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
7.21.1.0a	$7$	$21$	$21$	$1$	$0$	$[\ ]$	$[ ]$	$\langle \rangle$	$( )$	$x$	$21$	$1$	$1$	$1/21$	$1/21$	$100\%$	$0$	$1$
7.7.3.14a	$7$	$21$	$7$	$3$	$14$	$[\ ]$	$[ ]$	$\langle \rangle$	$( )$	$x^3 + 7 d_{0}$	$21$	$3$	$1$	$1/7$	$1/7$	$100\%$	$0$
7.3.7.21a	$7$	$21$	$3$	$7$	$21$	$[\frac{7}{6}]$	$[\frac{1}{6}]$	$\langle\frac{1}{7}\rangle$	$(\frac{1}{6})$	$x^7 + 7 a_{1} x + 7$	$3$	$118$	$342$	$114$	$114$	$100\%$	$1$
7.3.7.24a	$7$	$21$	$3$	$7$	$24$	$[\frac{4}{3}]$	$[\frac{1}{3}]$	$\langle\frac{2}{7}\rangle$	$(\frac{1}{3})$	$x^7 + 7 a_{2} x^2 + 7$	$3$	$118$	$342$	$114$	$114$	$100\%$	$1$
7.3.7.27a	$7$	$21$	$3$	$7$	$27$	$[\frac{3}{2}]$	$[\frac{1}{2}]$	$\langle\frac{3}{7}\rangle$	$(\frac{1}{2})$	$x^7 + 7 a_{3} x^3 + 7$	$3$	$118$	$342$	$114$	$114$	$100\%$	$1$
7.3.7.30a	$7$	$21$	$3$	$7$	$30$	$[\frac{5}{3}]$	$[\frac{2}{3}]$	$\langle\frac{4}{7}\rangle$	$(\frac{2}{3})$	$x^7 + 7 a_{4} x^4 + 7$	$3$	$118$	$342$	$114$	$114$	$100\%$	$1$
7.3.7.33a	$7$	$21$	$3$	$7$	$33$	$[\frac{11}{6}]$	$[\frac{5}{6}]$	$\langle\frac{5}{7}\rangle$	$(\frac{5}{6})$	$x^7 + 7 a_{5} x^5 + 7$	$3$	$118$	$342$	$114$	$114$	$100\%$	$1$
7.3.7.36a	$7$	$21$	$3$	$7$	$36$	$[2]$	$[1]$	$\langle\frac{6}{7}\rangle$	$(1)$	$x^7 + 7 a_{6} x^6 + 49 c_{7} + 7$	$21$	$236$	$342$	$114$	$114$	$100\%$	$1$
7.3.7.39a	$7$	$21$	$3$	$7$	$39$	$[\frac{13}{6}]$	$[\frac{7}{6}]$	$\langle1\rangle$	$(\frac{7}{6})$	$x^7 + 49 b_{8} x + 7$	$3$	$119$	$343$	$343/3$	$343/3$	$100\%$	$1$
7.1.21.21a	$7$	$21$	$1$	$21$	$21$	$[\frac{19}{18}]$	$[\frac{1}{18}]$	$\langle\frac{1}{21}\rangle$	$(\frac{1}{6})$	$x^{21} + 7 a_{1} x + 7 d_{0}$	$3$	$6$	$6$	$6$	$6$	$100\%$	$1$
7.1.21.22a	$7$	$21$	$1$	$21$	$22$	$[\frac{10}{9}]$	$[\frac{1}{9}]$	$\langle\frac{2}{21}\rangle$	$(\frac{1}{3})$	$x^{21} + 7 a_{2} x^2 + 7 d_{0}$	$3$	$6$	$6$	$6$	$6$	$100\%$	$1$
7.1.21.23a	$7$	$21$	$1$	$21$	$23$	$[\frac{7}{6}]$	$[\frac{1}{6}]$	$\langle\frac{1}{7}\rangle$	$(\frac{1}{2})$	$x^{21} + 7 a_{3} x^3 + 7 d_{0}$	$3$	$18$	$6$	$6$	$6$	$100\%$	$1$
7.1.21.24a	$7$	$21$	$1$	$21$	$24$	$[\frac{11}{9}]$	$[\frac{2}{9}]$	$\langle\frac{4}{21}\rangle$	$(\frac{2}{3})$	$x^{21} + 7 a_{4} x^4 + 7 d_{0}$	$3$	$6$	$6$	$6$	$6$	$100\%$	$1$
7.1.21.25a	$7$	$21$	$1$	$21$	$25$	$[\frac{23}{18}]$	$[\frac{5}{18}]$	$\langle\frac{5}{21}\rangle$	$(\frac{5}{6})$	$x^{21} + 7 a_{5} x^5 + 7 d_{0}$	$3$	$6$	$6$	$6$	$6$	$100\%$	$1$
7.1.21.26a	$7$	$21$	$1$	$21$	$26$	$[\frac{4}{3}]$	$[\frac{1}{3}]$	$\langle\frac{2}{7}\rangle$	$(1)$	$x^{21} + 7 c_{7} x^7 + 7 a_{6} x^6 + 7 d_{0}$	$21$	$24$	$6$	$6$	$6$	$100\%$	$1$
7.1.21.28a	$7$	$21$	$1$	$21$	$28$	$[\frac{13}{9}]$	$[\frac{4}{9}]$	$\langle\frac{8}{21}\rangle$	$(\frac{4}{3})$	$x^{21} + 7 b_{9} x^9 + 7 a_{8} x^8 + 7 d_{0}$	$3$	$42$	$42$	$42$	$42$	$100\%$	$1$
7.1.21.29a	$7$	$21$	$1$	$21$	$29$	$[\frac{3}{2}]$	$[\frac{1}{2}]$	$\langle\frac{3}{7}\rangle$	$(\frac{3}{2})$	$x^{21} + 7 b_{10} x^{10} + 7 a_{9} x^9 + 7 d_{0}$	$3$	$54$	$42$	$42$	$42$	$100\%$	$1$
7.1.21.30a	$7$	$21$	$1$	$21$	$30$	$[\frac{14}{9}]$	$[\frac{5}{9}]$	$\langle\frac{10}{21}\rangle$	$(\frac{5}{3})$	$x^{21} + 7 b_{11} x^{11} + 7 a_{10} x^{10} + 7 d_{0}$	$3$	$42$	$42$	$42$	$42$	$100\%$	$1$
7.1.21.31a	$7$	$21$	$1$	$21$	$31$	$[\frac{29}{18}]$	$[\frac{11}{18}]$	$\langle\frac{11}{21}\rangle$	$(\frac{11}{6})$	$x^{21} + 7 b_{12} x^{12} + 7 a_{11} x^{11} + 7 d_{0}$	$3$	$42$	$42$	$42$	$42$	$100\%$	$1$
7.1.21.32a	$7$	$21$	$1$	$21$	$32$	$[\frac{5}{3}]$	$[\frac{2}{3}]$	$\langle\frac{4}{7}\rangle$	$(2)$	$x^{21} + 7 c_{14} x^{14} + 7 b_{13} x^{13} + 7 a_{12} x^{12} + 7 d_{0}$	$21$	$96$	$42$	$42$	$42$	$100\%$	$1$
7.1.21.33a	$7$	$21$	$1$	$21$	$33$	$[\frac{31}{18}]$	$[\frac{13}{18}]$	$\langle\frac{13}{21}\rangle$	$(\frac{13}{6})$	$x^{21} + 7 b_{15} x^{15} + 7 a_{13} x^{13} + 7 d_{0}$	$3$	$42$	$42$	$42$	$42$	$100\%$	$1$
7.1.21.35a	$7$	$21$	$1$	$21$	$35$	$[\frac{11}{6}]$	$[\frac{5}{6}]$	$\langle\frac{5}{7}\rangle$	$(\frac{5}{2})$	$x^{21} + 7 b_{17} x^{17} + 7 b_{16} x^{16} + 7 a_{15} x^{15} + 7 d_{0}$	$3$	$306$	$294$	$294$	$294$	$100\%$	$1$
7.1.21.36a	$7$	$21$	$1$	$21$	$36$	$[\frac{17}{9}]$	$[\frac{8}{9}]$	$\langle\frac{16}{21}\rangle$	$(\frac{8}{3})$	$x^{21} + 7 b_{18} x^{18} + 7 b_{17} x^{17} + 7 a_{16} x^{16} + 7 d_{0}$	$3$	$294$	$294$	$294$	$294$	$100\%$	$1$
7.1.21.37a	$7$	$21$	$1$	$21$	$37$	$[\frac{35}{18}]$	$[\frac{17}{18}]$	$\langle\frac{17}{21}\rangle$	$(\frac{17}{6})$	$x^{21} + 7 b_{19} x^{19} + 7 b_{18} x^{18} + 7 a_{17} x^{17} + 7 d_{0}$	$3$	$294$	$294$	$294$	$294$	$100\%$	$1$
7.1.21.38a	$7$	$21$	$1$	$21$	$38$	$[2]$	$[1]$	$\langle\frac{6}{7}\rangle$	$(3)$	$x^{21} + 7 b_{20} x^{20} + 7 b_{19} x^{19} + 7 a_{18} x^{18} + 7 d_{0} + 49 c_{21}$	$21$	$612$	$294$	$294$	$294$	$100\%$	$1$
7.1.21.39a	$7$	$21$	$1$	$21$	$39$	$[\frac{37}{18}]$	$[\frac{19}{18}]$	$\langle\frac{19}{21}\rangle$	$(\frac{19}{6})$	$x^{21} + 7 b_{20} x^{20} + 7 a_{19} x^{19} + 49 b_{22} x + 7 d_{0}$	$3$	$294$	$294$	$294$	$294$	$100\%$	$1$
7.1.21.40a	$7$	$21$	$1$	$21$	$40$	$[\frac{19}{9}]$	$[\frac{10}{9}]$	$\langle\frac{20}{21}\rangle$	$(\frac{10}{3})$	$x^{21} + 7 a_{20} x^{20} + 49 b_{23} x^2 + 49 b_{22} x + 7 d_{0}$	$3$	$294$	$294$	$294$	$294$	$100\%$	$1$
7.1.21.41a	$7$	$21$	$1$	$21$	$41$	$[\frac{13}{6}]$	$[\frac{7}{6}]$	$\langle1\rangle$	$(\frac{7}{2})$	$x^{21} + 49 b_{24} x^3 + 49 b_{23} x^2 + 49 b_{22} x + 7 d_{0}$	$3$	$357$	$343$	$343$	$343$	$100\%$	$1$

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