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.E.1.1a	$1$	$4$	$3$	$\mathrm{SU}(2)_{2}$	$E_1$	$1$	$0$	$4$	$32$	$320$	$3584$	$43008$	$43008$	$3$	$10$	$37$	$150$	$654$	$3012$					✓	$[1, 4, 5, 10, 20, 14, 20, 49, 56, 30]$
1.6.G.2.1a	$1$	$6$	$5$	$\mathrm{U}(1)^2\times\mathrm{SU}(2)$	$F_{ab}\times \mathrm{SU}(2)$	$2$	$0$	$3$	$32$	$535$	$10864$	$246204$	$246204$	$3$	$13$	$75$	$567$	$5133$	$51639$	$14$	$1316$	$223520$		✓	$[1, 3, 8, 5, 11, 42, 40, 58, 75, 30, 25, 161, 169, 347, 620, 271, 291, 591, 456, 113]$
1.6.K.6.1a	$1$	$6$	$4$	$\mathrm{SU}(2)\times\mathrm{U}(1)_2$	$\mathrm{SU}(2)\times D_3$	$6$	$0$	$3$	$32$	$555$	$11984$	$291144$	$291144$	$2$	$10$	$66$	$560$	$5492$	$58886$	$13$	$1370$	$263715$		✓	$[1, 3, 7, 6, 10, 44, 43, 58, 87, 35, 28, 188, 206, 440, 800, 362, 380, 834, 648, 174]$
1.6.K.6.1b	$1$	$6$	$4$	$\mathrm{SU}(2)\times\mathrm{U}(1)_2$	$\mathrm{SU}(2)\times D_{3,2}$	$6$	$0$	$3$	$32$	$555$	$11984$	$291144$	$291144$	$3$	$13$	$76$	$591$	$5588$	$59180$	$14$	$1380$	$263825$		✓	$[1, 3, 8, 5, 11, 44, 42, 64, 85, 34, 29, 191, 203, 441, 800, 359, 396, 826, 649, 166]$
1.6.K.6.2a	$1$	$6$	$4$	$\mathrm{SU}(2)\times\mathrm{U}(1)_2$	$\mathrm{SU}(2)\times J(C_3)$	$6$	$0$	$3$	$32$	$555$	$11984$	$291144$	$291144$	$2$	$10$	$65$	$556$	$5477$	$58837$	$13$	$1370$	$263720$		✓	$[1, 3, 7, 6, 10, 44, 43, 58, 89, 37, 28, 188, 208, 440, 800, 364, 381, 845, 655, 185]$
1.6.K.6.2b	$1$	$6$	$4$	$\mathrm{SU}(2)\times\mathrm{U}(1)_2$	$\mathrm{SU}(2)\times C_{6,1}$	$6$	$0$	$3$	$32$	$555$	$11984$	$291144$	$291144$	$2$	$10$	$67$	$564$	$5507$	$58937$	$13$	$1370$	$263720$		✓	$[1, 3, 7, 6, 10, 44, 43, 58, 85, 33, 28, 188, 204, 440, 800, 360, 381, 825, 643, 165]$
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.K.8.3b	$1$	$6$	$4$	$\mathrm{SU}(2)\times\mathrm{U}(1)_2$	$\mathrm{SU}(2)\times D_4$	$8$	$0$	$3$	$32$	$535$	$10934$	$251874$	$251874$	$2$	$10$	$65$	$537$	$5072$	$52236$	$13$	$1308$	$228690$		✓	$[1, 3, 7, 6, 10, 42, 41, 53, 78, 32, 24, 161, 175, 364, 652, 293, 304, 663, 511, 139]$
1.6.K.8.3c	$1$	$6$	$4$	$\mathrm{SU}(2)\times\mathrm{U}(1)_2$	$\mathrm{SU}(2)\times D_{4,2}$	$8$	$0$	$3$	$32$	$535$	$10934$	$251874$	$251874$	$3$	$13$	$75$	$568$	$5168$	$52530$	$14$	$1318$	$228800$		✓	$[1, 3, 8, 5, 11, 42, 40, 59, 76, 31, 25, 164, 172, 365, 652, 290, 320, 655, 512, 131]$
1.6.K.12.4c	$1$	$6$	$4$	$\mathrm{SU}(2)\times\mathrm{U}(1)_2$	$\mathrm{SU}(2)\times D_6$	$12$	$0$	$3$	$32$	$535$	$10864$	$246204$	$246204$	$2$	$10$	$65$	$536$	$5037$	$51346$	$13$	$1306$	$223415$		✓	$[1, 3, 7, 6, 10, 42, 41, 52, 77, 31, 24, 158, 172, 346, 620, 274, 276, 600, 456, 122]$
1.6.K.12.4d	$1$	$6$	$4$	$\mathrm{SU}(2)\times\mathrm{U}(1)_2$	$\mathrm{SU}(2)\times D_{6,2}$	$12$	$0$	$3$	$32$	$535$	$10864$	$246204$	$246204$	$3$	$13$	$75$	$567$	$5133$	$51640$	$14$	$1316$	$223525$		✓	$[1, 3, 8, 5, 11, 42, 40, 58, 75, 30, 25, 161, 169, 347, 620, 271, 292, 592, 457, 114]$
1.6.K.12.5a	$1$	$6$	$4$	$\mathrm{SU}(2)\times\mathrm{U}(1)_2$	$\mathrm{SU}(2)\times J(C_6)$	$12$	$0$	$3$	$32$	$535$	$10864$	$246204$	$246204$	$2$	$10$	$65$	$536$	$5037$	$51347$	$13$	$1306$	$223420$		✓	$[1, 3, 7, 6, 10, 42, 41, 52, 77, 31, 24, 158, 172, 346, 620, 274, 277, 601, 457, 123]$