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 93 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
19.2.1.0a1.1-2.1.0a	$19$	$2$	$2$	$4$	$2$	$2$	$4$	$1$	$1$	$1$	$0$	$0$	$0$	$\Q_{19}(\sqrt{2})$	$[\ ]$	$[ ]$	$\langle \rangle$	$( )$	$x$	$2$	$1$	$1$	$1/4$	$1/4$	$100\%$	$0$
19.2.1.0a1.1-1.2.1a	$19$	$2$	$2$	$4$	$1$	$2$	$2$	$2$	$1$	$2$	$1$	$0$	$1$	$\Q_{19}(\sqrt{2})$	$[\ ]$	$[ ]$	$\langle \rangle$	$( )$	$x^2 + 19 d_{0}$	$2$	$2$	$1$	$1/2$	$1/2$	$100\%$	$0$
19.2.1.0a1.1-3.1.0a	$19$	$3$	$2$	$6$	$3$	$2$	$6$	$1$	$1$	$1$	$0$	$0$	$0$	$\Q_{19}(\sqrt{2})$	$[\ ]$	$[ ]$	$\langle \rangle$	$( )$	$x$	$3$	$1$	$1$	$1/6$	$1/6$	$100\%$	$0$
19.2.1.0a1.1-1.3.2a	$19$	$3$	$2$	$6$	$1$	$2$	$2$	$3$	$1$	$3$	$2$	$0$	$2$	$\Q_{19}(\sqrt{2})$	$[\ ]$	$[ ]$	$\langle \rangle$	$( )$	$x^3 + 19 d_{0}$	$3$	$3$	$1$	$1/2$	$1/2$	$100\%$	$0$
19.2.1.0a1.1-4.1.0a	$19$	$4$	$2$	$8$	$4$	$2$	$8$	$1$	$1$	$1$	$0$	$0$	$0$	$\Q_{19}(\sqrt{2})$	$[\ ]$	$[ ]$	$\langle \rangle$	$( )$	$x$	$4$	$1$	$1$	$1/8$	$1/8$	$100\%$	$0$
19.2.1.0a1.1-2.2.2a	$19$	$4$	$2$	$8$	$2$	$2$	$4$	$2$	$1$	$2$	$2$	$0$	$2$	$\Q_{19}(\sqrt{2})$	$[\ ]$	$[ ]$	$\langle \rangle$	$( )$	$x^2 + 19 d_{0}$	$4$	$2$	$1$	$1/4$	$1/4$	$100\%$	$0$
19.2.1.0a1.1-1.4.3a	$19$	$4$	$2$	$8$	$1$	$2$	$2$	$4$	$1$	$4$	$3$	$0$	$3$	$\Q_{19}(\sqrt{2})$	$[\ ]$	$[ ]$	$\langle \rangle$	$( )$	$x^4 + 19 d_{0}$	$4$	$3$	$1$	$1/2$	$1/2$	$100\%$	$0$
19.2.1.0a1.1-5.1.0a	$19$	$5$	$2$	$10$	$5$	$2$	$10$	$1$	$1$	$1$	$0$	$0$	$0$	$\Q_{19}(\sqrt{2})$	$[\ ]$	$[ ]$	$\langle \rangle$	$( )$	$x$	$5$	$1$	$1$	$1/10$	$1/10$	$100\%$	$0$
19.2.1.0a1.1-1.5.4a	$19$	$5$	$2$	$10$	$1$	$2$	$2$	$5$	$1$	$5$	$4$	$0$	$4$	$\Q_{19}(\sqrt{2})$	$[\ ]$	$[ ]$	$\langle \rangle$	$( )$	$x^5 + 19 d_{0}$	$5$	$3$	$1$	$1/2$	$1/2$	$100\%$	$0$
19.2.1.0a1.1-6.1.0a	$19$	$6$	$2$	$12$	$6$	$2$	$12$	$1$	$1$	$1$	$0$	$0$	$0$	$\Q_{19}(\sqrt{2})$	$[\ ]$	$[ ]$	$\langle \rangle$	$( )$	$x$	$6$	$1$	$1$	$1/12$	$1/12$	$100\%$	$0$
19.2.1.0a1.1-3.2.3a	$19$	$6$	$2$	$12$	$3$	$2$	$6$	$2$	$1$	$2$	$3$	$0$	$3$	$\Q_{19}(\sqrt{2})$	$[\ ]$	$[ ]$	$\langle \rangle$	$( )$	$x^2 + 19 d_{0}$	$6$	$2$	$1$	$1/6$	$1/6$	$100\%$	$0$
19.2.1.0a1.1-2.3.4a	$19$	$6$	$2$	$12$	$2$	$2$	$4$	$3$	$1$	$3$	$4$	$0$	$4$	$\Q_{19}(\sqrt{2})$	$[\ ]$	$[ ]$	$\langle \rangle$	$( )$	$x^3 + 19 d_{0}$	$6$	$3$	$1$	$1/4$	$1/4$	$100\%$	$0$
19.2.1.0a1.1-1.6.5a	$19$	$6$	$2$	$12$	$1$	$2$	$2$	$6$	$1$	$6$	$5$	$0$	$5$	$\Q_{19}(\sqrt{2})$	$[\ ]$	$[ ]$	$\langle \rangle$	$( )$	$x^6 + 19 d_{0}$	$6$	$6$	$1$	$1/2$	$1/2$	$100\%$	$0$
19.2.1.0a1.1-7.1.0a	$19$	$7$	$2$	$14$	$7$	$2$	$14$	$1$	$1$	$1$	$0$	$0$	$0$	$\Q_{19}(\sqrt{2})$	$[\ ]$	$[ ]$	$\langle \rangle$	$( )$	$x$	$7$	$1$	$1$	$1/14$	$1/14$	$100\%$	$0$
19.2.1.0a1.1-1.7.6a	$19$	$7$	$2$	$14$	$1$	$2$	$2$	$7$	$1$	$7$	$6$	$0$	$6$	$\Q_{19}(\sqrt{2})$	$[\ ]$	$[ ]$	$\langle \rangle$	$( )$	$x^7 + 19$	$1$	$1$	$1$	$1/2$	$1/2$	$100\%$	$0$
19.2.1.0a1.1-8.1.0a	$19$	$8$	$2$	$16$	$8$	$2$	$16$	$1$	$1$	$1$	$0$	$0$	$0$	$\Q_{19}(\sqrt{2})$	$[\ ]$	$[ ]$	$\langle \rangle$	$( )$	$x$	$8$	$1$	$1$	$1/16$	$1/16$	$100\%$	$0$
19.2.1.0a1.1-4.2.4a	$19$	$8$	$2$	$16$	$4$	$2$	$8$	$2$	$1$	$2$	$4$	$0$	$4$	$\Q_{19}(\sqrt{2})$	$[\ ]$	$[ ]$	$\langle \rangle$	$( )$	$x^2 + 19 d_{0}$	$8$	$2$	$1$	$1/8$	$1/8$	$100\%$	$0$
19.2.1.0a1.1-2.4.6a	$19$	$8$	$2$	$16$	$2$	$2$	$4$	$4$	$1$	$4$	$6$	$0$	$6$	$\Q_{19}(\sqrt{2})$	$[\ ]$	$[ ]$	$\langle \rangle$	$( )$	$x^4 + 19 d_{0}$	$8$	$3$	$1$	$1/4$	$1/4$	$100\%$	$0$
19.2.1.0a1.1-1.8.7a	$19$	$8$	$2$	$16$	$1$	$2$	$2$	$8$	$1$	$8$	$7$	$0$	$7$	$\Q_{19}(\sqrt{2})$	$[\ ]$	$[ ]$	$\langle \rangle$	$( )$	$x^8 + 19 d_{0}$	$8$	$5$	$1$	$1/2$	$1/2$	$100\%$	$0$
19.2.1.0a1.1-9.1.0a	$19$	$9$	$2$	$18$	$9$	$2$	$18$	$1$	$1$	$1$	$0$	$0$	$0$	$\Q_{19}(\sqrt{2})$	$[\ ]$	$[ ]$	$\langle \rangle$	$( )$	$x$	$9$	$1$	$1$	$1/18$	$1/18$	$100\%$	$0$
19.2.1.0a1.1-3.3.6a	$19$	$9$	$2$	$18$	$3$	$2$	$6$	$3$	$1$	$3$	$6$	$0$	$6$	$\Q_{19}(\sqrt{2})$	$[\ ]$	$[ ]$	$\langle \rangle$	$( )$	$x^3 + 19 d_{0}$	$9$	$3$	$1$	$1/6$	$1/6$	$100\%$	$0$
19.2.1.0a1.1-1.9.8a	$19$	$9$	$2$	$18$	$1$	$2$	$2$	$9$	$1$	$9$	$8$	$0$	$8$	$\Q_{19}(\sqrt{2})$	$[\ ]$	$[ ]$	$\langle \rangle$	$( )$	$x^9 + 19 d_{0}$	$9$	$9$	$1$	$1/2$	$1/2$	$100\%$	$0$
19.2.1.0a1.1-10.1.0a	$19$	$10$	$2$	$20$	$10$	$2$	$20$	$1$	$1$	$1$	$0$	$0$	$0$	$\Q_{19}(\sqrt{2})$	$[\ ]$	$[ ]$	$\langle \rangle$	$( )$	$x$	$10$	$1$	$1$	$1/20$	$1/20$	$100\%$	$0$
19.2.1.0a1.1-5.2.5a	$19$	$10$	$2$	$20$	$5$	$2$	$10$	$2$	$1$	$2$	$5$	$0$	$5$	$\Q_{19}(\sqrt{2})$	$[\ ]$	$[ ]$	$\langle \rangle$	$( )$	$x^2 + 19 d_{0}$	$10$	$2$	$1$	$1/10$	$1/10$	$100\%$	$0$
19.2.1.0a1.1-2.5.8a	$19$	$10$	$2$	$20$	$2$	$2$	$4$	$5$	$1$	$5$	$8$	$0$	$8$	$\Q_{19}(\sqrt{2})$	$[\ ]$	$[ ]$	$\langle \rangle$	$( )$	$x^5 + 19 d_{0}$	$10$	$3$	$1$	$1/4$	$1/4$	$100\%$	$0$
19.2.1.0a1.1-1.10.9a	$19$	$10$	$2$	$20$	$1$	$2$	$2$	$10$	$1$	$10$	$9$	$0$	$9$	$\Q_{19}(\sqrt{2})$	$[\ ]$	$[ ]$	$\langle \rangle$	$( )$	$x^{10} + 19 d_{0}$	$10$	$6$	$1$	$1/2$	$1/2$	$100\%$	$0$
19.2.1.0a1.1-11.1.0a	$19$	$11$	$2$	$22$	$11$	$2$	$22$	$1$	$1$	$1$	$0$	$0$	$0$	$\Q_{19}(\sqrt{2})$	$[\ ]$	$[ ]$	$\langle \rangle$	$( )$	$x$	$11$	$1$	$1$	$1/22$	$1/22$	$100\%$	$0$
19.2.1.0a1.1-1.11.10a	$19$	$11$	$2$	$22$	$1$	$2$	$2$	$11$	$1$	$11$	$10$	$0$	$10$	$\Q_{19}(\sqrt{2})$	$[\ ]$	$[ ]$	$\langle \rangle$	$( )$	$x^{11} + 19$	$1$	$1$	$1$	$1/2$	$1/2$	$100\%$	$0$
19.2.1.0a1.1-12.1.0a	$19$	$12$	$2$	$24$	$12$	$2$	$24$	$1$	$1$	$1$	$0$	$0$	$0$	$\Q_{19}(\sqrt{2})$	$[\ ]$	$[ ]$	$\langle \rangle$	$( )$	$x$	$12$	$0$	$1$	$1/24$	$0$	$0\%$	$0$
19.2.1.0a1.1-6.2.6a	$19$	$12$	$2$	$24$	$6$	$2$	$12$	$2$	$1$	$2$	$6$	$0$	$6$	$\Q_{19}(\sqrt{2})$	$[\ ]$	$[ ]$	$\langle \rangle$	$( )$	$x^2 + 19 d_{0}$	$12$	$0$	$1$	$1/12$	$0$	$0\%$	$0$
19.2.1.0a1.1-4.3.8a	$19$	$12$	$2$	$24$	$4$	$2$	$8$	$3$	$1$	$3$	$8$	$0$	$8$	$\Q_{19}(\sqrt{2})$	$[\ ]$	$[ ]$	$\langle \rangle$	$( )$	$x^3 + 19 d_{0}$	$12$	$0$	$1$	$1/8$	$0$	$0\%$	$0$
19.2.1.0a1.1-3.4.9a	$19$	$12$	$2$	$24$	$3$	$2$	$6$	$4$	$1$	$4$	$9$	$0$	$9$	$\Q_{19}(\sqrt{2})$	$[\ ]$	$[ ]$	$\langle \rangle$	$( )$	$x^4 + 19 d_{0}$	$12$	$0$	$1$	$1/6$	$0$	$0\%$	$0$
19.2.1.0a1.1-2.6.10a	$19$	$12$	$2$	$24$	$2$	$2$	$4$	$6$	$1$	$6$	$10$	$0$	$10$	$\Q_{19}(\sqrt{2})$	$[\ ]$	$[ ]$	$\langle \rangle$	$( )$	$x^6 + 19 d_{0}$	$12$	$0$	$1$	$1/4$	$0$	$0\%$	$0$
19.2.1.0a1.1-1.12.11a	$19$	$12$	$2$	$24$	$1$	$2$	$2$	$12$	$1$	$12$	$11$	$0$	$11$	$\Q_{19}(\sqrt{2})$	$[\ ]$	$[ ]$	$\langle \rangle$	$( )$	$x^{12} + 19 d_{0}$	$12$	$0$	$1$	$1/2$	$0$	$0\%$	$0$
19.2.1.0a1.1-13.1.0a	$19$	$13$	$2$	$26$	$13$	$2$	$26$	$1$	$1$	$1$	$0$	$0$	$0$	$\Q_{19}(\sqrt{2})$	$[\ ]$	$[ ]$	$\langle \rangle$	$( )$	$x$	$13$	$0$	$1$	$1/26$	$0$	$0\%$	$0$
19.2.1.0a1.1-1.13.12a	$19$	$13$	$2$	$26$	$1$	$2$	$2$	$13$	$1$	$13$	$12$	$0$	$12$	$\Q_{19}(\sqrt{2})$	$[\ ]$	$[ ]$	$\langle \rangle$	$( )$	$x^{13} + 19$	$1$	$0$	$1$	$1/2$	$0$	$0\%$	$0$
19.2.1.0a1.1-14.1.0a	$19$	$14$	$2$	$28$	$14$	$2$	$28$	$1$	$1$	$1$	$0$	$0$	$0$	$\Q_{19}(\sqrt{2})$	$[\ ]$	$[ ]$	$\langle \rangle$	$( )$	$x$	$14$	$0$	$1$	$1/28$	$0$	$0\%$	$0$
19.2.1.0a1.1-7.2.7a	$19$	$14$	$2$	$28$	$7$	$2$	$14$	$2$	$1$	$2$	$7$	$0$	$7$	$\Q_{19}(\sqrt{2})$	$[\ ]$	$[ ]$	$\langle \rangle$	$( )$	$x^2 + 19 d_{0}$	$14$	$0$	$1$	$1/14$	$0$	$0\%$	$0$
19.2.1.0a1.1-2.7.12a	$19$	$14$	$2$	$28$	$2$	$2$	$4$	$7$	$1$	$7$	$12$	$0$	$12$	$\Q_{19}(\sqrt{2})$	$[\ ]$	$[ ]$	$\langle \rangle$	$( )$	$x^7 + 19$	$2$	$0$	$1$	$1/4$	$0$	$0\%$	$0$
19.2.1.0a1.1-1.14.13a	$19$	$14$	$2$	$28$	$1$	$2$	$2$	$14$	$1$	$14$	$13$	$0$	$13$	$\Q_{19}(\sqrt{2})$	$[\ ]$	$[ ]$	$\langle \rangle$	$( )$	$x^{14} + 19 d_{0}$	$2$	$0$	$1$	$1/2$	$0$	$0\%$	$0$
19.2.1.0a1.1-15.1.0a	$19$	$15$	$2$	$30$	$15$	$2$	$30$	$1$	$1$	$1$	$0$	$0$	$0$	$\Q_{19}(\sqrt{2})$	$[\ ]$	$[ ]$	$\langle \rangle$	$( )$	$x$	$15$	$0$	$1$	$1/30$	$0$	$0\%$	$0$
19.2.1.0a1.1-5.3.10a	$19$	$15$	$2$	$30$	$5$	$2$	$10$	$3$	$1$	$3$	$10$	$0$	$10$	$\Q_{19}(\sqrt{2})$	$[\ ]$	$[ ]$	$\langle \rangle$	$( )$	$x^3 + 19 d_{0}$	$15$	$0$	$1$	$1/10$	$0$	$0\%$	$0$
19.2.1.0a1.1-3.5.12a	$19$	$15$	$2$	$30$	$3$	$2$	$6$	$5$	$1$	$5$	$12$	$0$	$12$	$\Q_{19}(\sqrt{2})$	$[\ ]$	$[ ]$	$\langle \rangle$	$( )$	$x^5 + 19 d_{0}$	$15$	$0$	$1$	$1/6$	$0$	$0\%$	$0$
19.2.1.0a1.1-1.15.14a	$19$	$15$	$2$	$30$	$1$	$2$	$2$	$15$	$1$	$15$	$14$	$0$	$14$	$\Q_{19}(\sqrt{2})$	$[\ ]$	$[ ]$	$\langle \rangle$	$( )$	$x^{15} + 19 d_{0}$	$15$	$0$	$1$	$1/2$	$0$	$0\%$	$0$
19.2.1.0a1.1-16.1.0a	$19$	$16$	$2$	$32$	$16$	$2$	$32$	$1$	$1$	$1$	$0$	$0$	$0$	$\Q_{19}(\sqrt{2})$	$[\ ]$	$[ ]$	$\langle \rangle$	$( )$	$x$	$16$	$0$	$1$	$1/32$	$0$	$0\%$	$0$
19.2.1.0a1.1-8.2.8a	$19$	$16$	$2$	$32$	$8$	$2$	$16$	$2$	$1$	$2$	$8$	$0$	$8$	$\Q_{19}(\sqrt{2})$	$[\ ]$	$[ ]$	$\langle \rangle$	$( )$	$x^2 + 19 d_{0}$	$16$	$0$	$1$	$1/16$	$0$	$0\%$	$0$
19.2.1.0a1.1-4.4.12a	$19$	$16$	$2$	$32$	$4$	$2$	$8$	$4$	$1$	$4$	$12$	$0$	$12$	$\Q_{19}(\sqrt{2})$	$[\ ]$	$[ ]$	$\langle \rangle$	$( )$	$x^4 + 19 d_{0}$	$16$	$0$	$1$	$1/8$	$0$	$0\%$	$0$
19.2.1.0a1.1-2.8.14a	$19$	$16$	$2$	$32$	$2$	$2$	$4$	$8$	$1$	$8$	$14$	$0$	$14$	$\Q_{19}(\sqrt{2})$	$[\ ]$	$[ ]$	$\langle \rangle$	$( )$	$x^8 + 19 d_{0}$	$16$	$0$	$1$	$1/4$	$0$	$0\%$	$0$
19.2.1.0a1.1-1.16.15a	$19$	$16$	$2$	$32$	$1$	$2$	$2$	$16$	$1$	$16$	$15$	$0$	$15$	$\Q_{19}(\sqrt{2})$	$[\ ]$	$[ ]$	$\langle \rangle$	$( )$	$x^{16} + 19 d_{0}$	$8$	$0$	$1$	$1/2$	$0$	$0\%$	$0$
19.2.1.0a1.1-17.1.0a	$19$	$17$	$2$	$34$	$17$	$2$	$34$	$1$	$1$	$1$	$0$	$0$	$0$	$\Q_{19}(\sqrt{2})$	$[\ ]$	$[ ]$	$\langle \rangle$	$( )$	$x$	$17$	$0$	$1$	$1/34$	$0$	$0\%$	$0$

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