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 (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
3.15.1.0a	$3$	$15$	$15$	$1$	$0$	$[\ ]$	$[ ]$	$\langle \rangle$	$( )$	$x$	$15$	$1$	$1$	$1/15$	$1/15$	$100\%$	$0$	$1$
3.5.3.15a	$3$	$15$	$5$	$3$	$15$	$[\frac{3}{2}]$	$[\frac{1}{2}]$	$\langle\frac{1}{3}\rangle$	$(\frac{1}{2})$	$x^3 + 3 a_{1} x + 3$	$5$	$50$	$242$	$242/5$	$242/5$	$100\%$	$1$	$50$
3.5.3.20a	$3$	$15$	$5$	$3$	$20$	$[2]$	$[1]$	$\langle\frac{2}{3}\rangle$	$(1)$	$x^3 + 3 a_{2} x^2 + 9 c_{3} + 3$	$15$	$100$	$242$	$242/5$	$242/5$	$100\%$	$1$	$58$
3.5.3.25a	$3$	$15$	$5$	$3$	$25$	$[\frac{5}{2}]$	$[\frac{3}{2}]$	$\langle1\rangle$	$(\frac{3}{2})$	$x^3 + 9 b_{4} x + 3$	$5$	$51$	$243$	$243/5$	$243/5$	$100\%$	$1$	$2$
3.3.5.12a	$3$	$15$	$3$	$5$	$12$	$[\ ]$	$[ ]$	$\langle \rangle$	$( )$	$x^5 + 3$	$3$	$1$	$1$	$1/3$	$1/3$	$100\%$	$0$	$1$
3.1.15.15a	$3$	$15$	$1$	$15$	$15$	$[\frac{11}{10}]$	$[\frac{1}{10}]$	$\langle\frac{1}{15}\rangle$	$(\frac{1}{2})$	$x^{15} + 3 a_{1} x + 3$	$1$	$2$	$2$	$2$	$2$	$100\%$	$1$	$1$
3.1.15.16a	$3$	$15$	$1$	$15$	$16$	$[\frac{6}{5}]$	$[\frac{1}{5}]$	$\langle\frac{2}{15}\rangle$	$(1)$	$x^{15} + 3 c_{3} x^3 + 3 a_{2} x^2 + 3$	$3$	$4$	$2$	$2$	$2$	$100\%$	$1$	$3$
3.1.15.18a	$3$	$15$	$1$	$15$	$18$	$[\frac{7}{5}]$	$[\frac{2}{5}]$	$\langle\frac{4}{15}\rangle$	$(2)$	$x^{15} + 3 c_{6} x^6 + 3 b_{5} x^5 + 3 a_{4} x^4 + 3$	$3$	$12$	$6$	$6$	$6$	$100\%$	$1$	$3$
3.1.15.19a	$3$	$15$	$1$	$15$	$19$	$[\frac{3}{2}]$	$[\frac{1}{2}]$	$\langle\frac{1}{3}\rangle$	$(\frac{5}{2})$	$x^{15} + 3 b_{7} x^7 + 3 a_{5} x^5 + 3$	$1$	$6$	$6$	$6$	$6$	$100\%$	$1$	$2$
3.1.15.21a	$3$	$15$	$1$	$15$	$21$	$[\frac{17}{10}]$	$[\frac{7}{10}]$	$\langle\frac{7}{15}\rangle$	$(\frac{7}{2})$	$x^{15} + 3 b_{10} x^{10} + 3 b_{8} x^8 + 3 a_{7} x^7 + 3$	$1$	$18$	$18$	$18$	$18$	$100\%$	$1$	$2$
3.1.15.22a	$3$	$15$	$1$	$15$	$22$	$[\frac{9}{5}]$	$[\frac{4}{5}]$	$\langle\frac{8}{15}\rangle$	$(4)$	$x^{15} + 3 c_{12} x^{12} + 3 b_{11} x^{11} + 3 b_{10} x^{10} + 3 a_{8} x^8 + 3$	$3$	$36$	$18$	$18$	$18$	$100\%$	$1$	$3$
3.1.15.24a	$3$	$15$	$1$	$15$	$24$	$[2]$	$[1]$	$\langle\frac{2}{3}\rangle$	$(5)$	$x^{15} + 3 b_{14} x^{14} + 3 b_{13} x^{13} + 3 b_{11} x^{11} + 3 a_{10} x^{10} + 9 c_{15} + 3$	$3$	$108$	$54$	$54$	$54$	$100\%$	$1$	$8$
3.1.15.25a	$3$	$15$	$1$	$15$	$25$	$[\frac{21}{10}]$	$[\frac{11}{10}]$	$\langle\frac{11}{15}\rangle$	$(\frac{11}{2})$	$x^{15} + 3 b_{14} x^{14} + 3 b_{13} x^{13} + 3 a_{11} x^{11} + 9 b_{16} x + 3$	$1$	$54$	$54$	$54$	$54$	$100\%$	$1$	$2$
3.1.15.27a	$3$	$15$	$1$	$15$	$27$	$[\frac{23}{10}]$	$[\frac{13}{10}]$	$\langle\frac{13}{15}\rangle$	$(\frac{13}{2})$	$x^{15} + 3 b_{14} x^{14} + 3 a_{13} x^{13} + 9 b_{19} x^4 + 9 b_{17} x^2 + 9 b_{16} x + 3$	$1$	$162$	$162$	$162$	$162$	$100\%$	$1$	$2$
3.1.15.28a	$3$	$15$	$1$	$15$	$28$	$[\frac{12}{5}]$	$[\frac{7}{5}]$	$\langle\frac{14}{15}\rangle$	$(7)$	$x^{15} + 3 a_{14} x^{14} + 9 c_{21} x^6 + 9 b_{20} x^5 + 9 b_{19} x^4 + 9 b_{17} x^2 + 9 b_{16} x + 3$	$3$	$324$	$162$	$162$	$162$	$100\%$	$1$	$5$
3.1.15.29a	$3$	$15$	$1$	$15$	$29$	$[\frac{5}{2}]$	$[\frac{3}{2}]$	$\langle1\rangle$	$(\frac{15}{2})$	$x^{15} + 9 b_{22} x^7 + 9 b_{20} x^5 + 9 b_{19} x^4 + 9 b_{17} x^2 + 9 b_{16} x + 3$	$1$	$243$	$243$	$243$	$243$	$100\%$	$1$	$5$

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