{2}, \frac{17}{4}]$ $[1, \frac{5}{2}, \frac{13}{4}]$ $\langle\frac{1}{2}, \frac{3}{2}, \frac{19}{8}\rangle$ $(1, 4, 7)$ $x^8 + 8 b_{23} x^7 + 4 b_{14} x^6 + 8 b_{21} x^5 + (2 a_{4} + 8 c_{20}) x^4 + 8 a_{19} x^3 + (8 b_{18} + 16 c_{26}) x^2 + 16 b_{25} x + 4 c_{8} + 2$ $8$ $64$ $32$ $3$
2.1.8.26c $2$ $8$ $1$ $8$ $26$ $[3, \frac{7}{2}, 4]$ $[2, \frac{5}{2}, 3]$ $\langle1, \frac{7}{4}, \frac{19}{8}\rangle$ $(2, 3, 5)$ $x^8 + 8 b_{23} x^7 + 4 a_{14} x^6 + 8 b_{21} x^5 + (4 b_{12} + 8 c_{20}) x^4 + 8 a_{19} x^3 + 8 b_{18} x^2 + 8 c_{16} + 16 c_{24} + 2$ $8$ $48$ $16$ $3$
2.1.8.27a $2$ $8$ $1$ $8$ $27$ $[2, \frac{7}{2}, \frac{9}{2}]$ $[1, \frac{5}{2}, \frac{7}{2}]$ $\langle\frac{1}{2}, \frac{3}{2}, \frac{5}{2}\rangle$ $(1, 4, 8)$ $x^8 + 8 b_{23} x^7 + 4 b_{14} x^6 + 8 b_{21} x^5 + (2 a_{4} + 8 c_{20} + 16 c_{28}) x^4 + 16 b_{27} x^3 + 8 b_{18} x^2 + 16 b_{25} x + 4 c_{8} + 2$ $8$ $144$ $64$ $7$
2.1.8.28a $2$ $8$ $1$ $8$ $28$ $[3, \frac{7}{2}, \frac{9}{2}]$ $[2, \frac{5}{2}, \frac{7}{2}]$ $\langle1, \frac{7}{4}, \frac{21}{8}\rangle$ $(2, 3, 7)$ $x^8 + 8 b_{23} x^7 + 4 a_{14} x^6 + 8 a_{21} x^5 + (4 b_{12} + 8 c_{20} + 16 c_{28}) x^4 + 16 b_{27} x^3 + 8 b_{18} x^2 + 16 b_{25} x + 8 c_{16} + 2$ $8$ $64$ $32$ $4$
2.1.8.28b $2$ $8$ $1$ $8$ $28$ $[3, 4, \frac{17}{4}]$ $[2, 3, \frac{13}{4}]$ $\langle1, 2, \frac{21}{8}\rangle$ $(2, 4, 5)$ $x^8 + 8 b_{23} x^7 + 8 b_{22} x^6 + 8 a_{21} x^5 + 4 b_{12} x^4 + (8 b_{18} + 16 c_{26}) x^2 + 16 b_{25} x + 8 c_{16} + 16 c_{24} + 2$ $8$ $64$ $32$ $3$
2.1.8.29a $2$ $8$ $1$ $8$ $29$ $[3, \frac{7}{2}, \frac{19}{4}]$ $[2, \frac{5}{2}, \frac{15}{4}]$ $\langle1, \frac{7}{4}, \frac{11}{4}\rangle$ $(2, 3, 8)$ $x^8 + 8 b_{23} x^7 + (4 a_{14} + 16 c_{30}) x^6 + 16 b_{29} x^5 + (4 b_{12} + 8 c_{20}) x^4 + 16 b_{27} x^3 + 8 b_{18} x^2 + 16 b_{25} x + 8 c_{16} + 2$ $8$ $128$ $64$ $3$
2.1.8.30a $2$ $8$ $1$ $8$ $30$ $[3, 4, \frac{19}{4}]$ $[2, 3, \frac{15}{4}]$ $\langle1, 2, \frac{23}{8}\rangle$ $(2, 4, 7)$ $x^8 + 8 a_{23} x^7 + (8 b_{22} + 16 c_{30}) x^6 + 16 b_{29} x^5 + 4 b_{12} x^4 + 16 b_{27} x^3 + 8 b_{18} x^2 + 16 b_{25} x + 8 c_{16} + 16 c_{24} + 2$ $8$ $128$ $64$ $3$
2.1.8.31a $2$ $8$ $1$ $8$ $31$ $[3, 4, 5]$ $[2, 3, 4]$ $\langle1, 2, 3\rangle$ $(2, 4, 8)$ $x^8 + 16 b_{31} x^7 + 8 b_{22} x^6 + 16 b_{29} x^5 + 4 b_{12} x^4 + 16 b_{27} x^3 + 8 b_{18} x^2 + 16 b_{25} x + 8 c_{16} + 16 c_{24} + 32 c_{32} + 2$ $8$ $296$ $128$ $14$
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