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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 (16 matches)

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Label	$p$	$n$	$f$	$e$	$c$	Abs. Artin slopes	Swan slopes	Means	Rams	Generic poly	Ambiguity	Field count	Mass	Mass (absolute)	Mass stored	Mass found	Wild segments	Num. Packets
5.10.1.0a	$5$	$10$	$10$	$1$	$0$	$[\ ]$	$[ ]$	$\langle \rangle$	$( )$	$x$	$10$	$1$	$1$	$1/10$	$1/10$	$100\%$	$0$	$1$
5.5.2.5a	$5$	$10$	$5$	$2$	$5$	$[\ ]$	$[ ]$	$\langle \rangle$	$( )$	$x^2 + 5 d_{0}$	$10$	$2$	$1$	$1/5$	$1/5$	$100\%$	$0$	$1$
5.2.5.10a	$5$	$10$	$2$	$5$	$10$	$[\frac{5}{4}]$	$[\frac{1}{4}]$	$\langle\frac{1}{5}\rangle$	$(\frac{1}{4})$	$x^5 + 5 a_{1} x + 5$	$2$	$14$	$24$	$12$	$12$	$100\%$	$1$	$14$
5.2.5.12a	$5$	$10$	$2$	$5$	$12$	$[\frac{3}{2}]$	$[\frac{1}{2}]$	$\langle\frac{2}{5}\rangle$	$(\frac{1}{2})$	$x^5 + 5 a_{2} x^2 + 5$	$2$	$14$	$24$	$12$	$12$	$100\%$	$1$	$14$
5.2.5.14a	$5$	$10$	$2$	$5$	$14$	$[\frac{7}{4}]$	$[\frac{3}{4}]$	$\langle\frac{3}{5}\rangle$	$(\frac{3}{4})$	$x^5 + 5 a_{3} x^3 + 5$	$2$	$14$	$24$	$12$	$12$	$100\%$	$1$	$14$
5.2.5.16a	$5$	$10$	$2$	$5$	$16$	$[2]$	$[1]$	$\langle\frac{4}{5}\rangle$	$(1)$	$x^5 + 5 a_{4} x^4 + 25 c_{5} + 5$	$10$	$28$	$24$	$12$	$12$	$100\%$	$1$	$15$
5.2.5.18a	$5$	$10$	$2$	$5$	$18$	$[\frac{9}{4}]$	$[\frac{5}{4}]$	$\langle1\rangle$	$(\frac{5}{4})$	$x^5 + 25 b_{6} x + 5$	$2$	$15$	$25$	$25/2$	$25/2$	$100\%$	$1$	$2$
5.1.10.10a	$5$	$10$	$1$	$10$	$10$	$[\frac{9}{8}]$	$[\frac{1}{8}]$	$\langle\frac{1}{10}\rangle$	$(\frac{1}{4})$	$x^{10} + 5 a_{1} x + 5 d_{0}$	$2$	$4$	$4$	$4$	$4$	$100\%$	$1$	$1$
5.1.10.11a	$5$	$10$	$1$	$10$	$11$	$[\frac{5}{4}]$	$[\frac{1}{4}]$	$\langle\frac{1}{5}\rangle$	$(\frac{1}{2})$	$x^{10} + 5 a_{2} x^2 + 5 d_{0}$	$2$	$8$	$4$	$4$	$4$	$100\%$	$1$	$2$
5.1.10.12a	$5$	$10$	$1$	$10$	$12$	$[\frac{11}{8}]$	$[\frac{3}{8}]$	$\langle\frac{3}{10}\rangle$	$(\frac{3}{4})$	$x^{10} + 5 a_{3} x^3 + 5 d_{0}$	$2$	$4$	$4$	$4$	$4$	$100\%$	$1$	$1$
5.1.10.13a	$5$	$10$	$1$	$10$	$13$	$[\frac{3}{2}]$	$[\frac{1}{2}]$	$\langle\frac{2}{5}\rangle$	$(1)$	$x^{10} + 5 c_{5} x^5 + 5 a_{4} x^4 + 5 d_{0}$	$10$	$12$	$4$	$4$	$4$	$100\%$	$1$	$5$
5.1.10.15a	$5$	$10$	$1$	$10$	$15$	$[\frac{7}{4}]$	$[\frac{3}{4}]$	$\langle\frac{3}{5}\rangle$	$(\frac{3}{2})$	$x^{10} + 5 b_{7} x^7 + 5 a_{6} x^6 + 5 d_{0}$	$2$	$24$	$20$	$20$	$20$	$100\%$	$1$	$4$
5.1.10.16a	$5$	$10$	$1$	$10$	$16$	$[\frac{15}{8}]$	$[\frac{7}{8}]$	$\langle\frac{7}{10}\rangle$	$(\frac{7}{4})$	$x^{10} + 5 b_{8} x^8 + 5 a_{7} x^7 + 5 d_{0}$	$2$	$20$	$20$	$20$	$20$	$100\%$	$1$	$1$
5.1.10.17a	$5$	$10$	$1$	$10$	$17$	$[2]$	$[1]$	$\langle\frac{4}{5}\rangle$	$(2)$	$x^{10} + 5 b_{9} x^9 + 5 a_{8} x^8 + 5 d_{0} + 25 c_{10}$	$10$	$48$	$20$	$20$	$20$	$100\%$	$1$	$8$
5.1.10.18a	$5$	$10$	$1$	$10$	$18$	$[\frac{17}{8}]$	$[\frac{9}{8}]$	$\langle\frac{9}{10}\rangle$	$(\frac{9}{4})$	$x^{10} + 5 a_{9} x^9 + 25 b_{11} x + 5 d_{0}$	$2$	$20$	$20$	$20$	$20$	$100\%$	$1$	$1$
5.1.10.19a	$5$	$10$	$1$	$10$	$19$	$[\frac{9}{4}]$	$[\frac{5}{4}]$	$\langle1\rangle$	$(\frac{5}{2})$	$x^{10} + 25 b_{12} x^2 + 25 b_{11} x + 5 d_{0}$	$2$	$30$	$25$	$25$	$25$	$100\%$	$1$	$4$

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