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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 (18 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
17.17.1.0a $17$ $17$ $17$ $1$ $0$ $[\ ]$ $[ ]$ $\langle \rangle$ $( )$ $x$ $17$ $1$ $1$ $1$
17.1.17.17a $17$ $17$ $1$ $17$ $17$ $[\frac{17}{16}]$ $[\frac{1}{16}]$ $\langle\frac{1}{17}\rangle$ $(\frac{1}{16})$ $x^{17} + 17 a_{1} x + 17$ $1$ $16$ $16$ $1$
17.1.17.18a $17$ $17$ $1$ $17$ $18$ $[\frac{9}{8}]$ $[\frac{1}{8}]$ $\langle\frac{2}{17}\rangle$ $(\frac{1}{8})$ $x^{17} + 17 a_{2} x^2 + 17$ $1$ $16$ $16$ $2$
17.1.17.19a $17$ $17$ $1$ $17$ $19$ $[\frac{19}{16}]$ $[\frac{3}{16}]$ $\langle\frac{3}{17}\rangle$ $(\frac{3}{16})$ $x^{17} + 17 a_{3} x^3 + 17$ $1$ $16$ $16$ $1$
17.1.17.20a $17$ $17$ $1$ $17$ $20$ $[\frac{5}{4}]$ $[\frac{1}{4}]$ $\langle\frac{4}{17}\rangle$ $(\frac{1}{4})$ $x^{17} + 17 a_{4} x^4 + 17$ $1$ $16$ $16$ $4$
17.1.17.21a $17$ $17$ $1$ $17$ $21$ $[\frac{21}{16}]$ $[\frac{5}{16}]$ $\langle\frac{5}{17}\rangle$ $(\frac{5}{16})$ $x^{17} + 17 a_{5} x^5 + 17$ $1$ $16$ $16$ $1$
17.1.17.22a $17$ $17$ $1$ $17$ $22$ $[\frac{11}{8}]$ $[\frac{3}{8}]$ $\langle\frac{6}{17}\rangle$ $(\frac{3}{8})$ $x^{17} + 17 a_{6} x^6 + 17$ $1$ $16$ $16$ $2$
17.1.17.23a $17$ $17$ $1$ $17$ $23$ $[\frac{23}{16}]$ $[\frac{7}{16}]$ $\langle\frac{7}{17}\rangle$ $(\frac{7}{16})$ $x^{17} + 17 a_{7} x^7 + 17$ $1$ $16$ $16$ $1$
17.1.17.24a $17$ $17$ $1$ $17$ $24$ $[\frac{3}{2}]$ $[\frac{1}{2}]$ $\langle\frac{8}{17}\rangle$ $(\frac{1}{2})$ $x^{17} + 17 a_{8} x^8 + 17$ $1$ $16$ $16$ $8$
17.1.17.25a $17$ $17$ $1$ $17$ $25$ $[\frac{25}{16}]$ $[\frac{9}{16}]$ $\langle\frac{9}{17}\rangle$ $(\frac{9}{16})$ $x^{17} + 17 a_{9} x^9 + 17$ $1$ $16$ $16$ $1$
17.1.17.26a $17$ $17$ $1$ $17$ $26$ $[\frac{13}{8}]$ $[\frac{5}{8}]$ $\langle\frac{10}{17}\rangle$ $(\frac{5}{8})$ $x^{17} + 17 a_{10} x^{10} + 17$ $1$ $16$ $16$ $2$
17.1.17.27a $17$ $17$ $1$ $17$ $27$ $[\frac{27}{16}]$ $[\frac{11}{16}]$ $\langle\frac{11}{17}\rangle$ $(\frac{11}{16})$ $x^{17} + 17 a_{11} x^{11} + 17$ $1$ $16$ $16$ $1$
17.1.17.28a $17$ $17$ $1$ $17$ $28$ $[\frac{7}{4}]$ $[\frac{3}{4}]$ $\langle\frac{12}{17}\rangle$ $(\frac{3}{4})$ $x^{17} + 17 a_{12} x^{12} + 17$ $1$ $16$ $16$ $4$
17.1.17.29a $17$ $17$ $1$ $17$ $29$ $[\frac{29}{16}]$ $[\frac{13}{16}]$ $\langle\frac{13}{17}\rangle$ $(\frac{13}{16})$ $x^{17} + 17 a_{13} x^{13} + 17$ $1$ $16$ $16$ $1$
17.1.17.30a $17$ $17$ $1$ $17$ $30$ $[\frac{15}{8}]$ $[\frac{7}{8}]$ $\langle\frac{14}{17}\rangle$ $(\frac{7}{8})$ $x^{17} + 17 a_{14} x^{14} + 17$ $1$ $16$ $16$ $2$
17.1.17.31a $17$ $17$ $1$ $17$ $31$ $[\frac{31}{16}]$ $[\frac{15}{16}]$ $\langle\frac{15}{17}\rangle$ $(\frac{15}{16})$ $x^{17} + 17 a_{15} x^{15} + 17$ $1$ $16$ $16$ $1$
17.1.17.32a $17$ $17$ $1$ $17$ $32$ $[2]$ $[1]$ $\langle\frac{16}{17}\rangle$ $(1)$ $x^{17} + 17 a_{16} x^{16} + 289 c_{17} + 17$ $17$ $32$ $16$ $16$
17.1.17.33a $17$ $17$ $1$ $17$ $33$ $[\frac{33}{16}]$ $[\frac{17}{16}]$ $\langle1\rangle$ $(\frac{17}{16})$ $x^{17} + 289 b_{18} x + 17$ $1$ $17$ $17$ $1$
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