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

Refine search

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

Mass	Ambiguity	Field count	Wild segments	Herbrand invariant

			Sort order	Select

Results (1-50 of 389 matches)

Next Download displayed columns for results to

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
2.16.1.0a	$2$	$16$	$16$	$1$	$0$	$[\ ]$	$[ ]$	$\langle \rangle$	$( )$	$x$	$16$	$1$	$1$	$1/16$	$1/16$	$100\%$	$0$	$1$
2.8.2.16a	$2$	$16$	$8$	$2$	$16$	$[2]$	$[1]$	$\langle\frac{1}{2}\rangle$	$(1)$	$x^2 + 2 a_{1} x + 4 c_{2} + 2$	$16$	$70$	$255$	$255/8$	$255/8$	$100\%$	$1$
2.8.2.24a	$2$	$16$	$8$	$2$	$24$	$[3]$	$[2]$	$\langle1\rangle$	$(2)$	$x^2 + 4 b_{3} x + 8 c_{4} + 2$	$16$	$72$	$256$	$32$	$32$	$100\%$	$1$
2.4.4.16a	$2$	$16$	$4$	$4$	$16$	$[\frac{4}{3}, \frac{4}{3}]$	$[\frac{1}{3}, \frac{1}{3}]$	$\langle\frac{1}{6}, \frac{1}{4}\rangle$	$(\frac{1}{3}, \frac{1}{3})$	$x^4 + 2 a_{1} x + 2$	$4$	$5$	$15$	$15/4$	$15/4$	$100\%$	$1$	$5$
2.4.4.24a	$2$	$16$	$4$	$4$	$24$	$[2, 2]$	$[1, 1]$	$\langle\frac{1}{2}, \frac{3}{4}\rangle$	$(1, 1)$	$x^4 + 2 a_{3} x^3 + 2 b_{2} x^2 + 4 c_{4} + 2$	$16$	$123$	$240$	$60$	$60$	$100\%$	$1$
2.4.4.32a	$2$	$16$	$4$	$4$	$32$	$[\frac{8}{3}, \frac{8}{3}]$	$[\frac{5}{3}, \frac{5}{3}]$	$\langle\frac{5}{6}, \frac{5}{4}\rangle$	$(\frac{5}{3}, \frac{5}{3})$	$x^4 + 4 b_{6} x^2 + 4 a_{5} x + 2$	$4$	$64$	$240$	$60$	$60$	$100\%$	$1$
2.4.4.32b	$2$	$16$	$4$	$4$	$32$	$[2, 3]$	$[1, 2]$	$\langle\frac{1}{2}, \frac{5}{4}\rangle$	$(1, 3)$	$x^4 + 4 b_{7} x^3 + 2 a_{2} x^2 + 4 a_{5} x + 4 c_{4} + 8 c_{8} + 2$	$16$	$1942$	$3600$	$900$	$900$	$100\%$	$2$
2.4.4.36a	$2$	$16$	$4$	$4$	$36$	$[2, \frac{7}{2}]$	$[1, \frac{5}{2}]$	$\langle\frac{1}{2}, \frac{3}{2}\rangle$	$(1, 4)$	$x^4 + 4 b_{7} x^3 + (2 a_{2} + 8 c_{10}) x^2 + 8 b_{9} x + 4 c_{4} + 2$	$16$	$1948$	$3840$	$960$	$960$	$100\%$	$2$
2.4.4.40a	$2$	$16$	$4$	$4$	$40$	$[3, \frac{7}{2}]$	$[2, \frac{5}{2}]$	$\langle1, \frac{7}{4}\rangle$	$(2, 3)$	$x^4 + 4 a_{7} x^3 + (4 b_{6} + 8 c_{10}) x^2 + 8 b_{9} x + 8 c_{8} + 2$	$16$	$1948$	$3840$	$960$	$960$	$100\%$	$2$
2.4.4.44a	$2$	$16$	$4$	$4$	$44$	$[3, 4]$	$[2, 3]$	$\langle1, 2\rangle$	$(2, 4)$	$x^4 + 8 b_{11} x^3 + 4 b_{6} x^2 + 8 b_{9} x + 8 c_{8} + 16 c_{12} + 2$	$16$	$2158$	$4096$	$1024$	$1024$	$100\%$	$2$
2.2.8.16a	$2$	$16$	$2$	$8$	$16$	$[\frac{8}{7}, \frac{8}{7}, \frac{8}{7}]$	$[\frac{1}{7}, \frac{1}{7}, \frac{1}{7}]$	$\langle\frac{1}{14}, \frac{3}{28}, \frac{1}{8}\rangle$	$(\frac{1}{7}, \frac{1}{7}, \frac{1}{7})$	$x^8 + 2 a_{1} x + 2$	$2$	$2$	$3$	$3/2$	$3/2$	$100\%$	$1$
2.2.8.20a	$2$	$16$	$2$	$8$	$20$	$[\frac{10}{7}, \frac{10}{7}, \frac{10}{7}]$	$[\frac{3}{7}, \frac{3}{7}, \frac{3}{7}]$	$\langle\frac{3}{14}, \frac{9}{28}, \frac{3}{8}\rangle$	$(\frac{3}{7}, \frac{3}{7}, \frac{3}{7})$	$x^8 + 2 a_{3} x^3 + 2$	$2$	$2$	$3$	$3/2$	$3/2$	$100\%$	$1$
2.2.8.20b	$2$	$16$	$2$	$8$	$20$	$[\frac{4}{3}, \frac{4}{3}, \frac{3}{2}]$	$[\frac{1}{3}, \frac{1}{3}, \frac{1}{2}]$	$\langle\frac{1}{6}, \frac{1}{4}, \frac{3}{8}\rangle$	$(\frac{1}{3}, \frac{1}{3}, 1)$	$x^8 + 2 c_{4} x^4 + 2 a_{3} x^3 + 2 a_{2} x^2 + 2$	$4$	$10$	$9$	$9/2$	$9/2$	$100\%$	$2$
2.2.8.24a	$2$	$16$	$2$	$8$	$24$	$[\frac{12}{7}, \frac{12}{7}, \frac{12}{7}]$	$[\frac{5}{7}, \frac{5}{7}, \frac{5}{7}]$	$\langle\frac{5}{14}, \frac{15}{28}, \frac{5}{8}\rangle$	$(\frac{5}{7}, \frac{5}{7}, \frac{5}{7})$	$x^8 + 2 a_{5} x^5 + 2 b_{4} x^4 + 2$	$2$	$7$	$12$	$6$	$6$	$100\%$	$1$
2.2.8.24b	$2$	$16$	$2$	$8$	$24$	$[\frac{4}{3}, \frac{4}{3}, 2]$	$[\frac{1}{3}, \frac{1}{3}, 1]$	$\langle\frac{1}{6}, \frac{1}{4}, \frac{5}{8}\rangle$	$(\frac{1}{3}, \frac{1}{3}, 3)$	$x^8 + 2 b_{7} x^7 + 2 a_{5} x^5 + 2 a_{2} x^2 + 4 c_{8} + 2$	$4$	$38$	$36$	$18$	$18$	$100\%$	$2$
2.2.8.28a	$2$	$16$	$2$	$8$	$28$	$[2, 2, 2]$	$[1, 1, 1]$	$\langle\frac{1}{2}, \frac{3}{4}, \frac{7}{8}\rangle$	$(1, 1, 1)$	$x^8 + 2 a_{7} x^7 + 2 b_{6} x^6 + 2 b_{4} x^4 + 4 c_{8} + 2$	$8$	$45$	$48$	$24$	$24$	$100\%$	$1$	$33$
2.2.8.28b	$2$	$16$	$2$	$8$	$28$	$[\frac{4}{3}, \frac{4}{3}, \frac{5}{2}]$	$[\frac{1}{3}, \frac{1}{3}, \frac{3}{2}]$	$\langle\frac{1}{6}, \frac{1}{4}, \frac{7}{8}\rangle$	$(\frac{1}{3}, \frac{1}{3}, 5)$	$x^8 + 2 a_{7} x^7 + 4 c_{12} x^4 + 4 b_{11} x^3 + 2 a_{2} x^2 + 4 b_{9} x + 2$	$4$	$148$	$144$	$72$	$72$	$100\%$	$2$
2.2.8.32a	$2$	$16$	$2$	$8$	$32$	$[\frac{16}{7}, \frac{16}{7}, \frac{16}{7}]$	$[\frac{9}{7}, \frac{9}{7}, \frac{9}{7}]$	$\langle\frac{9}{14}, \frac{27}{28}, \frac{9}{8}\rangle$	$(\frac{9}{7}, \frac{9}{7}, \frac{9}{7})$	$x^8 + 4 b_{10} x^2 + 4 a_{9} x + 2$	$2$	$7$	$12$	$6$	$6$	$100\%$	$1$
2.2.8.32b	$2$	$16$	$2$	$8$	$32$	$[\frac{4}{3}, \frac{4}{3}, 3]$	$[\frac{1}{3}, \frac{1}{3}, 2]$	$\langle\frac{1}{6}, \frac{1}{4}, \frac{9}{8}\rangle$	$(\frac{1}{3}, \frac{1}{3}, 7)$	$x^8 + 4 b_{15} x^7 + 4 b_{13} x^5 + 4 b_{11} x^3 + 2 a_{2} x^2 + 4 a_{9} x + 8 c_{16} + 2$	$4$	$584$	$576$	$288$	$288$	$100\%$	$2$
2.2.8.32c	$2$	$16$	$2$	$8$	$32$	$[2, 2, \frac{5}{2}]$	$[1, 1, \frac{3}{2}]$	$\langle\frac{1}{2}, \frac{3}{4}, \frac{9}{8}\rangle$	$(1, 1, 3)$	$x^8 + 2 a_{6} x^6 + (2 b_{4} + 4 c_{12}) x^4 + 4 b_{11} x^3 + 4 a_{9} x + 4 c_{8} + 2$	$16$	$167$	$144$	$72$	$72$	$100\%$	$2$
2.2.8.32d	$2$	$16$	$2$	$8$	$32$	$[2, \frac{7}{3}, \frac{7}{3}]$	$[1, \frac{4}{3}, \frac{4}{3}]$	$\langle\frac{1}{2}, \frac{11}{12}, \frac{9}{8}\rangle$	$(1, \frac{5}{3}, \frac{5}{3})$	$x^8 + 2 a_{4} x^4 + 4 b_{10} x^2 + 4 a_{9} x + 4 c_{8} + 2$	$4$	$19$	$36$	$18$	$18$	$100\%$	$2$
2.2.8.34a	$2$	$16$	$2$	$8$	$34$	$[\frac{4}{3}, \frac{4}{3}, \frac{13}{4}]$	$[\frac{1}{3}, \frac{1}{3}, \frac{9}{4}]$	$\langle\frac{1}{6}, \frac{1}{4}, \frac{5}{4}\rangle$	$(\frac{1}{3}, \frac{1}{3}, 8)$	$x^8 + 4 b_{15} x^7 + 4 b_{13} x^5 + 4 b_{11} x^3 + (2 a_{2} + 8 c_{18}) x^2 + 8 b_{17} x + 2$	$4$	$784$	$768$	$384$	$384$	$100\%$	$2$
2.2.8.36a	$2$	$16$	$2$	$8$	$36$	$[\frac{18}{7}, \frac{18}{7}, \frac{18}{7}]$	$[\frac{11}{7}, \frac{11}{7}, \frac{11}{7}]$	$\langle\frac{11}{14}, \frac{33}{28}, \frac{11}{8}\rangle$	$(\frac{11}{7}, \frac{11}{7}, \frac{11}{7})$	$x^8 + 4 b_{12} x^4 + 4 a_{11} x^3 + 4 b_{10} x^2 + 2$	$2$	$26$	$48$	$24$	$24$	$100\%$	$1$
2.2.8.36b	$2$	$16$	$2$	$8$	$36$	$[2, 2, 3]$	$[1, 1, 2]$	$\langle\frac{1}{2}, \frac{3}{4}, \frac{11}{8}\rangle$	$(1, 1, 5)$	$x^8 + 4 b_{15} x^7 + 2 a_{6} x^6 + 4 b_{13} x^5 + 2 b_{4} x^4 + 4 a_{11} x^3 + 4 c_{8} + 8 c_{16} + 2$	$16$	$694$	$576$	$288$	$288$	$100\%$	$2$
2.2.8.36c	$2$	$16$	$2$	$8$	$36$	$[2, \frac{8}{3}, \frac{8}{3}]$	$[1, \frac{5}{3}, \frac{5}{3}]$	$\langle\frac{1}{2}, \frac{13}{12}, \frac{11}{8}\rangle$	$(1, \frac{7}{3}, \frac{7}{3})$	$x^8 + 4 b_{13} x^5 + 2 a_{4} x^4 + 4 a_{11} x^3 + 4 b_{10} x^2 + 4 c_{8} + 2$	$4$	$93$	$144$	$72$	$72$	$100\%$	$2$
2.2.8.40a	$2$	$16$	$2$	$8$	$40$	$[\frac{20}{7}, \frac{20}{7}, \frac{20}{7}]$	$[\frac{13}{7}, \frac{13}{7}, \frac{13}{7}]$	$\langle\frac{13}{14}, \frac{39}{28}, \frac{13}{8}\rangle$	$(\frac{13}{7}, \frac{13}{7}, \frac{13}{7})$	$x^8 + 4 b_{14} x^6 + 4 a_{13} x^5 + 4 b_{12} x^4 + 2$	$2$	$26$	$48$	$24$	$24$	$100\%$	$1$
2.2.8.40b	$2$	$16$	$2$	$8$	$40$	$[2, 2, \frac{7}{2}]$	$[1, 1, \frac{5}{2}]$	$\langle\frac{1}{2}, \frac{3}{4}, \frac{13}{8}\rangle$	$(1, 1, 7)$	$x^8 + 4 b_{15} x^7 + 2 a_{6} x^6 + 4 a_{13} x^5 + (2 b_{4} + 8 c_{20}) x^4 + 8 b_{19} x^3 + 8 b_{17} x + 4 c_{8} + 2$	$16$	$2468$	$2304$	$1152$	$1152$	$100\%$	$2$
2.2.8.40c	$2$	$16$	$2$	$8$	$40$	$[\frac{8}{3}, \frac{8}{3}, 3]$	$[\frac{5}{3}, \frac{5}{3}, 2]$	$\langle\frac{5}{6}, \frac{5}{4}, \frac{13}{8}\rangle$	$(\frac{5}{3}, \frac{5}{3}, 3)$	$x^8 + 4 b_{15} x^7 + 4 a_{13} x^5 + 4 b_{12} x^4 + 4 a_{10} x^2 + 8 c_{16} + 2$	$4$	$148$	$144$	$72$	$72$	$100\%$	$2$
2.2.8.40d	$2$	$16$	$2$	$8$	$40$	$[2, 3, 3]$	$[1, 2, 2]$	$\langle\frac{1}{2}, \frac{5}{4}, \frac{13}{8}\rangle$	$(1, 3, 3)$	$x^8 + 4 b_{15} x^7 + 4 b_{14} x^6 + 4 a_{13} x^5 + 2 a_{4} x^4 + 4 b_{10} x^2 + 4 c_{8} + 8 c_{16} + 2$	$16$	$536$	$576$	$288$	$288$	$100\%$	$2$
2.2.8.42a	$2$	$16$	$2$	$8$	$42$	$[2, 2, \frac{15}{4}]$	$[1, 1, \frac{11}{4}]$	$\langle\frac{1}{2}, \frac{3}{4}, \frac{7}{4}\rangle$	$(1, 1, 8)$	$x^8 + 4 b_{15} x^7 + (2 a_{6} + 8 c_{22}) x^6 + 8 b_{21} x^5 + 2 b_{4} x^4 + 8 b_{19} x^3 + 8 b_{17} x + 4 c_{8} + 2$	$16$	$3104$	$3072$	$1536$	$1536$	$100\%$	$2$
2.2.8.44a	$2$	$16$	$2$	$8$	$44$	$[\frac{8}{3}, \frac{8}{3}, \frac{7}{2}]$	$[\frac{5}{3}, \frac{5}{3}, \frac{5}{2}]$	$\langle\frac{5}{6}, \frac{5}{4}, \frac{15}{8}\rangle$	$(\frac{5}{3}, \frac{5}{3}, 5)$	$x^8 + 4 a_{15} x^7 + (4 b_{12} + 8 c_{20}) x^4 + 8 b_{19} x^3 + 4 a_{10} x^2 + 8 b_{17} x + 2$	$4$	$584$	$576$	$288$	$288$	$100\%$	$2$
2.2.8.44b	$2$	$16$	$2$	$8$	$44$	$[2, \frac{10}{3}, \frac{10}{3}]$	$[1, \frac{7}{3}, \frac{7}{3}]$	$\langle\frac{1}{2}, \frac{17}{12}, \frac{15}{8}\rangle$	$(1, \frac{11}{3}, \frac{11}{3})$	$x^8 + 4 a_{15} x^7 + 4 b_{14} x^6 + 2 a_{4} x^4 + 8 b_{18} x^2 + 8 b_{17} x + 4 c_{8} + 2$	$4$	$292$	$576$	$288$	$288$	$100\%$	$2$
2.2.8.44c	$2$	$16$	$2$	$8$	$44$	$[3, \frac{19}{6}, \frac{19}{6}]$	$[2, \frac{13}{6}, \frac{13}{6}]$	$\langle1, \frac{19}{12}, \frac{15}{8}\rangle$	$(2, \frac{7}{3}, \frac{7}{3})$	$x^8 + 4 a_{15} x^7 + 4 b_{14} x^6 + 4 b_{12} x^4 + 8 b_{17} x + 8 c_{16} + 2$	$4$	$100$	$192$	$96$	$96$	$100\%$	$2$
2.2.8.44d	$2$	$16$	$2$	$8$	$44$	$[2, 3, \frac{7}{2}]$	$[1, 2, \frac{5}{2}]$	$\langle\frac{1}{2}, \frac{5}{4}, \frac{15}{8}\rangle$	$(1, 3, 5)$	$x^8 + 4 a_{15} x^7 + 4 b_{14} x^6 + (2 a_{4} + 8 c_{20}) x^4 + 8 b_{19} x^3 + 4 a_{10} x^2 + 8 b_{17} x + 4 c_{8} + 8 c_{16} + 2$	$16$	$2176$	$1728$	$864$	$864$	$100\%$	$3$
2.2.8.48a	$2$	$16$	$2$	$8$	$48$	$[\frac{8}{3}, \frac{8}{3}, 4]$	$[\frac{5}{3}, \frac{5}{3}, 3]$	$\langle\frac{5}{6}, \frac{5}{4}, \frac{17}{8}\rangle$	$(\frac{5}{3}, \frac{5}{3}, 7)$	$x^8 + 8 b_{23} x^7 + 8 b_{21} x^5 + 4 b_{12} x^4 + 8 b_{19} x^3 + 4 a_{10} x^2 + 8 a_{17} x + 16 c_{24} + 2$	$4$	$2320$	$2304$	$1152$	$1152$	$100\%$	$2$
2.2.8.48b	$2$	$16$	$2$	$8$	$48$	$[3, \frac{7}{2}, \frac{7}{2}]$	$[2, \frac{5}{2}, \frac{5}{2}]$	$\langle1, \frac{7}{4}, \frac{17}{8}\rangle$	$(2, 3, 3)$	$x^8 + 4 b_{14} x^6 + (4 b_{12} + 8 c_{20}) x^4 + 8 b_{19} x^3 + 8 b_{18} x^2 + 8 a_{17} x + 8 c_{16} + 2$	$16$	$684$	$768$	$384$	$384$	$100\%$	$2$
2.2.8.48c	$2$	$16$	$2$	$8$	$48$	$[2, 3, 4]$	$[1, 2, 3]$	$\langle\frac{1}{2}, \frac{5}{4}, \frac{17}{8}\rangle$	$(1, 3, 7)$	$x^8 + 8 b_{23} x^7 + 4 b_{14} x^6 + 8 b_{21} x^5 + 2 a_{4} x^4 + 8 b_{19} x^3 + 4 a_{10} x^2 + 8 a_{17} x + 4 c_{8} + 8 c_{16} + 16 c_{24} + 2$	$16$	$7472$	$6912$	$3456$	$3456$	$100\%$	$3$
2.2.8.48d	$2$	$16$	$2$	$8$	$48$	$[2, \frac{7}{2}, \frac{15}{4}]$	$[1, \frac{5}{2}, \frac{11}{4}]$	$\langle\frac{1}{2}, \frac{3}{2}, \frac{17}{8}\rangle$	$(1, 4, 5)$	$x^8 + (4 b_{14} + 8 c_{22}) x^6 + 8 b_{21} x^5 + (2 a_{4} + 8 c_{20}) x^4 + 8 b_{19} x^3 + 8 b_{18} x^2 + 8 a_{17} x + 4 c_{8} + 2$	$16$	$2320$	$2304$	$1152$	$1152$	$100\%$	$3$
2.2.8.50a	$2$	$16$	$2$	$8$	$50$	$[\frac{8}{3}, \frac{8}{3}, \frac{17}{4}]$	$[\frac{5}{3}, \frac{5}{3}, \frac{13}{4}]$	$\langle\frac{5}{6}, \frac{5}{4}, \frac{9}{4}\rangle$	$(\frac{5}{3}, \frac{5}{3}, 8)$	$x^8 + 8 b_{23} x^7 + 8 b_{21} x^5 + 4 b_{12} x^4 + 8 b_{19} x^3 + (4 a_{10} + 16 c_{26}) x^2 + 16 b_{25} x + 2$	$4$	$3104$	$3072$	$1536$	$1536$	$100\%$	$2$
2.2.8.50b	$2$	$16$	$2$	$8$	$50$	$[2, 3, \frac{17}{4}]$	$[1, 2, \frac{13}{4}]$	$\langle\frac{1}{2}, \frac{5}{4}, \frac{9}{4}\rangle$	$(1, 3, 8)$	$x^8 + 8 b_{23} x^7 + 4 b_{14} x^6 + 8 b_{21} x^5 + 2 a_{4} x^4 + 8 b_{19} x^3 + (4 a_{10} + 16 c_{26}) x^2 + 16 b_{25} x + 4 c_{8} + 8 c_{16} + 2$	$16$	$9248$	$9216$	$4608$	$4608$	$100\%$	$3$
2.2.8.52a	$2$	$16$	$2$	$8$	$52$	$[3, \frac{23}{6}, \frac{23}{6}]$	$[2, \frac{17}{6}, \frac{17}{6}]$	$\langle1, \frac{23}{12}, \frac{19}{8}\rangle$	$(2, \frac{11}{3}, \frac{11}{3})$	$x^8 + 8 b_{22} x^6 + 8 b_{21} x^5 + 4 b_{12} x^4 + 8 a_{19} x^3 + 8 b_{18} x^2 + 8 c_{16} + 2$	$4$	$392$	$768$	$384$	$384$	$100\%$	$2$
2.2.8.52b	$2$	$16$	$2$	$8$	$52$	$[2, \frac{7}{2}, \frac{17}{4}]$	$[1, \frac{5}{2}, \frac{13}{4}]$	$\langle\frac{1}{2}, \frac{3}{2}, \frac{19}{8}\rangle$	$(1, 4, 7)$	$x^8 + 8 b_{23} x^7 + 4 b_{14} x^6 + 8 b_{21} x^5 + (2 a_{4} + 8 c_{20}) x^4 + 8 a_{19} x^3 + (8 b_{18} + 16 c_{26}) x^2 + 16 b_{25} x + 4 c_{8} + 2$	$16$	$9248$	$9216$	$4608$	$4608$	$100\%$	$3$
2.2.8.52c	$2$	$16$	$2$	$8$	$52$	$[3, \frac{7}{2}, 4]$	$[2, \frac{5}{2}, 3]$	$\langle1, \frac{7}{4}, \frac{19}{8}\rangle$	$(2, 3, 5)$	$x^8 + 8 b_{23} x^7 + 4 a_{14} x^6 + 8 b_{21} x^5 + (4 b_{12} + 8 c_{20}) x^4 + 8 a_{19} x^3 + 8 b_{18} x^2 + 8 c_{16} + 16 c_{24} + 2$	$16$	$2712$	$2304$	$1152$	$1152$	$100\%$	$3$
2.2.8.54a	$2$	$16$	$2$	$8$	$54$	$[2, \frac{7}{2}, \frac{9}{2}]$	$[1, \frac{5}{2}, \frac{7}{2}]$	$\langle\frac{1}{2}, \frac{3}{2}, \frac{5}{2}\rangle$	$(1, 4, 8)$	$x^8 + 8 b_{23} x^7 + 4 b_{14} x^6 + 8 b_{21} x^5 + (2 a_{4} + 8 c_{20} + 16 c_{28}) x^4 + 16 b_{27} x^3 + 8 b_{18} x^2 + 16 b_{25} x + 4 c_{8} + 2$	$16$	$12744$	$12288$	$6144$	$6144$	$100\%$	$3$
2.2.8.56a	$2$	$16$	$2$	$8$	$56$	$[3, \frac{7}{2}, \frac{9}{2}]$	$[2, \frac{5}{2}, \frac{7}{2}]$	$\langle1, \frac{7}{4}, \frac{21}{8}\rangle$	$(2, 3, 7)$	$x^8 + 8 b_{23} x^7 + 4 a_{14} x^6 + 8 a_{21} x^5 + (4 b_{12} + 8 c_{20} + 16 c_{28}) x^4 + 16 b_{27} x^3 + 8 b_{18} x^2 + 16 b_{25} x + 8 c_{16} + 2$	$16$	$9504$	$9216$	$4608$	$4608$	$100\%$	$3$
2.2.8.56b	$2$	$16$	$2$	$8$	$56$	$[3, 4, \frac{17}{4}]$	$[2, 3, \frac{13}{4}]$	$\langle1, 2, \frac{21}{8}\rangle$	$(2, 4, 5)$	$x^8 + 8 b_{23} x^7 + 8 b_{22} x^6 + 8 a_{21} x^5 + 4 b_{12} x^4 + (8 b_{18} + 16 c_{26}) x^2 + 16 b_{25} x + 8 c_{16} + 16 c_{24} + 2$	$16$	$3104$	$3072$	$1536$	$1536$	$100\%$	$3$
2.2.8.58a	$2$	$16$	$2$	$8$	$58$	$[3, \frac{7}{2}, \frac{19}{4}]$	$[2, \frac{5}{2}, \frac{15}{4}]$	$\langle1, \frac{7}{4}, \frac{11}{4}\rangle$	$(2, 3, 8)$	$x^8 + 8 b_{23} x^7 + (4 a_{14} + 16 c_{30}) x^6 + 16 b_{29} x^5 + (4 b_{12} + 8 c_{20}) x^4 + 16 b_{27} x^3 + 8 b_{18} x^2 + 16 b_{25} x + 8 c_{16} + 2$	$16$	$12352$	$12288$	$6144$	$6144$	$100\%$	$3$
2.2.8.60a	$2$	$16$	$2$	$8$	$60$	$[3, 4, \frac{19}{4}]$	$[2, 3, \frac{15}{4}]$	$\langle1, 2, \frac{23}{8}\rangle$	$(2, 4, 7)$	$x^8 + 8 a_{23} x^7 + (8 b_{22} + 16 c_{30}) x^6 + 16 b_{29} x^5 + 4 b_{12} x^4 + 16 b_{27} x^3 + 8 b_{18} x^2 + 16 b_{25} x + 8 c_{16} + 16 c_{24} + 2$	$16$	$12352$	$12288$	$6144$	$6144$	$100\%$	$3$
2.2.8.62a	$2$	$16$	$2$	$8$	$62$	$[3, 4, 5]$	$[2, 3, 4]$	$\langle1, 2, 3\rangle$	$(2, 4, 8)$	$x^8 + 16 b_{31} x^7 + 8 b_{22} x^6 + 16 b_{29} x^5 + 4 b_{12} x^4 + 16 b_{27} x^3 + 8 b_{18} x^2 + 16 b_{25} x + 8 c_{16} + 16 c_{24} + 32 c_{32} + 2$	$16$	$17076$	$16384$	$8192$	$8192$	$100\%$	$3$
2.1.16.16a	$2$	$16$	$1$	$16$	$16$	$[\frac{16}{15}, \frac{16}{15}, \frac{16}{15}, \frac{16}{15}]$	$[\frac{1}{15}, \frac{1}{15}, \frac{1}{15}, \frac{1}{15}]$	$\langle\frac{1}{30}, \frac{1}{20}, \frac{7}{120}, \frac{1}{16}\rangle$	$(\frac{1}{15}, \frac{1}{15}, \frac{1}{15}, \frac{1}{15})$	$x^{16} + 2 a_{1} x + 2$	$1$	$1$	$1$	$1$	$1$	$100\%$	$1$	$1$

Next Download displayed columns for results to

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Learn more

Refine search

Results (1-50 of 389 matches)

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.