Absolute $p$-adic families search results

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

Results (28 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
3.9.1.0a	$3$	$9$	$9$	$1$	$0$	$[\ ]$	$[ ]$	$\langle \rangle$	$( )$	$x$	$9$	$1$	$1$	$1/9$	$1/9$	$100\%$	$0$	$1$
3.3.3.9a	$3$	$9$	$3$	$3$	$9$	$[\frac{3}{2}]$	$[\frac{1}{2}]$	$\langle\frac{1}{3}\rangle$	$(\frac{1}{2})$	$x^3 + 3 a_{1} x + 3$	$3$	$10$	$26$	$26/3$	$26/3$	$100\%$	$1$	$10$
3.3.3.12a	$3$	$9$	$3$	$3$	$12$	$[2]$	$[1]$	$\langle\frac{2}{3}\rangle$	$(1)$	$x^3 + 3 a_{2} x^2 + 9 c_{3} + 3$	$9$	$20$	$26$	$26/3$	$26/3$	$100\%$	$1$	$12$
3.3.3.15a	$3$	$9$	$3$	$3$	$15$	$[\frac{5}{2}]$	$[\frac{3}{2}]$	$\langle1\rangle$	$(\frac{3}{2})$	$x^3 + 9 b_{4} x + 3$	$3$	$11$	$27$	$9$	$9$	$100\%$	$1$	$3$
3.1.9.9a	$3$	$9$	$1$	$9$	$9$	$[\frac{9}{8}, \frac{9}{8}]$	$[\frac{1}{8}, \frac{1}{8}]$	$\langle\frac{1}{12}, \frac{1}{9}\rangle$	$(\frac{1}{8}, \frac{1}{8})$	$x^9 + 3 a_{1} x + 3$	$1$	$2$	$2$	$2$	$2$	$100\%$	$1$	$1$
3.1.9.10a	$3$	$9$	$1$	$9$	$10$	$[\frac{5}{4}, \frac{5}{4}]$	$[\frac{1}{4}, \frac{1}{4}]$	$\langle\frac{1}{6}, \frac{2}{9}\rangle$	$(\frac{1}{4}, \frac{1}{4})$	$x^9 + 3 a_{2} x^2 + 3$	$1$	$2$	$2$	$2$	$2$	$100\%$	$1$	$2$
3.1.9.12a	$3$	$9$	$1$	$9$	$12$	$[\frac{3}{2}, \frac{3}{2}]$	$[\frac{1}{2}, \frac{1}{2}]$	$\langle\frac{1}{3}, \frac{4}{9}\rangle$	$(\frac{1}{2}, \frac{1}{2})$	$x^9 + 3 a_{4} x^4 + 3 b_{3} x^3 + 3$	$1$	$6$	$6$	$6$	$6$	$100\%$	$1$	$4$
3.1.9.13a	$3$	$9$	$1$	$9$	$13$	$[\frac{13}{8}, \frac{13}{8}]$	$[\frac{5}{8}, \frac{5}{8}]$	$\langle\frac{5}{12}, \frac{5}{9}\rangle$	$(\frac{5}{8}, \frac{5}{8})$	$x^9 + 3 a_{5} x^5 + 3$	$1$	$2$	$2$	$2$	$2$	$100\%$	$1$	$1$
3.1.9.13b	$3$	$9$	$1$	$9$	$13$	$[\frac{3}{2}, \frac{5}{3}]$	$[\frac{1}{2}, \frac{2}{3}]$	$\langle\frac{1}{3}, \frac{5}{9}\rangle$	$(\frac{1}{2}, 1)$	$x^9 + 3 c_{6} x^6 + 3 a_{5} x^5 + 3 a_{3} x^3 + 3$	$3$	$8$	$4$	$4$	$4$	$100\%$	$2$	$2$
3.1.9.15a	$3$	$9$	$1$	$9$	$15$	$[\frac{15}{8}, \frac{15}{8}]$	$[\frac{7}{8}, \frac{7}{8}]$	$\langle\frac{7}{12}, \frac{7}{9}\rangle$	$(\frac{7}{8}, \frac{7}{8})$	$x^9 + 3 a_{7} x^7 + 3 b_{6} x^6 + 3$	$1$	$6$	$6$	$6$	$6$	$100\%$	$1$	$1$
3.1.9.15b	$3$	$9$	$1$	$9$	$15$	$[\frac{3}{2}, 2]$	$[\frac{1}{2}, 1]$	$\langle\frac{1}{3}, \frac{7}{9}\rangle$	$(\frac{1}{2}, 2)$	$x^9 + 3 b_{8} x^8 + 3 a_{7} x^7 + 3 a_{3} x^3 + 9 c_{9} + 3$	$3$	$24$	$12$	$12$	$12$	$100\%$	$2$	$4$
3.1.9.16a	$3$	$9$	$1$	$9$	$16$	$[2, 2]$	$[1, 1]$	$\langle\frac{2}{3}, \frac{8}{9}\rangle$	$(1, 1)$	$x^9 + 3 a_{8} x^8 + 3 b_{6} x^6 + 9 c_{9} + 3$	$3$	$10$	$6$	$6$	$6$	$100\%$	$1$	$6$
3.1.9.16b	$3$	$9$	$1$	$9$	$16$	$[\frac{3}{2}, \frac{13}{6}]$	$[\frac{1}{2}, \frac{7}{6}]$	$\langle\frac{1}{3}, \frac{8}{9}\rangle$	$(\frac{1}{2}, \frac{5}{2})$	$x^9 + 3 a_{8} x^8 + 3 a_{3} x^3 + 9 b_{10} x + 3$	$1$	$12$	$12$	$12$	$12$	$100\%$	$2$	$2$
3.1.9.18a	$3$	$9$	$1$	$9$	$18$	$[\frac{9}{4}, \frac{9}{4}]$	$[\frac{5}{4}, \frac{5}{4}]$	$\langle\frac{5}{6}, \frac{10}{9}\rangle$	$(\frac{5}{4}, \frac{5}{4})$	$x^9 + 9 b_{11} x^2 + 9 a_{10} x + 3$	$1$	$6$	$6$	$6$	$6$	$100\%$	$1$	$2$
3.1.9.18b	$3$	$9$	$1$	$9$	$18$	$[\frac{3}{2}, \frac{5}{2}]$	$[\frac{1}{2}, \frac{3}{2}]$	$\langle\frac{1}{3}, \frac{10}{9}\rangle$	$(\frac{1}{2}, \frac{7}{2})$	$x^9 + 9 b_{13} x^4 + 3 a_{3} x^3 + 9 b_{11} x^2 + 9 a_{10} x + 3$	$1$	$36$	$36$	$36$	$36$	$100\%$	$2$	$10$
3.1.9.18c	$3$	$9$	$1$	$9$	$18$	$[2, \frac{7}{3}]$	$[1, \frac{4}{3}]$	$\langle\frac{2}{3}, \frac{10}{9}\rangle$	$(1, 2)$	$x^9 + 3 a_{6} x^6 + 9 c_{12} x^3 + 9 b_{11} x^2 + 9 a_{10} x + 9 c_{9} + 3$	$9$	$24$	$12$	$12$	$12$	$100\%$	$2$	$4$
3.1.9.19a	$3$	$9$	$1$	$9$	$19$	$[\frac{19}{8}, \frac{19}{8}]$	$[\frac{11}{8}, \frac{11}{8}]$	$\langle\frac{11}{12}, \frac{11}{9}\rangle$	$(\frac{11}{8}, \frac{11}{8})$	$x^9 + 9 b_{12} x^3 + 9 a_{11} x^2 + 3$	$1$	$6$	$6$	$6$	$6$	$100\%$	$1$	$1$
3.1.9.19b	$3$	$9$	$1$	$9$	$19$	$[\frac{3}{2}, \frac{8}{3}]$	$[\frac{1}{2}, \frac{5}{3}]$	$\langle\frac{1}{3}, \frac{11}{9}\rangle$	$(\frac{1}{2}, 4)$	$x^9 + 9 c_{15} x^6 + 9 b_{14} x^5 + 9 b_{13} x^4 + 3 a_{3} x^3 + 9 a_{11} x^2 + 3$	$3$	$72$	$36$	$36$	$36$	$100\%$	$2$	$5$
3.1.9.19c	$3$	$9$	$1$	$9$	$19$	$[2, \frac{5}{2}]$	$[1, \frac{3}{2}]$	$\langle\frac{2}{3}, \frac{11}{9}\rangle$	$(1, \frac{5}{2})$	$x^9 + 3 a_{6} x^6 + 9 b_{13} x^4 + 9 a_{11} x^2 + 9 c_{9} + 3$	$3$	$18$	$12$	$12$	$12$	$100\%$	$2$	$4$
3.1.9.20a	$3$	$9$	$1$	$9$	$20$	$[\frac{3}{2}, \frac{17}{6}]$	$[\frac{1}{2}, \frac{11}{6}]$	$\langle\frac{1}{3}, \frac{4}{3}\rangle$	$(\frac{1}{2}, \frac{9}{2})$	$x^9 + 9 b_{16} x^7 + 9 b_{14} x^5 + 9 b_{13} x^4 + 3 a_{3} x^3 + 3$	$1$	$54$	$54$	$54$	$54$	$100\%$	$2$	$2$
3.1.9.21a	$3$	$9$	$1$	$9$	$21$	$[2, \frac{17}{6}]$	$[1, \frac{11}{6}]$	$\langle\frac{2}{3}, \frac{13}{9}\rangle$	$(1, \frac{7}{2})$	$x^9 + 9 b_{16} x^7 + 3 a_{6} x^6 + 9 b_{14} x^5 + 9 a_{13} x^4 + 9 c_{9} + 3$	$3$	$36$	$36$	$36$	$36$	$100\%$	$2$	$4$
3.1.9.21b	$3$	$9$	$1$	$9$	$21$	$[\frac{5}{2}, \frac{8}{3}]$	$[\frac{3}{2}, \frac{5}{3}]$	$\langle1, \frac{13}{9}\rangle$	$(\frac{3}{2}, 2)$	$x^9 + 9 c_{15} x^6 + 9 b_{14} x^5 + 9 a_{13} x^4 + 9 b_{12} x^3 + 3$	$3$	$36$	$18$	$18$	$18$	$100\%$	$2$	$2$
3.1.9.22a	$3$	$9$	$1$	$9$	$22$	$[2, 3]$	$[1, 2]$	$\langle\frac{2}{3}, \frac{14}{9}\rangle$	$(1, 4)$	$x^9 + 9 b_{17} x^8 + 9 b_{16} x^7 + 3 a_{6} x^6 + 9 a_{14} x^5 + 9 c_{9} + 27 c_{18} + 3$	$9$	$78$	$36$	$36$	$36$	$100\%$	$2$	$8$
3.1.9.22b	$3$	$9$	$1$	$9$	$22$	$[\frac{5}{2}, \frac{17}{6}]$	$[\frac{3}{2}, \frac{11}{6}]$	$\langle1, \frac{14}{9}\rangle$	$(\frac{3}{2}, \frac{5}{2})$	$x^9 + 9 b_{16} x^7 + 9 a_{14} x^5 + 9 b_{12} x^3 + 3$	$1$	$18$	$18$	$18$	$18$	$100\%$	$2$	$2$
3.1.9.23a	$3$	$9$	$1$	$9$	$23$	$[2, \frac{19}{6}]$	$[1, \frac{13}{6}]$	$\langle\frac{2}{3}, \frac{5}{3}\rangle$	$(1, \frac{9}{2})$	$x^9 + 9 b_{17} x^8 + 9 b_{16} x^7 + 3 a_{6} x^6 + 27 b_{19} x + 9 c_{9} + 3$	$3$	$54$	$54$	$54$	$54$	$100\%$	$2$	$2$
3.1.9.24a	$3$	$9$	$1$	$9$	$24$	$[\frac{5}{2}, \frac{19}{6}]$	$[\frac{3}{2}, \frac{13}{6}]$	$\langle1, \frac{16}{9}\rangle$	$(\frac{3}{2}, \frac{7}{2})$	$x^9 + 9 b_{17} x^8 + 9 a_{16} x^7 + 9 b_{12} x^3 + 27 b_{19} x + 3$	$1$	$54$	$54$	$54$	$54$	$100\%$	$2$	$2$
3.1.9.25a	$3$	$9$	$1$	$9$	$25$	$[\frac{5}{2}, \frac{10}{3}]$	$[\frac{3}{2}, \frac{7}{3}]$	$\langle1, \frac{17}{9}\rangle$	$(\frac{3}{2}, 4)$	$x^9 + 9 a_{17} x^8 + (9 b_{12} + 27 c_{21}) x^3 + 27 b_{20} x^2 + 27 b_{19} x + 3$	$3$	$108$	$54$	$54$	$54$	$100\%$	$2$	$2$
3.1.9.26a	$3$	$9$	$1$	$9$	$26$	$[\frac{5}{2}, \frac{7}{2}]$	$[\frac{3}{2}, \frac{5}{2}]$	$\langle1, 2\rangle$	$(\frac{3}{2}, \frac{9}{2})$	$x^9 + 27 b_{22} x^4 + 9 b_{12} x^3 + 27 b_{20} x^2 + 27 b_{19} x + 3$	$1$	$81$	$81$	$81$	$81$	$100\%$	$2$	$4$

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