Sato-Tate group search results

Results (32 matches)

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Label	Wt	Deg	$\mathrm{dim}_{\mathbb{R}}$	$\mathrm{G}^0$	Name	$\mathrm{G}/\mathrm{G}^0$	$\mathrm{Pr}[t\!=\!0]$	$\mathrm{E}[a_1^2]$	$\mathrm{E}[a_1^4]$	$\mathrm{E}[a_1^6]$	$\mathrm{E}[a_1^8]$	$\mathrm{E}[a_1^{10}]$	$\mathrm{E}[a_1^{12}]$	$\mathrm{E}[a_2]$	$\mathrm{E}[a_2^2]$	$\mathrm{E}[a_2^3]$	$\mathrm{E}[a_2^4]$	$\mathrm{E}[a_2^5]$	$\mathrm{E}[a_2^6]$	$\mathrm{E}[a_3^2]$	$\mathrm{E}[a_3^4]$	$\mathrm{E}[a_3^6]$	Maximal	Rational	Diagonal
1.4.F.1.1a	$1$	$4$	$1$	$\mathrm{U}(1)_{2}$	$C_1$	$1$	$0$	$8$	$96$	$1280$	$17920$	$258048$	$258048$	$4$	$18$	$88$	$454$	$2424$	$13236$					✓	$[1, 8, 11, 34, 80, 56, 104, 301, 368, 192]$
1.4.F.2.1a	$1$	$4$	$1$	$\mathrm{U}(1)_{2}$	$J(C_1)$	$2$	$1/2$	$4$	$48$	$640$	$8960$	$129024$	$129024$	$1$	$11$	$40$	$235$	$1196$	$6650$					✓	$[1, 4, 10, 19, 40, 46, 52, 163, 184, 146]$
1.4.F.2.1b	$1$	$4$	$1$	$\mathrm{U}(1)_{2}$	$C_2$	$2$	$1/2$	$4$	$48$	$640$	$8960$	$129024$	$129024$	$2$	$10$	$44$	$230$	$1212$	$6628$					✓	$[1, 4, 7, 18, 40, 32, 52, 153, 184, 104]$
1.4.F.2.1c	$1$	$4$	$1$	$\mathrm{U}(1)_{2}$	$C_{2,1}$	$2$	$1/2$	$4$	$48$	$640$	$8960$	$129024$	$129024$	$3$	$11$	$48$	$235$	$1228$	$6650$					✓	$[1, 4, 6, 19, 40, 30, 52, 151, 184, 98]$
1.4.F.3.1a	$1$	$4$	$1$	$\mathrm{U}(1)_{2}$	$C_3$	$3$	$0$	$4$	$36$	$440$	$6020$	$86184$	$86184$	$2$	$8$	$34$	$164$	$842$	$4506$					✓	$[1, 4, 5, 12, 28, 20, 36, 101, 124, 66]$
1.4.F.4.1a	$1$	$4$	$1$	$\mathrm{U}(1)_{2}$	$C_{4,1}$	$4$	$3/4$	$2$	$24$	$320$	$4480$	$64512$	$64512$	$1$	$5$	$22$	$115$	$606$	$3314$					✓	$[1, 2, 4, 9, 20, 16, 26, 77, 92, 52]$
1.4.F.4.1b	$1$	$4$	$1$	$\mathrm{U}(1)_{2}$	$C_4$	$4$	$1/4$	$4$	$36$	$400$	$5040$	$68544$	$68544$	$2$	$8$	$32$	$150$	$732$	$3776$					✓	$[1, 4, 5, 12, 24, 18, 28, 79, 96, 54]$
1.4.F.4.2a	$1$	$4$	$1$	$\mathrm{U}(1)_{2}$	$D_2$	$4$	$3/4$	$2$	$24$	$320$	$4480$	$64512$	$64512$	$1$	$6$	$22$	$118$	$606$	$3324$					✓	$[1, 2, 5, 10, 20, 20, 26, 79, 92, 60]$
1.4.F.4.2b	$1$	$4$	$1$	$\mathrm{U}(1)_{2}$	$J(C_2)$	$4$	$3/4$	$2$	$24$	$320$	$4480$	$64512$	$64512$	$1$	$7$	$22$	$123$	$606$	$3346$					✓	$[1, 2, 6, 11, 20, 26, 26, 83, 92, 78]$
1.4.F.4.2c	$1$	$4$	$1$	$\mathrm{U}(1)_{2}$	$D_{2,1}$	$4$	$3/4$	$2$	$24$	$320$	$4480$	$64512$	$64512$	$2$	$7$	$26$	$123$	$622$	$3346$					✓	$[1, 2, 4, 11, 20, 18, 26, 77, 92, 54]$
1.4.F.6.1a	$1$	$4$	$1$	$\mathrm{U}(1)_{2}$	$D_3$	$6$	$1/2$	$2$	$18$	$220$	$3010$	$43092$	$43092$	$1$	$5$	$17$	$85$	$421$	$2263$					✓	$[1, 2, 4, 7, 14, 14, 18, 53, 62, 41]$
1.4.F.6.1b	$1$	$4$	$1$	$\mathrm{U}(1)_{2}$	$D_{3,2}$	$6$	$1/2$	$2$	$18$	$220$	$3010$	$43092$	$43092$	$2$	$6$	$21$	$90$	$437$	$2285$					✓	$[1, 2, 3, 8, 14, 12, 18, 51, 62, 35]$
1.4.F.6.2a	$1$	$4$	$1$	$\mathrm{U}(1)_{2}$	$J(C_3)$	$6$	$1/2$	$2$	$18$	$220$	$3010$	$43092$	$43092$	$1$	$5$	$16$	$85$	$416$	$2264$					✓	$[1, 2, 4, 7, 14, 16, 18, 55, 62, 50]$
1.4.F.6.2b	$1$	$4$	$1$	$\mathrm{U}(1)_{2}$	$C_{6,1}$	$6$	$1/2$	$2$	$18$	$220$	$3010$	$43092$	$43092$	$1$	$5$	$18$	$85$	$426$	$2264$					✓	$[1, 2, 4, 7, 14, 12, 18, 51, 62, 34]$
1.4.F.6.2c	$1$	$4$	$1$	$\mathrm{U}(1)_{2}$	$C_6$	$6$	$1/6$	$4$	$36$	$400$	$4900$	$63504$	$63504$	$2$	$8$	$32$	$148$	$712$	$3586$					✓	$[1, 4, 5, 12, 24, 16, 28, 73, 80, 42]$
1.4.F.8.2a	$1$	$4$	$1$	$\mathrm{U}(1)_{2}$	$J(C_4)$	$8$	$5/8$	$2$	$18$	$200$	$2520$	$34272$	$34272$	$1$	$5$	$16$	$79$	$366$	$1904$					✓	$[1, 2, 4, 7, 12, 14, 14, 43, 48, 40]$
1.4.F.8.3a	$1$	$4$	$1$	$\mathrm{U}(1)_{2}$	$D_{4,1}$	$8$	$7/8$	$1$	$12$	$160$	$2240$	$32256$	$32256$	$1$	$4$	$13$	$63$	$311$	$1678$					✓	$[1, 1, 3, 6, 10, 11, 13, 40, 46, 31]$
1.4.F.8.3b	$1$	$4$	$1$	$\mathrm{U}(1)_{2}$	$D_4$	$8$	$5/8$	$2$	$18$	$200$	$2520$	$34272$	$34272$	$1$	$5$	$16$	$78$	$366$	$1898$					✓	$[1, 2, 4, 7, 12, 13, 14, 42, 48, 35]$
1.4.F.8.3c	$1$	$4$	$1$	$\mathrm{U}(1)_{2}$	$D_{4,2}$	$8$	$5/8$	$2$	$18$	$200$	$2520$	$34272$	$34272$	$2$	$6$	$20$	$83$	$382$	$1920$					✓	$[1, 2, 3, 8, 12, 11, 14, 40, 48, 29]$
1.4.F.8.5a	$1$	$4$	$1$	$\mathrm{U}(1)_{2}$	$J(D_2)$	$8$	$7/8$	$1$	$12$	$160$	$2240$	$32256$	$32256$	$1$	$5$	$13$	$67$	$311$	$1694$					✓	$[1, 1, 4, 7, 10, 16, 13, 43, 46, 44]$
1.4.F.12.3a	$1$	$4$	$1$	$\mathrm{U}(1)_{2}$	$T$	$12$	$1/4$	$2$	$12$	$120$	$1540$	$21672$	$21672$	$1$	$4$	$12$	$52$	$236$	$1202$					✓	$[1, 2, 3, 4, 8, 8, 10, 27, 32, 22]$
1.4.F.12.4a	$1$	$4$	$1$	$\mathrm{U}(1)_{2}$	$J(D_3)$	$12$	$3/4$	$1$	$9$	$110$	$1505$	$21546$	$21546$	$1$	$4$	$10$	$48$	$216$	$1153$					✓	$[1, 1, 3, 5, 7, 11, 9, 29, 31, 30]$
1.4.F.12.4b	$1$	$4$	$1$	$\mathrm{U}(1)_{2}$	$D_{6,1}$	$12$	$3/4$	$1$	$9$	$110$	$1505$	$21546$	$21546$	$1$	$4$	$11$	$48$	$221$	$1153$					✓	$[1, 1, 3, 5, 7, 9, 9, 27, 31, 22]$
1.4.F.12.4c	$1$	$4$	$1$	$\mathrm{U}(1)_{2}$	$D_6$	$12$	$7/12$	$2$	$18$	$200$	$2450$	$31752$	$31752$	$1$	$5$	$16$	$77$	$356$	$1803$					✓	$[1, 2, 4, 7, 12, 12, 14, 39, 40, 29]$
1.4.F.12.4d	$1$	$4$	$1$	$\mathrm{U}(1)_{2}$	$D_{6,2}$	$12$	$7/12$	$2$	$18$	$200$	$2450$	$31752$	$31752$	$2$	$6$	$20$	$82$	$372$	$1825$					✓	$[1, 2, 3, 8, 12, 10, 14, 37, 40, 23]$
1.4.F.12.5a	$1$	$4$	$1$	$\mathrm{U}(1)_{2}$	$J(C_6)$	$12$	$7/12$	$2$	$18$	$200$	$2450$	$31752$	$31752$	$1$	$5$	$16$	$77$	$356$	$1804$					✓	$[1, 2, 4, 7, 12, 12, 14, 39, 40, 30]$
1.4.F.16.11a	$1$	$4$	$1$	$\mathrm{U}(1)_{2}$	$J(D_4)$	$16$	$13/16$	$1$	$9$	$100$	$1260$	$17136$	$17136$	$1$	$4$	$10$	$45$	$191$	$973$					✓	$[1, 1, 3, 5, 6, 10, 7, 23, 24, 25]$
1.4.F.24.12a	$1$	$4$	$1$	$\mathrm{U}(1)_{2}$	$O_1$	$24$	$5/8$	$1$	$6$	$60$	$770$	$10836$	$10836$	$1$	$3$	$8$	$30$	$126$	$617$					✓	$[1, 1, 2, 3, 4, 5, 5, 14, 16, 12]$
1.4.F.24.12b	$1$	$4$	$1$	$\mathrm{U}(1)_{2}$	$O$	$24$	$3/8$	$2$	$12$	$100$	$1050$	$12852$	$12852$	$1$	$4$	$11$	$45$	$181$	$837$					✓	$[1, 2, 3, 4, 6, 7, 6, 16, 18, 16]$
1.4.F.24.13a	$1$	$4$	$1$	$\mathrm{U}(1)_{2}$	$J(T)$	$24$	$5/8$	$1$	$6$	$60$	$770$	$10836$	$10836$	$1$	$3$	$7$	$29$	$121$	$612$					✓	$[1, 1, 2, 3, 4, 6, 5, 15, 16, 16]$
1.4.F.24.14a	$1$	$4$	$1$	$\mathrm{U}(1)_{2}$	$J(D_6)$	$24$	$19/24$	$1$	$9$	$100$	$1225$	$15876$	$15876$	$1$	$4$	$10$	$44$	$186$	$923$				✓	✓	$[1, 1, 3, 5, 6, 9, 7, 21, 20, 20]$
1.4.F.48.48a	$1$	$4$	$1$	$\mathrm{U}(1)_{2}$	$J(O)$	$48$	$11/16$	$1$	$6$	$50$	$525$	$6426$	$6426$	$1$	$3$	$7$	$26$	$96$	$432$				✓	✓	$[1, 1, 2, 3, 3, 5, 3, 9, 9, 11]$

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