Sato-Tate group search results

Results (15 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.E.6.1a	$1$	$6$	$9$	$\mathrm{SU}(2)^3$	$E_{s,t}$	$6$	$1/3$	$1$	$5$	$50$	$714$	$12222$	$12222$	$1$	$3$	$12$	$65$	$436$	$3377$	$3$	$124$	$12275$	✓	✓	$[1, 1, 2, 2, 2, 4, 5, 6, 6, 4, 3, 8, 10, 16, 24, 12, 15, 23, 15, 7]$
1.6.J.12.4a	$1$	$6$	$4$	$\mathrm{U}(1)\times\mathrm{SU}(2)_2$	$J(J(E_6),J(E_3))$	$12$	$1/3$	$2$	$15$	$195$	$3605$	$81333$	$81333$	$2$	$7$	$32$	$208$	$1767$	$17680$	$7$	$471$	$78750$		✓	$[1, 2, 4, 3, 6, 14, 16, 22, 28, 15, 10, 53, 61, 125, 233, 113, 117, 245, 202, 56]$
1.6.L.12.4i	$1$	$6$	$6$	$\mathrm{U}(1)\times\mathrm{U}(1)_2$	$L(D_6,D_3)$	$12$	$1/3$	$3$	$33$	$570$	$12985$	$346878$	$346878$	$2$	$10$	$65$	$566$	$5917$	$69106$	$13$	$1455$	$335790$		✓	$[1, 3, 7, 6, 11, 44, 47, 63, 101, 49, 29, 216, 262, 585, 1150, 582, 586, 1403, 1192, 357]$
1.6.L.12.4m	$1$	$6$	$6$	$\mathrm{U}(1)\times\mathrm{U}(1)_2$	$L(D_{6,2},D_{3,2})$	$12$	$1/3$	$3$	$33$	$570$	$12985$	$346878$	$346878$	$3$	$13$	$75$	$597$	$6013$	$69400$	$14$	$1470$	$336010$		✓	$[1, 3, 8, 5, 12, 44, 45, 70, 99, 46, 28, 219, 252, 585, 1150, 571, 605, 1383, 1191, 333]$
1.6.L.12.5a	$1$	$6$	$6$	$\mathrm{U}(1)\times\mathrm{U}(1)_2$	$L(J(C_6),J(C_3))$	$12$	$1/3$	$3$	$33$	$570$	$12985$	$346878$	$346878$	$2$	$10$	$65$	$566$	$5917$	$69107$	$13$	$1455$	$335800$		✓	$[1, 3, 7, 6, 11, 44, 47, 65, 103, 53, 29, 216, 266, 585, 1150, 588, 593, 1424, 1206, 385]$
1.6.L.12.5b	$1$	$6$	$6$	$\mathrm{U}(1)\times\mathrm{U}(1)_2$	$L(J(C_6),C_{6,1})$	$12$	$1/3$	$3$	$33$	$570$	$12985$	$346878$	$346878$	$2$	$10$	$65$	$566$	$5917$	$69107$	$13$	$1455$	$335800$		✓	$[1, 3, 7, 6, 11, 44, 47, 61, 99, 45, 29, 216, 258, 585, 1150, 576, 581, 1384, 1182, 333]$
1.6.M.6.1a	$1$	$6$	$3$	$\mathrm{SU}(2)_{3}$	$M(D_3)$	$6$	$1/3$	$2$	$28$	$610$	$15316$	$413364$	$413364$	$2$	$10$	$74$	$706$	$7662$	$88950$	$12$	$1850$	$426888$		✓	$[1, 2, 7, 6, 10, 54, 59, 88, 136, 57, 30, 258, 312, 724, 1410, 678, 712, 1622, 1328, 364]$
1.6.M.6.2a	$1$	$6$	$3$	$\mathrm{SU}(2)_{3}$	$M(C_6)$	$6$	$1/3$	$3$	$38$	$715$	$16506$	$427686$	$427686$	$2$	$11$	$83$	$769$	$8078$	$91677$	$15$	$1984$	$434622$		✓	$[1, 3, 8, 6, 11, 60, 60, 86, 138, 54, 32, 265, 312, 727, 1416, 677, 705, 1620, 1328, 359]$
1.6.M.24.12a	$1$	$6$	$3$	$\mathrm{SU}(2)_{3}$	$M(S_4)$	$24$	$1/3$	$1$	$8$	$155$	$3836$	$103362$	$103362$	$1$	$4$	$22$	$186$	$1941$	$22308$	$4$	$466$	$106744$	✓	✓	$[1, 1, 3, 3, 4, 14, 17, 26, 35, 19, 9, 66, 81, 183, 354, 174, 186, 410, 338, 100]$
1.6.N.6.1a	$1$	$6$	$1$	$\mathrm{U}(1)_{3}$	$B(3,1)$	$6$	$1/3$	$4$	$84$	$2440$	$76580$	$2480184$	$2480184$	$2$	$18$	$206$	$2642$	$35382$	$484734$	$30$	$7882$	$2576100$		✓	$[1, 4, 15, 18, 30, 214, 255, 388, 708, 329, 150, 1506, 1952, 4770, 9858, 5188, 5276, 13174, 11680, 3570]$
1.6.N.6.2c	$1$	$6$	$1$	$\mathrm{U}(1)_{3}$	$A(3,2)$	$6$	$1/3$	$6$	$114$	$2860$	$82530$	$2566116$	$2566116$	$3$	$25$	$257$	$3009$	$38053$	$504399$	$40$	$8680$	$2642580$		✓	$[1, 6, 20, 18, 35, 244, 268, 398, 726, 310, 156, 1553, 1952, 4806, 9924, 5162, 5269, 13116, 11664, 3462]$
1.6.N.24.3b	$1$	$6$	$1$	$\mathrm{U}(1)_{3}$	$B(T,1)$	$24$	$1/3$	$4$	$54$	$1040$	$25130$	$706104$	$706104$	$2$	$13$	$106$	$1037$	$11542$	$140919$	$20$	$2792$	$710800$		✓	$[1, 4, 10, 8, 15, 84, 84, 114, 200, 84, 48, 425, 516, 1236, 2532, 1312, 1325, 3296, 2938, 876]$
1.6.N.24.12b	$1$	$6$	$1$	$\mathrm{U}(1)_{3}$	$D(2,2)$	$24$	$1/3$	$2$	$24$	$620$	$19180$	$620172$	$620172$	$1$	$6$	$55$	$670$	$8871$	$121254$	$10$	$1994$	$644320$		✓	$[1, 2, 5, 8, 10, 54, 71, 104, 182, 103, 42, 378, 516, 1200, 2466, 1338, 1332, 3354, 2954, 984]$
1.6.N.96.64b	$1$	$6$	$1$	$\mathrm{U}(1)_{3}$	$D(4,4)$	$96$	$1/3$	$2$	$18$	$320$	$7560$	$204372$	$204372$	$1$	$5$	$34$	$318$	$3451$	$40883$	$8$	$846$	$199940$		✓	$[1, 2, 4, 6, 7, 26, 32, 41, 64, 41, 20, 128, 170, 352, 686, 376, 365, 908, 783, 286]$
1.6.N.168.42a	$1$	$6$	$1$	$\mathrm{U}(1)_{3}$	$E(168)$	$168$	$1/3$	$2$	$12$	$140$	$3080$	$90972$	$90972$	$1$	$4$	$19$	$140$	$1451$	$18112$	$6$	$366$	$94080$		✓	$[1, 2, 3, 4, 4, 10, 15, 18, 30, 23, 10, 56, 84, 176, 356, 206, 198, 498, 436, 172]$