Sato-Tate group search results

Results (11 matches)

 

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
1.2.B.1.1a	$1$	$2$	$1$	$\mathrm{U}(1)$	$\mathrm{U}(1)$	$1$	$0$	$2$	$6$	$20$	$70$	$252$	$252$											✓
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.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.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.24.13a	$1$	$4$	$1$	$\mathrm{U}(1)_{2}$	$J(T)$	$24$	$5/8$	$1$	$6$	$60$	$770$	$10836$	$10836$	$1$	$3$	$7$	$29$	$121$	$612$					✓	$[1, 1, 2, 3, 4, 6, 5, 15, 16, 16]$
1.4.F.48.48a	$1$	$4$	$1$	$\mathrm{U}(1)_{2}$	$J(O)$	$48$	$11/16$	$1$	$6$	$50$	$525$	$6426$	$6426$	$1$	$3$	$7$	$26$	$96$	$432$				✓	✓	$[1, 1, 2, 3, 3, 5, 3, 9, 9, 11]$
1.6.B.2.1a	$1$	$6$	$9$	$\mathrm{U}(3)$	$N(\mathrm{U}(3))$	$2$	$1/2$	$1$	$6$	$60$	$805$	$12978$	$12978$	$1$	$3$	$11$	$58$	$382$	$2922$	$3$	$116$	$10630$	✓	✓	$[1, 1, 2, 2, 3, 4, 5, 6, 6, 6, 3, 9, 11, 13, 20, 12, 11, 20, 16, 10]$
1.6.N.144.182a	$1$	$6$	$1$	$\mathrm{U}(1)_{3}$	$J(E(72))$	$144$	$5/9$	$1$	$6$	$110$	$3220$	$103446$	$103446$	$1$	$3$	$14$	$125$	$1516$	$20317$	$3$	$347$	$107580$		✓	$[1, 1, 2, 2, 3, 9, 13, 21, 31, 20, 7, 65, 86, 202, 411, 225, 230, 559, 498, 166]$
1.6.N.336.208a	$1$	$6$	$1$	$\mathrm{U}(1)_{3}$	$J(E(168))$	$336$	$2/3$	$1$	$6$	$70$	$1540$	$45486$	$45486$	$1$	$3$	$12$	$77$	$746$	$9117$	$3$	$183$	$47040$	✓	✓	$[1, 1, 2, 2, 3, 5, 8, 12, 15, 13, 5, 29, 42, 88, 178, 103, 106, 249, 221, 86]$
1.6.N.432.734a	$1$	$6$	$1$	$\mathrm{U}(1)_{3}$	$J(E(216))$	$432$	$17/27$	$1$	$6$	$70$	$1400$	$37926$	$37926$	$1$	$3$	$12$	$75$	$676$	$7717$	$3$	$167$	$38120$	✓	✓	$[1, 1, 2, 2, 3, 5, 7, 11, 13, 10, 5, 25, 32, 70, 141, 79, 86, 191, 172, 60]$