LMFDB - 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

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Residue characteristic $p$	Degree $n$	Ramification index $e$	Residue field degree $f$	Discriminant exponent $c$

Mass	Ambiguity	Field count	Wild segments	Herbrand invariant

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Results (34 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
5.20.1.0a	$5$	$20$	$20$	$1$	$0$	$[\ ]$	$[ ]$	$\langle \rangle$	$( )$	$x$	$20$	$1$	$1$	$1/20$	$1/20$	$100\%$	$0$	$1$
5.10.2.10a	$5$	$20$	$10$	$2$	$10$	$[\ ]$	$[ ]$	$\langle \rangle$	$( )$	$x^2 + 5 d_{0}$	$20$	$2$	$1$	$1/10$	$1/10$	$100\%$	$0$
5.5.4.15a	$5$	$20$	$5$	$4$	$15$	$[\ ]$	$[ ]$	$\langle \rangle$	$( )$	$x^4 + 5 d_{0}$	$20$	$4$	$1$	$1/5$	$1/5$	$100\%$	$0$
5.4.5.20a	$5$	$20$	$4$	$5$	$20$	$[\frac{5}{4}]$	$[\frac{1}{4}]$	$\langle\frac{1}{5}\rangle$	$(\frac{1}{4})$	$x^5 + 5 a_{1} x + 5$	$4$	$164$	$624$	$156$	$156$	$100\%$	$1$
5.4.5.24a	$5$	$20$	$4$	$5$	$24$	$[\frac{3}{2}]$	$[\frac{1}{2}]$	$\langle\frac{2}{5}\rangle$	$(\frac{1}{2})$	$x^5 + 5 a_{2} x^2 + 5$	$4$	$164$	$624$	$156$	$156$	$100\%$	$1$
5.4.5.28a	$5$	$20$	$4$	$5$	$28$	$[\frac{7}{4}]$	$[\frac{3}{4}]$	$\langle\frac{3}{5}\rangle$	$(\frac{3}{4})$	$x^5 + 5 a_{3} x^3 + 5$	$4$	$164$	$624$	$156$	$156$	$100\%$	$1$
5.4.5.32a	$5$	$20$	$4$	$5$	$32$	$[2]$	$[1]$	$\langle\frac{4}{5}\rangle$	$(1)$	$x^5 + 5 a_{4} x^4 + 25 c_{5} + 5$	$20$	$328$	$624$	$156$	$156$	$100\%$	$1$
5.4.5.36a	$5$	$20$	$4$	$5$	$36$	$[\frac{9}{4}]$	$[\frac{5}{4}]$	$\langle1\rangle$	$(\frac{5}{4})$	$x^5 + 25 b_{6} x + 5$	$4$	$165$	$625$	$625/4$	$625/4$	$100\%$	$1$
5.2.10.20a	$5$	$20$	$2$	$10$	$20$	$[\frac{9}{8}]$	$[\frac{1}{8}]$	$\langle\frac{1}{10}\rangle$	$(\frac{1}{4})$	$x^{10} + 5 a_{1} x + 5 d_{0}$	$4$	$14$	$24$	$12$	$12$	$100\%$	$1$
5.2.10.22a	$5$	$20$	$2$	$10$	$22$	$[\frac{5}{4}]$	$[\frac{1}{4}]$	$\langle\frac{1}{5}\rangle$	$(\frac{1}{2})$	$x^{10} + 5 a_{2} x^2 + 5 d_{0}$	$4$	$28$	$24$	$12$	$12$	$100\%$	$1$
5.2.10.24a	$5$	$20$	$2$	$10$	$24$	$[\frac{11}{8}]$	$[\frac{3}{8}]$	$\langle\frac{3}{10}\rangle$	$(\frac{3}{4})$	$x^{10} + 5 a_{3} x^3 + 5 d_{0}$	$4$	$14$	$24$	$12$	$12$	$100\%$	$1$
5.2.10.26a	$5$	$20$	$2$	$10$	$26$	$[\frac{3}{2}]$	$[\frac{1}{2}]$	$\langle\frac{2}{5}\rangle$	$(1)$	$x^{10} + 5 c_{5} x^5 + 5 a_{4} x^4 + 5 d_{0}$	$20$	$42$	$24$	$12$	$12$	$100\%$	$1$
5.2.10.30a	$5$	$20$	$2$	$10$	$30$	$[\frac{7}{4}]$	$[\frac{3}{4}]$	$\langle\frac{3}{5}\rangle$	$(\frac{3}{2})$	$x^{10} + 5 b_{7} x^7 + 5 a_{6} x^6 + 5 d_{0}$	$4$	$324$	$600$	$300$	$300$	$100\%$	$1$
5.2.10.32a	$5$	$20$	$2$	$10$	$32$	$[\frac{15}{8}]$	$[\frac{7}{8}]$	$\langle\frac{7}{10}\rangle$	$(\frac{7}{4})$	$x^{10} + 5 b_{8} x^8 + 5 a_{7} x^7 + 5 d_{0}$	$4$	$310$	$600$	$300$	$300$	$100\%$	$1$
5.2.10.34a	$5$	$20$	$2$	$10$	$34$	$[2]$	$[1]$	$\langle\frac{4}{5}\rangle$	$(2)$	$x^{10} + 5 b_{9} x^9 + 5 a_{8} x^8 + 5 d_{0} + 25 c_{10}$	$20$	$648$	$600$	$300$	$300$	$100\%$	$1$
5.2.10.36a	$5$	$20$	$2$	$10$	$36$	$[\frac{17}{8}]$	$[\frac{9}{8}]$	$\langle\frac{9}{10}\rangle$	$(\frac{9}{4})$	$x^{10} + 5 a_{9} x^9 + 25 b_{11} x + 5 d_{0}$	$4$	$310$	$600$	$300$	$300$	$100\%$	$1$
5.2.10.38a	$5$	$20$	$2$	$10$	$38$	$[\frac{9}{4}]$	$[\frac{5}{4}]$	$\langle1\rangle$	$(\frac{5}{2})$	$x^{10} + 25 b_{12} x^2 + 25 b_{11} x + 5 d_{0}$	$4$	$340$	$625$	$625/2$	$625/2$	$100\%$	$1$
5.1.20.20a	$5$	$20$	$1$	$20$	$20$	$[\frac{17}{16}]$	$[\frac{1}{16}]$	$\langle\frac{1}{20}\rangle$	$(\frac{1}{4})$	$x^{20} + 5 a_{1} x + 5 d_{0}$	$4$	$4$	$4$	$4$	$4$	$100\%$	$1$
5.1.20.21a	$5$	$20$	$1$	$20$	$21$	$[\frac{9}{8}]$	$[\frac{1}{8}]$	$\langle\frac{1}{10}\rangle$	$(\frac{1}{2})$	$x^{20} + 5 a_{2} x^2 + 5 d_{0}$	$4$	$8$	$4$	$4$	$4$	$100\%$	$1$
5.1.20.22a	$5$	$20$	$1$	$20$	$22$	$[\frac{19}{16}]$	$[\frac{3}{16}]$	$\langle\frac{3}{20}\rangle$	$(\frac{3}{4})$	$x^{20} + 5 a_{3} x^3 + 5 d_{0}$	$4$	$4$	$4$	$4$	$4$	$100\%$	$1$
5.1.20.23a	$5$	$20$	$1$	$20$	$23$	$[\frac{5}{4}]$	$[\frac{1}{4}]$	$\langle\frac{1}{5}\rangle$	$(1)$	$x^{20} + 5 c_{5} x^5 + 5 a_{4} x^4 + 5 d_{0}$	$20$	$20$	$4$	$4$	$4$	$100\%$	$1$
5.1.20.25a	$5$	$20$	$1$	$20$	$25$	$[\frac{11}{8}]$	$[\frac{3}{8}]$	$\langle\frac{3}{10}\rangle$	$(\frac{3}{2})$	$x^{20} + 5 b_{7} x^7 + 5 a_{6} x^6 + 5 d_{0}$	$4$	$24$	$20$	$20$	$20$	$100\%$	$1$
5.1.20.26a	$5$	$20$	$1$	$20$	$26$	$[\frac{23}{16}]$	$[\frac{7}{16}]$	$\langle\frac{7}{20}\rangle$	$(\frac{7}{4})$	$x^{20} + 5 b_{8} x^8 + 5 a_{7} x^7 + 5 d_{0}$	$4$	$20$	$20$	$20$	$20$	$100\%$	$1$
5.1.20.27a	$5$	$20$	$1$	$20$	$27$	$[\frac{3}{2}]$	$[\frac{1}{2}]$	$\langle\frac{2}{5}\rangle$	$(2)$	$x^{20} + 5 c_{10} x^{10} + 5 b_{9} x^9 + 5 a_{8} x^8 + 5 d_{0}$	$20$	$56$	$20$	$20$	$20$	$100\%$	$1$
5.1.20.28a	$5$	$20$	$1$	$20$	$28$	$[\frac{25}{16}]$	$[\frac{9}{16}]$	$\langle\frac{9}{20}\rangle$	$(\frac{9}{4})$	$x^{20} + 5 b_{11} x^{11} + 5 a_{9} x^9 + 5 d_{0}$	$4$	$20$	$20$	$20$	$20$	$100\%$	$1$
5.1.20.30a	$5$	$20$	$1$	$20$	$30$	$[\frac{27}{16}]$	$[\frac{11}{16}]$	$\langle\frac{11}{20}\rangle$	$(\frac{11}{4})$	$x^{20} + 5 b_{13} x^{13} + 5 b_{12} x^{12} + 5 a_{11} x^{11} + 5 d_{0}$	$4$	$100$	$100$	$100$	$100$	$100\%$	$1$
5.1.20.31a	$5$	$20$	$1$	$20$	$31$	$[\frac{7}{4}]$	$[\frac{3}{4}]$	$\langle\frac{3}{5}\rangle$	$(3)$	$x^{20} + 5 c_{15} x^{15} + 5 b_{14} x^{14} + 5 b_{13} x^{13} + 5 a_{12} x^{12} + 5 d_{0}$	$20$	$228$	$100$	$100$	$100$	$100\%$	$1$
5.1.20.32a	$5$	$20$	$1$	$20$	$32$	$[\frac{29}{16}]$	$[\frac{13}{16}]$	$\langle\frac{13}{20}\rangle$	$(\frac{13}{4})$	$x^{20} + 5 b_{16} x^{16} + 5 b_{14} x^{14} + 5 a_{13} x^{13} + 5 d_{0}$	$4$	$100$	$100$	$100$	$100$	$100\%$	$1$
5.1.20.33a	$5$	$20$	$1$	$20$	$33$	$[\frac{15}{8}]$	$[\frac{7}{8}]$	$\langle\frac{7}{10}\rangle$	$(\frac{7}{2})$	$x^{20} + 5 b_{17} x^{17} + 5 b_{16} x^{16} + 5 a_{14} x^{14} + 5 d_{0}$	$4$	$120$	$100$	$100$	$100$	$100\%$	$1$
5.1.20.35a	$5$	$20$	$1$	$20$	$35$	$[2]$	$[1]$	$\langle\frac{4}{5}\rangle$	$(4)$	$x^{20} + 5 b_{19} x^{19} + 5 b_{18} x^{18} + 5 b_{17} x^{17} + 5 a_{16} x^{16} + 5 d_{0} + 25 c_{20}$	$20$	$1056$	$500$	$500$	$500$	$100\%$	$1$
5.1.20.36a	$5$	$20$	$1$	$20$	$36$	$[\frac{33}{16}]$	$[\frac{17}{16}]$	$\langle\frac{17}{20}\rangle$	$(\frac{17}{4})$	$x^{20} + 5 b_{19} x^{19} + 5 b_{18} x^{18} + 5 a_{17} x^{17} + 25 b_{21} x + 5 d_{0}$	$4$	$500$	$500$	$500$	$500$	$100\%$	$1$
5.1.20.37a	$5$	$20$	$1$	$20$	$37$	$[\frac{17}{8}]$	$[\frac{9}{8}]$	$\langle\frac{9}{10}\rangle$	$(\frac{9}{2})$	$x^{20} + 5 b_{19} x^{19} + 5 a_{18} x^{18} + 25 b_{22} x^2 + 25 b_{21} x + 5 d_{0}$	$4$	$520$	$500$	$500$	$500$	$100\%$	$1$
5.1.20.38a	$5$	$20$	$1$	$20$	$38$	$[\frac{35}{16}]$	$[\frac{19}{16}]$	$\langle\frac{19}{20}\rangle$	$(\frac{19}{4})$	$x^{20} + 5 a_{19} x^{19} + 25 b_{23} x^3 + 25 b_{22} x^2 + 25 b_{21} x + 5 d_{0}$	$4$	$500$	$500$	$500$	$500$	$100\%$	$1$
5.1.20.39a	$5$	$20$	$1$	$20$	$39$	$[\frac{9}{4}]$	$[\frac{5}{4}]$	$\langle1\rangle$	$(5)$	$x^{20} + 25 c_{25} x^5 + 25 b_{24} x^4 + 25 b_{23} x^3 + 25 b_{22} x^2 + 25 b_{21} x + 5 d_{0}$	$20$	$1285$	$625$	$625$	$625$	$100\%$	$1$

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Elliptic curves over $\Q$
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This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.