Sato-Tate group search results

Results (12 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
1.4.F.8.2a	$1$	$4$	$1$	$\mathrm{U}(1)_{2}$	$J(C_4)$	$8$	$5/8$	$2$	$18$	$200$	$2520$	$34272$	$34272$	$1$	$5$	$16$	$79$	$366$	$1904$					✓	$[1, 2, 4, 7, 12, 14, 14, 43, 48, 40]$
1.6.H.8.2a	$1$	$6$	$3$	$\mathrm{U}(1)^3$	$H_{c,at}$	$8$	$3/8$	$2$	$18$	$290$	$6230$	$154602$	$154602$	$2$	$7$	$38$	$293$	$2822$	$30805$	$7$	$699$	$142000$	✓	✓	$[1, 2, 4, 3, 7, 22, 23, 33, 44, 20, 15, 101, 110, 240, 450, 215, 228, 498, 416, 112]$
1.6.J.8.2a	$1$	$6$	$4$	$\mathrm{U}(1)\times\mathrm{SU}(2)_2$	$J_2(E_4)$	$8$	$1/8$	$3$	$27$	$380$	$6923$	$148260$	$148260$	$2$	$9$	$51$	$371$	$3198$	$31103$	$12$	$858$	$132960$		✓	$[1, 3, 6, 5, 8, 28, 27, 34, 47, 26, 18, 97, 106, 207, 368, 187, 178, 394, 321, 109]$
1.6.K.8.2a	$1$	$6$	$4$	$\mathrm{SU}(2)\times\mathrm{U}(1)_2$	$\mathrm{SU}(2)\times J(C_4)$	$8$	$0$	$3$	$32$	$535$	$10934$	$251874$	$251874$	$2$	$10$	$65$	$538$	$5077$	$52257$	$13$	$1310$	$228720$		✓	$[1, 3, 7, 6, 10, 42, 41, 54, 79, 33, 24, 162, 176, 364, 652, 294, 309, 669, 517, 145]$
1.6.L.8.2a	$1$	$6$	$6$	$\mathrm{U}(1)\times\mathrm{U}(1)_2$	$L(J(C_4),C_{4,1})$	$8$	$1/4$	$3$	$33$	$660$	$17115$	$491148$	$491148$	$2$	$10$	$71$	$694$	$7917$	$97537$	$13$	$1881$	$485860$		✓	$[1, 3, 7, 6, 11, 54, 61, 87, 143, 65, 35, 308, 372, 867, 1712, 852, 873, 2074, 1770, 505]$
1.6.L.8.2b	$1$	$6$	$6$	$\mathrm{U}(1)\times\mathrm{U}(1)_2$	$L(J(C_4),J(C_2))$	$8$	$1/4$	$3$	$33$	$660$	$17115$	$491148$	$491148$	$2$	$10$	$71$	$694$	$7917$	$97537$	$15$	$1905$	$486180$		✓	$[1, 3, 7, 8, 11, 54, 63, 89, 149, 79, 37, 308, 394, 871, 1712, 882, 877, 2136, 1800, 587]$
1.6.L.8.2c	$1$	$6$	$6$	$\mathrm{U}(1)\times\mathrm{U}(1)_2$	$L_2(C_{4,1})$	$8$	$3/8$	$3$	$39$	$780$	$19075$	$521388$	$521388$	$2$	$10$	$77$	$754$	$8397$	$101047$	$13$	$1977$	$493540$		✓	$[1, 3, 7, 6, 13, 62, 63, 87, 143, 61, 43, 330, 380, 875, 1712, 860, 867, 2082, 1790, 513]$
1.6.L.8.2d	$1$	$6$	$6$	$\mathrm{U}(1)\times\mathrm{U}(1)_2$	$L(J(C_4),C_4)$	$8$	$1/2$	$3$	$45$	$930$	$22435$	$595098$	$595098$	$2$	$12$	$95$	$934$	$10197$	$118947$	$16$	$2466$	$569440$		✓	$[1, 3, 9, 7, 15, 76, 78, 108, 173, 73, 46, 376, 432, 975, 1884, 911, 930, 2184, 1838, 517]$
1.6.L.8.2e	$1$	$6$	$6$	$\mathrm{U}(1)\times\mathrm{U}(1)_2$	$L_1(J(C_4))$	$8$	$0$	$4$	$48$	$940$	$22470$	$595224$	$595224$	$2$	$12$	$95$	$934$	$10197$	$118947$	$18$	$2490$	$569760$		✓	$[1, 4, 9, 10, 16, 76, 83, 110, 180, 87, 50, 376, 456, 980, 1884, 942, 935, 2248, 1871, 600]$
1.6.L.8.2f	$1$	$6$	$6$	$\mathrm{U}(1)\times\mathrm{U}(1)_2$	$L_2(C_4)$	$8$	$1/8$	$5$	$63$	$1130$	$24955$	$629370$	$629370$	$3$	$17$	$123$	$1091$	$11113$	$124451$	$24$	$2754$	$582240$		✓	$[1, 5, 12, 9, 18, 88, 83, 110, 175, 72, 54, 399, 440, 989, 1884, 925, 926, 2192, 1865, 531]$
1.6.N.8.2a	$1$	$6$	$1$	$\mathrm{U}(1)_{3}$	$J_s(A(1,4)_2)$	$8$	$1/2$	$3$	$63$	$1830$	$57435$	$1860138$	$1860138$	$2$	$16$	$161$	$2002$	$26597$	$363733$	$22$	$5910$	$1932070$		✓	$[1, 3, 13, 11, 23, 160, 187, 295, 527, 236, 108, 1134, 1436, 3573, 7392, 3853, 3968, 9820, 8748, 2589]$
1.6.N.8.2b	$1$	$6$	$1$	$\mathrm{U}(1)_{3}$	$A(2,4)$	$8$	$0$	$6$	$102$	$2460$	$68390$	$2057076$	$2057076$	$3$	$23$	$225$	$2555$	$31393$	$405617$	$36$	$7244$	$2086980$		✓	$[1, 6, 18, 18, 33, 208, 230, 334, 590, 264, 136, 1259, 1568, 3770, 7664, 3990, 4051, 10048, 8876, 2702]$