Sato-Tate group search results

Results (1-50 of 52 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.A.1.1a	$1$	$4$	$10$	$\mathrm{USp}(4)$	$\mathrm{USp}(4)$	$1$	$0$	$1$	$3$	$14$	$84$	$594$	$594$	$1$	$2$	$4$	$10$	$27$	$82$				✓	✓	$[1, 1, 1, 1, 1, 1, 1, 1, 1, 1]$
1.4.B.1.1a	$1$	$4$	$6$	$\mathrm{SU}(2)\times\mathrm{SU}(2)$	$\mathrm{SU}(2)\times\mathrm{SU}(2)$	$1$	$0$	$2$	$10$	$70$	$588$	$5544$	$5544$	$2$	$5$	$14$	$44$	$152$	$569$					✓	$[1, 2, 2, 3, 4, 3, 4, 6, 6, 4]$
1.4.B.2.1a	$1$	$4$	$6$	$\mathrm{SU}(2)\times\mathrm{SU}(2)$	$N(\mathrm{SU}(2)\times\mathrm{SU}(2))$	$2$	$1/2$	$1$	$5$	$35$	$294$	$2772$	$2772$	$1$	$3$	$7$	$23$	$76$	$287$				✓	✓	$[1, 1, 2, 2, 2, 3, 2, 4, 3, 4]$
1.4.C.1.1a	$1$	$4$	$4$	$\mathrm{U}(1)\times\mathrm{SU}(2)$	$\mathrm{U}(1)\times\mathrm{SU}(2)$	$1$	$0$	$3$	$20$	$175$	$1764$	$19404$	$19404$	$2$	$6$	$20$	$76$	$312$	$1364$					✓	$[1, 3, 3, 6, 10, 6, 10, 21, 21, 10]$
1.4.C.2.1a	$1$	$4$	$4$	$\mathrm{U}(1)\times\mathrm{SU}(2)$	$N(\mathrm{U}(1)\times\mathrm{SU}(2))$	$2$	$0$	$2$	$11$	$90$	$889$	$9723$	$9723$	$2$	$5$	$14$	$46$	$172$	$714$				✓	✓	$[1, 2, 2, 4, 5, 4, 6, 11, 11, 6]$
1.4.D.1.1a	$1$	$4$	$2$	$\mathrm{U}(1)\times\mathrm{U}(1)$	$F$	$1$	$0$	$4$	$36$	$400$	$4900$	$63504$	$63504$	$2$	$8$	$32$	$148$	$712$	$3584$				✓	✓	$[1, 4, 5, 12, 24, 16, 28, 73, 80, 40]$
1.4.D.2.1a	$1$	$4$	$2$	$\mathrm{U}(1)\times\mathrm{U}(1)$	$F_{ab}$	$2$	$1/2$	$2$	$18$	$200$	$2450$	$31752$	$31752$	$2$	$6$	$20$	$82$	$372$	$1824$					✓	$[1, 2, 3, 8, 12, 10, 14, 37, 40, 22]$
1.4.D.2.1b	$1$	$4$	$2$	$\mathrm{U}(1)\times\mathrm{U}(1)$	$F_a$	$2$	$0$	$3$	$21$	$210$	$2485$	$31878$	$31878$	$2$	$6$	$20$	$82$	$372$	$1824$					✓	$[1, 3, 3, 7, 12, 9, 15, 37, 42, 21]$
1.4.D.4.1a	$1$	$4$	$2$	$\mathrm{U}(1)\times\mathrm{U}(1)$	$F_{ac}$	$4$	$3/4$	$1$	$9$	$100$	$1225$	$15876$	$15876$	$1$	$3$	$10$	$41$	$186$	$912$				✓	✓	$[1, 1, 2, 4, 6, 5, 7, 19, 20, 11]$
1.4.D.4.2a	$1$	$4$	$2$	$\mathrm{U}(1)\times\mathrm{U}(1)$	$F_{a,b}$	$4$	$1/4$	$2$	$12$	$110$	$1260$	$16002$	$16002$	$2$	$5$	$14$	$49$	$202$	$944$				✓	✓	$[1, 2, 2, 5, 6, 6, 8, 19, 22, 12]$
1.4.E.1.1a	$1$	$4$	$3$	$\mathrm{SU}(2)_{2}$	$E_1$	$1$	$0$	$4$	$32$	$320$	$3584$	$43008$	$43008$	$3$	$10$	$37$	$150$	$654$	$3012$					✓	$[1, 4, 5, 10, 20, 14, 20, 49, 56, 30]$
1.4.E.2.1a	$1$	$4$	$3$	$\mathrm{SU}(2)_{2}$	$E_2$	$2$	$1/2$	$2$	$16$	$160$	$1792$	$21504$	$21504$	$1$	$6$	$17$	$78$	$322$	$1516$					✓	$[1, 2, 5, 6, 10, 14, 10, 29, 28, 30]$
1.4.E.2.1b	$1$	$4$	$3$	$\mathrm{SU}(2)_{2}$	$J(E_1)$	$2$	$1/2$	$2$	$16$	$160$	$1792$	$21504$	$21504$	$2$	$6$	$20$	$78$	$332$	$1516$					✓	$[1, 2, 3, 6, 10, 8, 10, 25, 28, 16]$
1.4.E.3.1a	$1$	$4$	$3$	$\mathrm{SU}(2)_{2}$	$E_3$	$3$	$0$	$2$	$12$	$110$	$1204$	$14364$	$14364$	$1$	$4$	$13$	$52$	$222$	$1014$					✓	$[1, 2, 3, 4, 8, 6, 8, 17, 20, 12]$
1.4.E.4.1a	$1$	$4$	$3$	$\mathrm{SU}(2)_{2}$	$E_4$	$4$	$1/4$	$2$	$12$	$100$	$1008$	$11424$	$11424$	$1$	$4$	$11$	$46$	$182$	$824$					✓	$[1, 2, 3, 4, 6, 8, 6, 15, 16, 16]$
1.4.E.4.2a	$1$	$4$	$3$	$\mathrm{SU}(2)_{2}$	$J(E_2)$	$4$	$3/4$	$1$	$8$	$80$	$896$	$10752$	$10752$	$1$	$4$	$10$	$42$	$166$	$768$					✓	$[1, 1, 3, 4, 5, 8, 5, 15, 14, 16]$
1.4.E.6.1a	$1$	$4$	$3$	$\mathrm{SU}(2)_{2}$	$J(E_3)$	$6$	$1/2$	$1$	$6$	$55$	$602$	$7182$	$7182$	$1$	$3$	$8$	$29$	$116$	$517$					✓	$[1, 1, 2, 3, 4, 4, 4, 9, 10, 7]$
1.4.E.6.2a	$1$	$4$	$3$	$\mathrm{SU}(2)_{2}$	$E_6$	$6$	$1/6$	$2$	$12$	$100$	$980$	$10584$	$10584$	$1$	$4$	$11$	$44$	$172$	$754$					✓	$[1, 2, 3, 4, 6, 6, 6, 13, 12, 12]$
1.4.E.8.3a	$1$	$4$	$3$	$\mathrm{SU}(2)_{2}$	$J(E_4)$	$8$	$5/8$	$1$	$6$	$50$	$504$	$5712$	$5712$	$1$	$3$	$7$	$26$	$96$	$422$				✓	✓	$[1, 1, 2, 3, 3, 5, 3, 8, 8, 9]$
1.4.E.12.4a	$1$	$4$	$3$	$\mathrm{SU}(2)_{2}$	$J(E_6)$	$12$	$7/12$	$1$	$6$	$50$	$490$	$5292$	$5292$	$1$	$3$	$7$	$25$	$91$	$387$				✓	✓	$[1, 1, 2, 3, 3, 4, 3, 7, 6, 7]$
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	$1$	$4$	$1$	$\mathrm{U}(1)_{2}$	$J(T)$	$24$	$5/8$	$1$	$6$	$60$	$770$	$10836$	$10836$	$1$	$3$	$7$	$29$	$121$	$612$					✓	$[1, 1, 2, 3, 4, 6, 5, 15, 16, 16]$

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