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 (19 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
2.18.1.0a	$2$	$18$	$18$	$1$	$0$	$[\ ]$	$[ ]$	$\langle \rangle$	$( )$	$x$	$18$	$1$	$1$	$1/18$	$1/18$	$100\%$	$0$	$1$
2.9.2.18a	$2$	$18$	$9$	$2$	$18$	$[2]$	$[1]$	$\langle\frac{1}{2}\rangle$	$(1)$	$x^2 + 2 a_{1} x + 4 c_{2} + 2$	$18$	$118$	$511$	$511/9$	$511/9$	$100\%$	$1$	$88$
2.9.2.27a	$2$	$18$	$9$	$2$	$27$	$[3]$	$[2]$	$\langle1\rangle$	$(2)$	$x^2 + 4 b_{3} x + 8 c_{4} + 2$	$18$	$120$	$512$	$512/9$	$512/9$	$100\%$	$1$	$4$
2.6.3.12a	$2$	$18$	$6$	$3$	$12$	$[\ ]$	$[ ]$	$\langle \rangle$	$( )$	$x^3 + 2 d_{0}$	$18$	$2$	$1$	$1/6$	$1/6$	$100\%$	$0$	$2$
2.3.6.18a	$2$	$18$	$3$	$6$	$18$	$[\frac{4}{3}]$	$[\frac{1}{3}]$	$\langle\frac{1}{6}\rangle$	$(1)$	$x^6 + 2 c_{2} x^2 + 2 a_{1} x + 2$	$6$	$6$	$7$	$7/3$	$7/3$	$100\%$	$1$	$6$
2.3.6.24a	$2$	$18$	$3$	$6$	$24$	$[2]$	$[1]$	$\langle\frac{1}{2}\rangle$	$(3)$	$x^6 + 2 b_{5} x^5 + 2 a_{3} x^3 + 4 c_{6} + 2$	$6$	$40$	$56$	$56/3$	$56/3$	$100\%$	$1$	$16$
2.3.6.30a	$2$	$18$	$3$	$6$	$30$	$[\frac{8}{3}]$	$[\frac{5}{3}]$	$\langle\frac{5}{6}\rangle$	$(5)$	$x^6 + 2 a_{5} x^5 + 4 c_{10} x^4 + 4 b_{9} x^3 + 4 b_{7} x + 2$	$6$	$304$	$448$	$448/3$	$448/3$	$100\%$	$1$	$30$
2.3.6.33a	$2$	$18$	$3$	$6$	$33$	$[3]$	$[2]$	$\langle1\rangle$	$(6)$	$x^6 + 4 b_{11} x^5 + 4 b_{9} x^3 + 4 b_{7} x + 8 c_{12} + 2$	$6$	$352$	$512$	$512/3$	$512/3$	$100\%$	$1$	$18$
2.2.9.16a	$2$	$18$	$2$	$9$	$16$	$[\ ]$	$[ ]$	$\langle \rangle$	$( )$	$x^9 + 2 d_{0}$	$6$	$2$	$1$	$1/2$	$1/2$	$100\%$	$0$	$2$
2.1.18.18a	$2$	$18$	$1$	$18$	$18$	$[\frac{10}{9}]$	$[\frac{1}{9}]$	$\langle\frac{1}{18}\rangle$	$(1)$	$x^{18} + 2 c_{2} x^2 + 2 a_{1} x + 2$	$2$	$2$	$1$	$1$	$1$	$100\%$	$1$	$2$
2.1.18.20a	$2$	$18$	$1$	$18$	$20$	$[\frac{4}{3}]$	$[\frac{1}{3}]$	$\langle\frac{1}{6}\rangle$	$(3)$	$x^{18} + 2 c_{6} x^6 + 2 b_{5} x^5 + 2 a_{3} x^3 + 2$	$2$	$4$	$2$	$2$	$2$	$100\%$	$1$	$4$
2.1.18.22a	$2$	$18$	$1$	$18$	$22$	$[\frac{14}{9}]$	$[\frac{5}{9}]$	$\langle\frac{5}{18}\rangle$	$(5)$	$x^{18} + 2 c_{10} x^{10} + 2 b_{9} x^9 + 2 b_{7} x^7 + 2 a_{5} x^5 + 2$	$2$	$8$	$4$	$4$	$4$	$100\%$	$1$	$4$
2.1.18.24a	$2$	$18$	$1$	$18$	$24$	$[\frac{16}{9}]$	$[\frac{7}{9}]$	$\langle\frac{7}{18}\rangle$	$(7)$	$x^{18} + 2 c_{14} x^{14} + 2 b_{13} x^{13} + 2 b_{11} x^{11} + 2 b_{9} x^9 + 2 a_{7} x^7 + 2$	$2$	$16$	$8$	$8$	$8$	$100\%$	$1$	$4$
2.1.18.26a	$2$	$18$	$1$	$18$	$26$	$[2]$	$[1]$	$\langle\frac{1}{2}\rangle$	$(9)$	$x^{18} + 2 b_{17} x^{17} + 2 b_{15} x^{15} + 2 b_{13} x^{13} + 2 b_{11} x^{11} + 2 a_{9} x^9 + 4 c_{18} + 2$	$2$	$32$	$16$	$16$	$16$	$100\%$	$1$	$8$
2.1.18.28a	$2$	$18$	$1$	$18$	$28$	$[\frac{20}{9}]$	$[\frac{11}{9}]$	$\langle\frac{11}{18}\rangle$	$(11)$	$x^{18} + 2 b_{17} x^{17} + 2 b_{15} x^{15} + 2 b_{13} x^{13} + 2 a_{11} x^{11} + 4 c_{22} x^4 + 4 b_{21} x^3 + 4 b_{19} x + 2$	$2$	$64$	$32$	$32$	$32$	$100\%$	$1$	$6$
2.1.18.30a	$2$	$18$	$1$	$18$	$30$	$[\frac{22}{9}]$	$[\frac{13}{9}]$	$\langle\frac{13}{18}\rangle$	$(13)$	$x^{18} + 2 b_{17} x^{17} + 2 b_{15} x^{15} + 2 a_{13} x^{13} + 4 c_{26} x^8 + 4 b_{25} x^7 + 4 b_{23} x^5 + 4 b_{21} x^3 + 4 b_{19} x + 2$	$2$	$128$	$64$	$64$	$64$	$100\%$	$1$	$6$
2.1.18.32a	$2$	$18$	$1$	$18$	$32$	$[\frac{8}{3}]$	$[\frac{5}{3}]$	$\langle\frac{5}{6}\rangle$	$(15)$	$x^{18} + 2 b_{17} x^{17} + 2 a_{15} x^{15} + 4 c_{30} x^{12} + 4 b_{29} x^{11} + 4 b_{27} x^9 + 4 b_{25} x^7 + 4 b_{23} x^5 + 4 b_{21} x^3 + 4 b_{19} x + 2$	$2$	$256$	$128$	$128$	$128$	$100\%$	$1$	$18$
2.1.18.34a	$2$	$18$	$1$	$18$	$34$	$[\frac{26}{9}]$	$[\frac{17}{9}]$	$\langle\frac{17}{18}\rangle$	$(17)$	$x^{18} + 2 a_{17} x^{17} + 4 c_{34} x^{16} + 4 b_{33} x^{15} + 4 b_{31} x^{13} + 4 b_{29} x^{11} + 4 b_{27} x^9 + 4 b_{25} x^7 + 4 b_{23} x^5 + 4 b_{21} x^3 + 4 b_{19} x + 2$	$2$	$512$	$256$	$256$	$256$	$100\%$	$1$	$9$
2.1.18.35a	$2$	$18$	$1$	$18$	$35$	$[3]$	$[2]$	$\langle1\rangle$	$(18)$	$x^{18} + 4 b_{35} x^{17} + 4 b_{33} x^{15} + 4 b_{31} x^{13} + 4 b_{29} x^{11} + 4 b_{27} x^9 + 4 b_{25} x^7 + 4 b_{23} x^5 + 4 b_{21} x^3 + 4 b_{19} x + 8 c_{36} + 2$	$2$	$1024$	$512$	$512$	$512$	$100\%$	$1$	$21$

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