LMFDB - p-adic families search results

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Residue characteristic $p$	Rel. degree $n$	Rel. ram. index $e$	Rel. res. field degree $f$	Rel. disc. exponent $c$

Base	Base degree $n_0$	Base ram. index $e_0$	Base res. field degree $f_0$	Base disc. exponent $c_0$

Herbrand invariant	Abs. degree $n_{\mathrm{abs}}$	Abs. ram. index $e_{\mathrm{abs}}$	Abs. res. field degree $f_{\mathrm{abs}}$	Abs. disc. exponent $c_{\mathrm{abs}}$

Mass	Absolute mass	Ambiguity	Field count	Wild segments

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Results (1-50 of 135 matches)

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Label	$p$	$n$	$n_0$	$n_{\mathrm{abs}}$	$f$	$f_0$	$f_{\mathrm{abs}}$	$e$	$e_0$	$e_{\mathrm{abs}}$	$c$	$c_0$	$c_{\mathrm{abs}}$	Base	Abs. Artin slopes	Swan slopes	Means	Rams	Generic poly	Ambiguity	Field count	Mass	Mass (absolute)	Mass stored	Mass found	Wild segments
5.2.1.0a1.1-2.1.0a	$5$	$2$	$2$	$4$	$2$	$2$	$4$	$1$	$1$	$1$	$0$	$0$	$0$	$\Q_{5}(\sqrt{2})$	$[\ ]$	$[ ]$	$\langle \rangle$	$( )$	$x$	$2$	$1$	$1$	$1/4$	$1/4$	$100\%$	$0$
5.2.1.0a1.1-1.2.1a	$5$	$2$	$2$	$4$	$1$	$2$	$2$	$2$	$1$	$2$	$1$	$0$	$1$	$\Q_{5}(\sqrt{2})$	$[\ ]$	$[ ]$	$\langle \rangle$	$( )$	$x^2 + 5 d_{0}$	$2$	$2$	$1$	$1/2$	$1/2$	$100\%$	$0$
5.2.1.0a1.1-3.1.0a	$5$	$3$	$2$	$6$	$3$	$2$	$6$	$1$	$1$	$1$	$0$	$0$	$0$	$\Q_{5}(\sqrt{2})$	$[\ ]$	$[ ]$	$\langle \rangle$	$( )$	$x$	$3$	$1$	$1$	$1/6$	$1/6$	$100\%$	$0$
5.2.1.0a1.1-1.3.2a	$5$	$3$	$2$	$6$	$1$	$2$	$2$	$3$	$1$	$3$	$2$	$0$	$2$	$\Q_{5}(\sqrt{2})$	$[\ ]$	$[ ]$	$\langle \rangle$	$( )$	$x^3 + 5 d_{0}$	$3$	$2$	$1$	$1/2$	$1/2$	$100\%$	$0$
5.2.1.0a1.1-4.1.0a	$5$	$4$	$2$	$8$	$4$	$2$	$8$	$1$	$1$	$1$	$0$	$0$	$0$	$\Q_{5}(\sqrt{2})$	$[\ ]$	$[ ]$	$\langle \rangle$	$( )$	$x$	$4$	$1$	$1$	$1/8$	$1/8$	$100\%$	$0$
5.2.1.0a1.1-2.2.2a	$5$	$4$	$2$	$8$	$2$	$2$	$4$	$2$	$1$	$2$	$2$	$0$	$2$	$\Q_{5}(\sqrt{2})$	$[\ ]$	$[ ]$	$\langle \rangle$	$( )$	$x^2 + 5 d_{0}$	$4$	$2$	$1$	$1/4$	$1/4$	$100\%$	$0$
5.2.1.0a1.1-1.4.3a	$5$	$4$	$2$	$8$	$1$	$2$	$2$	$4$	$1$	$4$	$3$	$0$	$3$	$\Q_{5}(\sqrt{2})$	$[\ ]$	$[ ]$	$\langle \rangle$	$( )$	$x^4 + 5 d_{0}$	$4$	$4$	$1$	$1/2$	$1/2$	$100\%$	$0$
5.2.1.0a1.1-5.1.0a	$5$	$5$	$2$	$10$	$5$	$2$	$10$	$1$	$1$	$1$	$0$	$0$	$0$	$\Q_{5}(\sqrt{2})$	$[\ ]$	$[ ]$	$\langle \rangle$	$( )$	$x$	$5$	$1$	$1$	$1/10$	$1/10$	$100\%$	$0$
5.2.1.0a1.1-1.5.5a	$5$	$5$	$2$	$10$	$1$	$2$	$2$	$5$	$1$	$5$	$5$	$0$	$5$	$\Q_{5}(\sqrt{2})$	$[\frac{5}{4}]$	$[\frac{1}{4}]$	$\langle\frac{1}{5}\rangle$	$(\frac{1}{4})$	$x^5 + 5 a_{1} x + 5$	$1$	$14$	$24$	$12$	$12$	$100\%$	$1$
5.2.1.0a1.1-1.5.6a	$5$	$5$	$2$	$10$	$1$	$2$	$2$	$5$	$1$	$5$	$6$	$0$	$6$	$\Q_{5}(\sqrt{2})$	$[\frac{3}{2}]$	$[\frac{1}{2}]$	$\langle\frac{2}{5}\rangle$	$(\frac{1}{2})$	$x^5 + 5 a_{2} x^2 + 5$	$1$	$14$	$24$	$12$	$12$	$100\%$	$1$
5.2.1.0a1.1-1.5.7a	$5$	$5$	$2$	$10$	$1$	$2$	$2$	$5$	$1$	$5$	$7$	$0$	$7$	$\Q_{5}(\sqrt{2})$	$[\frac{7}{4}]$	$[\frac{3}{4}]$	$\langle\frac{3}{5}\rangle$	$(\frac{3}{4})$	$x^5 + 5 a_{3} x^3 + 5$	$1$	$14$	$24$	$12$	$12$	$100\%$	$1$
5.2.1.0a1.1-1.5.8a	$5$	$5$	$2$	$10$	$1$	$2$	$2$	$5$	$1$	$5$	$8$	$0$	$8$	$\Q_{5}(\sqrt{2})$	$[2]$	$[1]$	$\langle\frac{4}{5}\rangle$	$(1)$	$x^5 + 5 a_{4} x^4 + 25 c_{5} + 5$	$5$	$28$	$24$	$12$	$12$	$100\%$	$1$
5.2.1.0a1.1-1.5.9a	$5$	$5$	$2$	$10$	$1$	$2$	$2$	$5$	$1$	$5$	$9$	$0$	$9$	$\Q_{5}(\sqrt{2})$	$[\frac{9}{4}]$	$[\frac{5}{4}]$	$\langle1\rangle$	$(\frac{5}{4})$	$x^5 + 25 b_{6} x + 5$	$1$	$15$	$25$	$25/2$	$25/2$	$100\%$	$1$
5.2.1.0a1.1-6.1.0a	$5$	$6$	$2$	$12$	$6$	$2$	$12$	$1$	$1$	$1$	$0$	$0$	$0$	$\Q_{5}(\sqrt{2})$	$[\ ]$	$[ ]$	$\langle \rangle$	$( )$	$x$	$6$	$1$	$1$	$1/12$	$1/12$	$100\%$	$0$
5.2.1.0a1.1-3.2.3a	$5$	$6$	$2$	$12$	$3$	$2$	$6$	$2$	$1$	$2$	$3$	$0$	$3$	$\Q_{5}(\sqrt{2})$	$[\ ]$	$[ ]$	$\langle \rangle$	$( )$	$x^2 + 5 d_{0}$	$6$	$2$	$1$	$1/6$	$1/6$	$100\%$	$0$
5.2.1.0a1.1-2.3.4a	$5$	$6$	$2$	$12$	$2$	$2$	$4$	$3$	$1$	$3$	$4$	$0$	$4$	$\Q_{5}(\sqrt{2})$	$[\ ]$	$[ ]$	$\langle \rangle$	$( )$	$x^3 + 5 d_{0}$	$6$	$2$	$1$	$1/4$	$1/4$	$100\%$	$0$
5.2.1.0a1.1-1.6.5a	$5$	$6$	$2$	$12$	$1$	$2$	$2$	$6$	$1$	$6$	$5$	$0$	$5$	$\Q_{5}(\sqrt{2})$	$[\ ]$	$[ ]$	$\langle \rangle$	$( )$	$x^6 + 5 d_{0}$	$6$	$4$	$1$	$1/2$	$1/2$	$100\%$	$0$
5.2.1.0a1.1-7.1.0a	$5$	$7$	$2$	$14$	$7$	$2$	$14$	$1$	$1$	$1$	$0$	$0$	$0$	$\Q_{5}(\sqrt{2})$	$[\ ]$	$[ ]$	$\langle \rangle$	$( )$	$x$	$7$	$1$	$1$	$1/14$	$1/14$	$100\%$	$0$
5.2.1.0a1.1-1.7.6a	$5$	$7$	$2$	$14$	$1$	$2$	$2$	$7$	$1$	$7$	$6$	$0$	$6$	$\Q_{5}(\sqrt{2})$	$[\ ]$	$[ ]$	$\langle \rangle$	$( )$	$x^7 + 5$	$1$	$1$	$1$	$1/2$	$1/2$	$100\%$	$0$
5.2.1.0a1.1-8.1.0a	$5$	$8$	$2$	$16$	$8$	$2$	$16$	$1$	$1$	$1$	$0$	$0$	$0$	$\Q_{5}(\sqrt{2})$	$[\ ]$	$[ ]$	$\langle \rangle$	$( )$	$x$	$8$	$1$	$1$	$1/16$	$1/16$	$100\%$	$0$
5.2.1.0a1.1-4.2.4a	$5$	$8$	$2$	$16$	$4$	$2$	$8$	$2$	$1$	$2$	$4$	$0$	$4$	$\Q_{5}(\sqrt{2})$	$[\ ]$	$[ ]$	$\langle \rangle$	$( )$	$x^2 + 5 d_{0}$	$8$	$2$	$1$	$1/8$	$1/8$	$100\%$	$0$
5.2.1.0a1.1-2.4.6a	$5$	$8$	$2$	$16$	$2$	$2$	$4$	$4$	$1$	$4$	$6$	$0$	$6$	$\Q_{5}(\sqrt{2})$	$[\ ]$	$[ ]$	$\langle \rangle$	$( )$	$x^4 + 5 d_{0}$	$8$	$4$	$1$	$1/4$	$1/4$	$100\%$	$0$
5.2.1.0a1.1-1.8.7a	$5$	$8$	$2$	$16$	$1$	$2$	$2$	$8$	$1$	$8$	$7$	$0$	$7$	$\Q_{5}(\sqrt{2})$	$[\ ]$	$[ ]$	$\langle \rangle$	$( )$	$x^8 + 5 d_{0}$	$8$	$6$	$1$	$1/2$	$1/2$	$100\%$	$0$
5.2.1.0a1.1-9.1.0a	$5$	$9$	$2$	$18$	$9$	$2$	$18$	$1$	$1$	$1$	$0$	$0$	$0$	$\Q_{5}(\sqrt{2})$	$[\ ]$	$[ ]$	$\langle \rangle$	$( )$	$x$	$9$	$1$	$1$	$1/18$	$1/18$	$100\%$	$0$
5.2.1.0a1.1-3.3.6a	$5$	$9$	$2$	$18$	$3$	$2$	$6$	$3$	$1$	$3$	$6$	$0$	$6$	$\Q_{5}(\sqrt{2})$	$[\ ]$	$[ ]$	$\langle \rangle$	$( )$	$x^3 + 5 d_{0}$	$9$	$2$	$1$	$1/6$	$1/6$	$100\%$	$0$
5.2.1.0a1.1-1.9.8a	$5$	$9$	$2$	$18$	$1$	$2$	$2$	$9$	$1$	$9$	$8$	$0$	$8$	$\Q_{5}(\sqrt{2})$	$[\ ]$	$[ ]$	$\langle \rangle$	$( )$	$x^9 + 5 d_{0}$	$3$	$2$	$1$	$1/2$	$1/2$	$100\%$	$0$
5.2.1.0a1.1-10.1.0a	$5$	$10$	$2$	$20$	$10$	$2$	$20$	$1$	$1$	$1$	$0$	$0$	$0$	$\Q_{5}(\sqrt{2})$	$[\ ]$	$[ ]$	$\langle \rangle$	$( )$	$x$	$10$	$1$	$1$	$1/20$	$1/20$	$100\%$	$0$
5.2.1.0a1.1-5.2.5a	$5$	$10$	$2$	$20$	$5$	$2$	$10$	$2$	$1$	$2$	$5$	$0$	$5$	$\Q_{5}(\sqrt{2})$	$[\ ]$	$[ ]$	$\langle \rangle$	$( )$	$x^2 + 5 d_{0}$	$10$	$2$	$1$	$1/10$	$1/10$	$100\%$	$0$
5.2.1.0a1.1-2.5.10a	$5$	$10$	$2$	$20$	$2$	$2$	$4$	$5$	$1$	$5$	$10$	$0$	$10$	$\Q_{5}(\sqrt{2})$	$[\frac{5}{4}]$	$[\frac{1}{4}]$	$\langle\frac{1}{5}\rangle$	$(\frac{1}{4})$	$x^5 + 5 a_{1} x + 5$	$2$	$164$	$624$	$156$	$156$	$100\%$	$1$
5.2.1.0a1.1-2.5.12a	$5$	$10$	$2$	$20$	$2$	$2$	$4$	$5$	$1$	$5$	$12$	$0$	$12$	$\Q_{5}(\sqrt{2})$	$[\frac{3}{2}]$	$[\frac{1}{2}]$	$\langle\frac{2}{5}\rangle$	$(\frac{1}{2})$	$x^5 + 5 a_{2} x^2 + 5$	$2$	$164$	$624$	$156$	$156$	$100\%$	$1$
5.2.1.0a1.1-2.5.14a	$5$	$10$	$2$	$20$	$2$	$2$	$4$	$5$	$1$	$5$	$14$	$0$	$14$	$\Q_{5}(\sqrt{2})$	$[\frac{7}{4}]$	$[\frac{3}{4}]$	$\langle\frac{3}{5}\rangle$	$(\frac{3}{4})$	$x^5 + 5 a_{3} x^3 + 5$	$2$	$164$	$624$	$156$	$156$	$100\%$	$1$
5.2.1.0a1.1-2.5.16a	$5$	$10$	$2$	$20$	$2$	$2$	$4$	$5$	$1$	$5$	$16$	$0$	$16$	$\Q_{5}(\sqrt{2})$	$[2]$	$[1]$	$\langle\frac{4}{5}\rangle$	$(1)$	$x^5 + 5 a_{4} x^4 + 25 c_{5} + 5$	$10$	$328$	$624$	$156$	$156$	$100\%$	$1$
5.2.1.0a1.1-2.5.18a	$5$	$10$	$2$	$20$	$2$	$2$	$4$	$5$	$1$	$5$	$18$	$0$	$18$	$\Q_{5}(\sqrt{2})$	$[\frac{9}{4}]$	$[\frac{5}{4}]$	$\langle1\rangle$	$(\frac{5}{4})$	$x^5 + 25 b_{6} x + 5$	$2$	$165$	$625$	$625/4$	$625/4$	$100\%$	$1$
5.2.1.0a1.1-1.10.10a	$5$	$10$	$2$	$20$	$1$	$2$	$2$	$10$	$1$	$10$	$10$	$0$	$10$	$\Q_{5}(\sqrt{2})$	$[\frac{9}{8}]$	$[\frac{1}{8}]$	$\langle\frac{1}{10}\rangle$	$(\frac{1}{4})$	$x^{10} + 5 a_{1} x + 5 d_{0}$	$2$	$14$	$24$	$12$	$12$	$100\%$	$1$
5.2.1.0a1.1-1.10.11a	$5$	$10$	$2$	$20$	$1$	$2$	$2$	$10$	$1$	$10$	$11$	$0$	$11$	$\Q_{5}(\sqrt{2})$	$[\frac{5}{4}]$	$[\frac{1}{4}]$	$\langle\frac{1}{5}\rangle$	$(\frac{1}{2})$	$x^{10} + 5 a_{2} x^2 + 5 d_{0}$	$2$	$28$	$24$	$12$	$12$	$100\%$	$1$
5.2.1.0a1.1-1.10.12a	$5$	$10$	$2$	$20$	$1$	$2$	$2$	$10$	$1$	$10$	$12$	$0$	$12$	$\Q_{5}(\sqrt{2})$	$[\frac{11}{8}]$	$[\frac{3}{8}]$	$\langle\frac{3}{10}\rangle$	$(\frac{3}{4})$	$x^{10} + 5 a_{3} x^3 + 5 d_{0}$	$2$	$14$	$24$	$12$	$12$	$100\%$	$1$
5.2.1.0a1.1-1.10.13a	$5$	$10$	$2$	$20$	$1$	$2$	$2$	$10$	$1$	$10$	$13$	$0$	$13$	$\Q_{5}(\sqrt{2})$	$[\frac{3}{2}]$	$[\frac{1}{2}]$	$\langle\frac{2}{5}\rangle$	$(1)$	$x^{10} + 5 c_{5} x^5 + 5 a_{4} x^4 + 5 d_{0}$	$10$	$42$	$24$	$12$	$12$	$100\%$	$1$
5.2.1.0a1.1-1.10.15a	$5$	$10$	$2$	$20$	$1$	$2$	$2$	$10$	$1$	$10$	$15$	$0$	$15$	$\Q_{5}(\sqrt{2})$	$[\frac{7}{4}]$	$[\frac{3}{4}]$	$\langle\frac{3}{5}\rangle$	$(\frac{3}{2})$	$x^{10} + 5 b_{7} x^7 + 5 a_{6} x^6 + 5 d_{0}$	$2$	$324$	$600$	$300$	$300$	$100\%$	$1$
5.2.1.0a1.1-1.10.16a	$5$	$10$	$2$	$20$	$1$	$2$	$2$	$10$	$1$	$10$	$16$	$0$	$16$	$\Q_{5}(\sqrt{2})$	$[\frac{15}{8}]$	$[\frac{7}{8}]$	$\langle\frac{7}{10}\rangle$	$(\frac{7}{4})$	$x^{10} + 5 b_{8} x^8 + 5 a_{7} x^7 + 5 d_{0}$	$2$	$310$	$600$	$300$	$300$	$100\%$	$1$
5.2.1.0a1.1-1.10.17a	$5$	$10$	$2$	$20$	$1$	$2$	$2$	$10$	$1$	$10$	$17$	$0$	$17$	$\Q_{5}(\sqrt{2})$	$[2]$	$[1]$	$\langle\frac{4}{5}\rangle$	$(2)$	$x^{10} + 5 b_{9} x^9 + 5 a_{8} x^8 + 5 d_{0} + 25 c_{10}$	$10$	$648$	$600$	$300$	$300$	$100\%$	$1$
5.2.1.0a1.1-1.10.18a	$5$	$10$	$2$	$20$	$1$	$2$	$2$	$10$	$1$	$10$	$18$	$0$	$18$	$\Q_{5}(\sqrt{2})$	$[\frac{17}{8}]$	$[\frac{9}{8}]$	$\langle\frac{9}{10}\rangle$	$(\frac{9}{4})$	$x^{10} + 5 a_{9} x^9 + 25 b_{11} x + 5 d_{0}$	$2$	$310$	$600$	$300$	$300$	$100\%$	$1$
5.2.1.0a1.1-1.10.19a	$5$	$10$	$2$	$20$	$1$	$2$	$2$	$10$	$1$	$10$	$19$	$0$	$19$	$\Q_{5}(\sqrt{2})$	$[\frac{9}{4}]$	$[\frac{5}{4}]$	$\langle1\rangle$	$(\frac{5}{2})$	$x^{10} + 25 b_{12} x^2 + 25 b_{11} x + 5 d_{0}$	$2$	$340$	$625$	$625/2$	$625/2$	$100\%$	$1$
5.2.1.0a1.1-11.1.0a	$5$	$11$	$2$	$22$	$11$	$2$	$22$	$1$	$1$	$1$	$0$	$0$	$0$	$\Q_{5}(\sqrt{2})$	$[\ ]$	$[ ]$	$\langle \rangle$	$( )$	$x$	$11$	$1$	$1$	$1/22$	$1/22$	$100\%$	$0$
5.2.1.0a1.1-1.11.10a	$5$	$11$	$2$	$22$	$1$	$2$	$2$	$11$	$1$	$11$	$10$	$0$	$10$	$\Q_{5}(\sqrt{2})$	$[\ ]$	$[ ]$	$\langle \rangle$	$( )$	$x^{11} + 5$	$1$	$1$	$1$	$1/2$	$1/2$	$100\%$	$0$
5.2.1.0a1.1-12.1.0a	$5$	$12$	$2$	$24$	$12$	$2$	$24$	$1$	$1$	$1$	$0$	$0$	$0$	$\Q_{5}(\sqrt{2})$	$[\ ]$	$[ ]$	$\langle \rangle$	$( )$	$x$	$12$	$0$	$1$	$1/24$	$0$	$0\%$	$0$
5.2.1.0a1.1-6.2.6a	$5$	$12$	$2$	$24$	$6$	$2$	$12$	$2$	$1$	$2$	$6$	$0$	$6$	$\Q_{5}(\sqrt{2})$	$[\ ]$	$[ ]$	$\langle \rangle$	$( )$	$x^2 + 5 d_{0}$	$12$	$0$	$1$	$1/12$	$0$	$0\%$	$0$
5.2.1.0a1.1-4.3.8a	$5$	$12$	$2$	$24$	$4$	$2$	$8$	$3$	$1$	$3$	$8$	$0$	$8$	$\Q_{5}(\sqrt{2})$	$[\ ]$	$[ ]$	$\langle \rangle$	$( )$	$x^3 + 5 d_{0}$	$12$	$0$	$1$	$1/8$	$0$	$0\%$	$0$
5.2.1.0a1.1-3.4.9a	$5$	$12$	$2$	$24$	$3$	$2$	$6$	$4$	$1$	$4$	$9$	$0$	$9$	$\Q_{5}(\sqrt{2})$	$[\ ]$	$[ ]$	$\langle \rangle$	$( )$	$x^4 + 5 d_{0}$	$12$	$0$	$1$	$1/6$	$0$	$0\%$	$0$
5.2.1.0a1.1-2.6.10a	$5$	$12$	$2$	$24$	$2$	$2$	$4$	$6$	$1$	$6$	$10$	$0$	$10$	$\Q_{5}(\sqrt{2})$	$[\ ]$	$[ ]$	$\langle \rangle$	$( )$	$x^6 + 5 d_{0}$	$12$	$0$	$1$	$1/4$	$0$	$0\%$	$0$
5.2.1.0a1.1-1.12.11a	$5$	$12$	$2$	$24$	$1$	$2$	$2$	$12$	$1$	$12$	$11$	$0$	$11$	$\Q_{5}(\sqrt{2})$	$[\ ]$	$[ ]$	$\langle \rangle$	$( )$	$x^{12} + 5 d_{0}$	$12$	$0$	$1$	$1/2$	$0$	$0\%$	$0$

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