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 (20 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
3.21.1.0a	$3$	$21$	$21$	$1$	$0$	$[\ ]$	$[ ]$	$\langle \rangle$	$( )$	$x$	$21$	$1$	$1$	$1/21$	$1/21$	$100\%$	$0$	$1$
3.7.3.21a	$3$	$21$	$7$	$3$	$21$	$[\frac{3}{2}]$	$[\frac{1}{2}]$	$\langle\frac{1}{3}\rangle$	$(\frac{1}{2})$	$x^3 + 3 a_{1} x + 3$	$7$	$314$	$2186$	$2186/7$	$2186/7$	$100\%$	$1$
3.7.3.28a	$3$	$21$	$7$	$3$	$28$	$[2]$	$[1]$	$\langle\frac{2}{3}\rangle$	$(1)$	$x^3 + 3 a_{2} x^2 + 9 c_{3} + 3$	$21$	$628$	$2186$	$2186/7$	$2186/7$	$100\%$	$1$
3.7.3.35a	$3$	$21$	$7$	$3$	$35$	$[\frac{5}{2}]$	$[\frac{3}{2}]$	$\langle1\rangle$	$(\frac{3}{2})$	$x^3 + 9 b_{4} x + 3$	$7$	$315$	$2187$	$2187/7$	$2187/7$	$100\%$	$1$
3.3.7.18a	$3$	$21$	$3$	$7$	$18$	$[\ ]$	$[ ]$	$\langle \rangle$	$( )$	$x^7 + 3$	$3$	$1$	$1$	$1/3$	$1/3$	$100\%$	$0$
3.1.21.21a	$3$	$21$	$1$	$21$	$21$	$[\frac{15}{14}]$	$[\frac{1}{14}]$	$\langle\frac{1}{21}\rangle$	$(\frac{1}{2})$	$x^{21} + 3 a_{1} x + 3$	$1$	$2$	$2$	$2$	$2$	$100\%$	$1$
3.1.21.22a	$3$	$21$	$1$	$21$	$22$	$[\frac{8}{7}]$	$[\frac{1}{7}]$	$\langle\frac{2}{21}\rangle$	$(1)$	$x^{21} + 3 c_{3} x^3 + 3 a_{2} x^2 + 3$	$3$	$4$	$2$	$2$	$2$	$100\%$	$1$
3.1.21.24a	$3$	$21$	$1$	$21$	$24$	$[\frac{9}{7}]$	$[\frac{2}{7}]$	$\langle\frac{4}{21}\rangle$	$(2)$	$x^{21} + 3 c_{6} x^6 + 3 b_{5} x^5 + 3 a_{4} x^4 + 3$	$3$	$12$	$6$	$6$	$6$	$100\%$	$1$
3.1.21.25a	$3$	$21$	$1$	$21$	$25$	$[\frac{19}{14}]$	$[\frac{5}{14}]$	$\langle\frac{5}{21}\rangle$	$(\frac{5}{2})$	$x^{21} + 3 b_{7} x^7 + 3 a_{5} x^5 + 3$	$1$	$6$	$6$	$6$	$6$	$100\%$	$1$
3.1.21.27a	$3$	$21$	$1$	$21$	$27$	$[\frac{3}{2}]$	$[\frac{1}{2}]$	$\langle\frac{1}{3}\rangle$	$(\frac{7}{2})$	$x^{21} + 3 b_{10} x^{10} + 3 b_{8} x^8 + 3 a_{7} x^7 + 3$	$1$	$18$	$18$	$18$	$18$	$100\%$	$1$
3.1.21.28a	$3$	$21$	$1$	$21$	$28$	$[\frac{11}{7}]$	$[\frac{4}{7}]$	$\langle\frac{8}{21}\rangle$	$(4)$	$x^{21} + 3 c_{12} x^{12} + 3 b_{11} x^{11} + 3 b_{10} x^{10} + 3 a_{8} x^8 + 3$	$3$	$36$	$18$	$18$	$18$	$100\%$	$1$
3.1.21.30a	$3$	$21$	$1$	$21$	$30$	$[\frac{12}{7}]$	$[\frac{5}{7}]$	$\langle\frac{10}{21}\rangle$	$(5)$	$x^{21} + 3 c_{15} x^{15} + 3 b_{14} x^{14} + 3 b_{13} x^{13} + 3 b_{11} x^{11} + 3 a_{10} x^{10} + 3$	$3$	$108$	$54$	$54$	$54$	$100\%$	$1$
3.1.21.31a	$3$	$21$	$1$	$21$	$31$	$[\frac{25}{14}]$	$[\frac{11}{14}]$	$\langle\frac{11}{21}\rangle$	$(\frac{11}{2})$	$x^{21} + 3 b_{16} x^{16} + 3 b_{14} x^{14} + 3 b_{13} x^{13} + 3 a_{11} x^{11} + 3$	$1$	$54$	$54$	$54$	$54$	$100\%$	$1$
3.1.21.33a	$3$	$21$	$1$	$21$	$33$	$[\frac{27}{14}]$	$[\frac{13}{14}]$	$\langle\frac{13}{21}\rangle$	$(\frac{13}{2})$	$x^{21} + 3 b_{19} x^{19} + 3 b_{17} x^{17} + 3 b_{16} x^{16} + 3 b_{14} x^{14} + 3 a_{13} x^{13} + 3$	$1$	$162$	$162$	$162$	$162$	$100\%$	$1$
3.1.21.34a	$3$	$21$	$1$	$21$	$34$	$[2]$	$[1]$	$\langle\frac{2}{3}\rangle$	$(7)$	$x^{21} + 3 b_{20} x^{20} + 3 b_{19} x^{19} + 3 b_{17} x^{17} + 3 b_{16} x^{16} + 3 a_{14} x^{14} + 9 c_{21} + 3$	$3$	$324$	$162$	$162$	$162$	$100\%$	$1$
3.1.21.36a	$3$	$21$	$1$	$21$	$36$	$[\frac{15}{7}]$	$[\frac{8}{7}]$	$\langle\frac{16}{21}\rangle$	$(8)$	$x^{21} + 3 b_{20} x^{20} + 3 b_{19} x^{19} + 3 b_{17} x^{17} + 3 a_{16} x^{16} + 9 c_{24} x^3 + 9 b_{23} x^2 + 9 b_{22} x + 3$	$3$	$972$	$486$	$486$	$486$	$100\%$	$1$
3.1.21.37a	$3$	$21$	$1$	$21$	$37$	$[\frac{31}{14}]$	$[\frac{17}{14}]$	$\langle\frac{17}{21}\rangle$	$(\frac{17}{2})$	$x^{21} + 3 b_{20} x^{20} + 3 b_{19} x^{19} + 3 a_{17} x^{17} + 9 b_{25} x^4 + 9 b_{23} x^2 + 9 b_{22} x + 3$	$1$	$486$	$486$	$486$	$486$	$100\%$	$1$
3.1.21.39a	$3$	$21$	$1$	$21$	$39$	$[\frac{33}{14}]$	$[\frac{19}{14}]$	$\langle\frac{19}{21}\rangle$	$(\frac{19}{2})$	$x^{21} + 3 b_{20} x^{20} + 3 a_{19} x^{19} + 9 b_{28} x^7 + 9 b_{26} x^5 + 9 b_{25} x^4 + 9 b_{23} x^2 + 9 b_{22} x + 3$	$1$	$1458$	$1458$	$1458$	$1458$	$100\%$	$1$
3.1.21.40a	$3$	$21$	$1$	$21$	$40$	$[\frac{17}{7}]$	$[\frac{10}{7}]$	$\langle\frac{20}{21}\rangle$	$(10)$	$x^{21} + 3 a_{20} x^{20} + 9 c_{30} x^9 + 9 b_{29} x^8 + 9 b_{28} x^7 + 9 b_{26} x^5 + 9 b_{25} x^4 + 9 b_{23} x^2 + 9 b_{22} x + 3$	$3$	$2916$	$1458$	$1458$	$1458$	$100\%$	$1$
3.1.21.41a	$3$	$21$	$1$	$21$	$41$	$[\frac{5}{2}]$	$[\frac{3}{2}]$	$\langle1\rangle$	$(\frac{21}{2})$	$x^{21} + 9 b_{31} x^{10} + 9 b_{29} x^8 + 9 b_{28} x^7 + 9 b_{26} x^5 + 9 b_{25} x^4 + 9 b_{23} x^2 + 9 b_{22} x + 3$	$1$	$2187$	$2187$	$2187$	$2187$	$100\%$	$1$

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