Sato-Tate group search results

Results (32 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
1.6.K.1.1a	$1$	$6$	$4$	$\mathrm{SU}(2)\times\mathrm{U}(1)_2$	$\mathrm{SU}(2)\times C_1$	$1$	$0$	$9$	$146$	$2965$	$68334$	$1707930$	$1707930$	$5$	$35$	$299$	$2899$	$30495$	$339085$	$50$	$7436$	$1543940$		✓	$[1, 9, 26, 19, 43, 240, 228, 304, 485, 170, 147, 1099, 1187, 2603, 4768, 2123, 2205, 4909, 3824, 965]$
1.6.K.2.1a	$1$	$6$	$4$	$\mathrm{SU}(2)\times\mathrm{U}(1)_2$	$\mathrm{SU}(2)\times J(C_1)$	$2$	$0$	$5$	$74$	$1485$	$34174$	$853986$	$853986$	$2$	$18$	$149$	$1450$	$15247$	$169543$	$27$	$3734$	$772130$		✓	$[1, 5, 15, 14, 24, 120, 119, 162, 255, 105, 76, 554, 616, 1304, 2384, 1084, 1125, 2517, 1957, 545]$
1.6.K.2.1b	$1$	$6$	$4$	$\mathrm{SU}(2)\times\mathrm{U}(1)_2$	$\mathrm{SU}(2)\times C_2$	$2$	$0$	$5$	$74$	$1485$	$34174$	$853986$	$853986$	$3$	$19$	$153$	$1459$	$15273$	$169613$	$26$	$3724$	$772020$		✓	$[1, 5, 14, 11, 23, 120, 116, 156, 245, 90, 75, 551, 599, 1303, 2384, 1067, 1109, 2465, 1920, 493]$
1.6.K.2.1c	$1$	$6$	$4$	$\mathrm{SU}(2)\times\mathrm{U}(1)_2$	$\mathrm{SU}(2)\times C_{2,1}$	$2$	$0$	$5$	$74$	$1485$	$34174$	$853986$	$853986$	$4$	$22$	$163$	$1490$	$15369$	$169907$	$27$	$3734$	$772130$		✓	$[1, 5, 15, 10, 24, 120, 115, 162, 243, 89, 76, 554, 596, 1304, 2384, 1064, 1125, 2457, 1921, 485]$
1.6.K.3.1a	$1$	$6$	$4$	$\mathrm{SU}(2)\times\mathrm{U}(1)_2$	$\mathrm{SU}(2)\times C_3$	$3$	$0$	$5$	$62$	$1105$	$23954$	$582246$	$582246$	$3$	$17$	$125$	$1101$	$10933$	$117631$	$24$	$2728$	$527330$		✓	$[1, 5, 12, 9, 17, 88, 82, 108, 169, 60, 53, 373, 401, 877, 1600, 713, 747, 1647, 1280, 327]$
1.6.K.4.1a	$1$	$6$	$4$	$\mathrm{SU}(2)\times\mathrm{U}(1)_2$	$\mathrm{SU}(2)\times C_{4,1}$	$4$	$0$	$3$	$38$	$745$	$17094$	$427014$	$427014$	$2$	$10$	$77$	$730$	$7637$	$84807$	$13$	$1862$	$386010$		✓	$[1, 3, 7, 6, 12, 60, 59, 78, 123, 45, 38, 276, 300, 652, 1192, 534, 555, 1233, 961, 247]$
1.6.K.4.1b	$1$	$6$	$4$	$\mathrm{SU}(2)\times\mathrm{U}(1)_2$	$\mathrm{SU}(2)\times C_4$	$4$	$0$	$5$	$62$	$1065$	$21854$	$503706$	$503706$	$3$	$17$	$123$	$1055$	$10093$	$104331$	$24$	$2604$	$457280$		✓	$[1, 5, 12, 9, 17, 84, 78, 98, 151, 54, 45, 319, 339, 725, 1304, 575, 595, 1305, 1006, 257]$
1.6.K.4.2a	$1$	$6$	$4$	$\mathrm{SU}(2)\times\mathrm{U}(1)_2$	$\mathrm{SU}(2)\times D_2$	$4$	$0$	$3$	$38$	$745$	$17094$	$427014$	$427014$	$2$	$11$	$80$	$739$	$7662$	$84877$	$14$	$1868$	$386060$		✓	$[1, 3, 8, 7, 13, 60, 60, 82, 125, 50, 39, 277, 305, 653, 1192, 539, 561, 1243, 968, 257]$
1.6.K.4.2b	$1$	$6$	$4$	$\mathrm{SU}(2)\times\mathrm{U}(1)_2$	$\mathrm{SU}(2)\times J(C_2)$	$4$	$0$	$3$	$38$	$745$	$17094$	$427014$	$427014$	$2$	$12$	$83$	$750$	$7697$	$84989$	$15$	$1878$	$386170$		✓	$[1, 3, 9, 8, 14, 60, 61, 88, 129, 57, 40, 280, 312, 654, 1192, 546, 577, 1265, 987, 279]$
1.6.K.4.2c	$1$	$6$	$4$	$\mathrm{SU}(2)\times\mathrm{U}(1)_2$	$\mathrm{SU}(2)\times D_{2,1}$	$4$	$0$	$3$	$38$	$745$	$17094$	$427014$	$427014$	$3$	$14$	$90$	$770$	$7758$	$85171$	$15$	$1878$	$386170$		✓	$[1, 3, 9, 6, 14, 60, 59, 88, 123, 49, 40, 280, 302, 654, 1192, 536, 577, 1235, 969, 249]$
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.6.2c	$1$	$6$	$4$	$\mathrm{SU}(2)\times\mathrm{U}(1)_2$	$\mathrm{SU}(2)\times C_6$	$6$	$0$	$5$	$62$	$1065$	$21714$	$492366$	$492366$	$3$	$17$	$123$	$1053$	$10023$	$102551$	$24$	$2600$	$446730$		✓	$[1, 5, 12, 9, 17, 84, 78, 96, 149, 52, 45, 313, 333, 689, 1240, 537, 539, 1179, 896, 223]$
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.8.3a	$1$	$6$	$4$	$\mathrm{SU}(2)\times\mathrm{U}(1)_2$	$\mathrm{SU}(2)\times D_{4,1}$	$8$	$0$	$2$	$20$	$375$	$8554$	$213528$	$213528$	$2$	$8$	$47$	$390$	$3892$	$42621$	$8$	$942$	$193110$		✓	$[1, 2, 5, 4, 8, 30, 31, 46, 63, 27, 21, 141, 154, 328, 596, 271, 292, 623, 489, 130]$
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.8.5a	$1$	$6$	$4$	$\mathrm{SU}(2)\times\mathrm{U}(1)_2$	$\mathrm{SU}(2)\times J(D_2)$	$8$	$0$	$2$	$20$	$375$	$8554$	$213528$	$213528$	$2$	$9$	$50$	$400$	$3922$	$42712$	$9$	$950$	$193190$		✓	$[1, 2, 6, 5, 9, 30, 32, 51, 66, 33, 22, 143, 160, 329, 596, 277, 303, 639, 502, 146]$
1.6.K.12.3a	$1$	$6$	$4$	$\mathrm{SU}(2)\times\mathrm{U}(1)_2$	$\mathrm{SU}(2)\times T$	$12$	$0$	$3$	$26$	$365$	$6874$	$155274$	$155274$	$2$	$9$	$52$	$381$	$3322$	$32895$	$12$	$872$	$141370$		✓	$[1, 3, 6, 5, 7, 28, 26, 34, 49, 20, 17, 99, 107, 227, 408, 185, 199, 425, 328, 91]$
1.6.K.12.4a	$1$	$6$	$4$	$\mathrm{SU}(2)\times\mathrm{U}(1)_2$	$\mathrm{SU}(2)\times J(D_3)$	$12$	$0$	$2$	$17$	$280$	$5999$	$145593$	$145593$	$2$	$8$	$41$	$303$	$2812$	$29636$	$8$	$696$	$131965$		✓	$[1, 2, 5, 4, 7, 22, 23, 36, 46, 23, 16, 97, 108, 222, 400, 186, 205, 429, 336, 99]$
1.6.K.12.4b	$1$	$6$	$4$	$\mathrm{SU}(2)\times\mathrm{U}(1)_2$	$\mathrm{SU}(2)\times D_{6,1}$	$12$	$0$	$2$	$17$	$280$	$5999$	$145593$	$145593$	$2$	$8$	$42$	$307$	$2827$	$29686$	$8$	$696$	$131965$		✓	$[1, 2, 5, 4, 7, 22, 23, 36, 44, 21, 16, 97, 106, 222, 400, 184, 205, 419, 330, 89]$
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	$1$	$6$	$4$	$\mathrm{SU}(2)\times\mathrm{U}(1)_2$	$\mathrm{SU}(2)\times J(C_6)$	$12$	$0$	$3$	$32$	$535$	$10864$	$246204$	$246204$	$2$	$10$	$65$	$536$	$5037$	$51347$	$13$	$1306$	$223420$		✓	$[1, 3, 7, 6, 10, 42, 41, 52, 77, 31, 24, 158, 172, 346, 620, 274, 277, 601, 457, 123]$
1.6.K.16.11a	$1$	$6$	$4$	$\mathrm{SU}(2)\times\mathrm{U}(1)_2$	$\mathrm{SU}(2)\times J(D_4)$	$16$	$0$	$2$	$17$	$270$	$5474$	$125958$	$125958$	$2$	$8$	$41$	$294$	$2612$	$26346$	$8$	$666$	$114465$		✓	$[1, 2, 5, 4, 7, 21, 22, 34, 41, 21, 14, 84, 92, 184, 326, 151, 169, 341, 267, 79]$
1.6.K.24.12a	$1$	$6$	$4$	$\mathrm{SU}(2)\times\mathrm{U}(1)_2$	$\mathrm{SU}(2)\times O_1$	$24$	$0$	$2$	$14$	$185$	$3444$	$77658$	$77658$	$2$	$7$	$33$	$211$	$1722$	$16630$	$7$	$444$	$70765$		✓	$[1, 2, 4, 3, 5, 14, 14, 22, 25, 12, 10, 52, 55, 115, 204, 94, 111, 214, 169, 47]$
1.6.K.24.12b	$1$	$6$	$4$	$\mathrm{SU}(2)\times\mathrm{U}(1)_2$	$\mathrm{SU}(2)\times O$	$24$	$0$	$3$	$26$	$345$	$5824$	$116004$	$116004$	$2$	$9$	$51$	$358$	$2902$	$26245$	$12$	$810$	$106345$		✓	$[1, 3, 6, 5, 7, 26, 24, 29, 40, 17, 13, 72, 76, 151, 260, 116, 123, 254, 191, 56]$
1.6.K.24.13a	$1$	$6$	$4$	$\mathrm{SU}(2)\times\mathrm{U}(1)_2$	$\mathrm{SU}(2)\times J(T)$	$24$	$0$	$2$	$14$	$185$	$3444$	$77658$	$77658$	$2$	$7$	$32$	$206$	$1702$	$16560$	$7$	$442$	$70740$		✓	$[1, 2, 4, 3, 5, 14, 14, 21, 26, 13, 10, 51, 56, 115, 204, 95, 107, 219, 170, 52]$
1.6.K.24.14a	$1$	$6$	$4$	$\mathrm{SU}(2)\times\mathrm{U}(1)_2$	$\mathrm{SU}(2)\times J(D_6)$	$24$	$0$	$2$	$17$	$270$	$5439$	$123123$	$123123$	$2$	$8$	$41$	$293$	$2592$	$25891$	$8$	$664$	$111815$	✓	✓	$[1, 2, 5, 4, 7, 21, 22, 33, 40, 20, 14, 82, 90, 175, 310, 141, 153, 307, 237, 68]$
1.6.K.48.48a	$1$	$6$	$4$	$\mathrm{SU}(2)\times\mathrm{U}(1)_2$	$\mathrm{SU}(2)\times J(O)$	$48$	$0$	$2$	$14$	$175$	$2919$	$58023$	$58023$	$2$	$7$	$32$	$197$	$1502$	$13270$	$7$	$412$	$53240$	✓	✓	$[1, 2, 4, 3, 5, 13, 13, 19, 21, 11, 8, 38, 40, 77, 130, 60, 71, 131, 101, 32]$