Sato-Tate group search results

Results (34 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.D.4.2a	$1$	$4$	$2$	$\mathrm{U}(1)\times\mathrm{U}(1)$	$F_{a,b}$	$4$	$1/4$	$2$	$12$	$110$	$1260$	$16002$	$16002$	$2$	$5$	$14$	$49$	$202$	$944$				✓	✓	$[1, 2, 2, 5, 6, 6, 8, 19, 22, 12]$
1.4.E.4.2a	$1$	$4$	$3$	$\mathrm{SU}(2)_{2}$	$J(E_2)$	$4$	$3/4$	$1$	$8$	$80$	$896$	$10752$	$10752$	$1$	$4$	$10$	$42$	$166$	$768$					✓	$[1, 1, 3, 4, 5, 8, 5, 15, 14, 16]$
1.4.F.4.2a	$1$	$4$	$1$	$\mathrm{U}(1)_{2}$	$D_2$	$4$	$3/4$	$2$	$24$	$320$	$4480$	$64512$	$64512$	$1$	$6$	$22$	$118$	$606$	$3324$					✓	$[1, 2, 5, 10, 20, 20, 26, 79, 92, 60]$
1.4.F.4.2b	$1$	$4$	$1$	$\mathrm{U}(1)_{2}$	$J(C_2)$	$4$	$3/4$	$2$	$24$	$320$	$4480$	$64512$	$64512$	$1$	$7$	$22$	$123$	$606$	$3346$					✓	$[1, 2, 6, 11, 20, 26, 26, 83, 92, 78]$
1.4.F.4.2c	$1$	$4$	$1$	$\mathrm{U}(1)_{2}$	$D_{2,1}$	$4$	$3/4$	$2$	$24$	$320$	$4480$	$64512$	$64512$	$2$	$7$	$26$	$123$	$622$	$3346$					✓	$[1, 2, 4, 11, 20, 18, 26, 77, 92, 54]$
1.6.F.4.2a	$1$	$6$	$7$	$\mathrm{U}(1)\times\mathrm{SU}(2)^2$	$F_{a,t}$	$4$	$1/4$	$2$	$14$	$165$	$2639$	$50253$	$50253$	$2$	$7$	$32$	$191$	$1402$	$11905$	$7$	$389$	$46510$	✓	✓	$[1, 2, 4, 3, 5, 12, 13, 17, 18, 10, 8, 33, 38, 64, 105, 51, 54, 97, 71, 24]$
1.6.G.4.2a	$1$	$6$	$5$	$\mathrm{U}(1)^2\times\mathrm{SU}(2)$	$F_{a,b}\times \mathrm{SU}(2)$	$4$	$0$	$3$	$26$	$355$	$6314$	$132804$	$132804$	$3$	$12$	$60$	$384$	$3048$	$28259$	$13$	$818$	$117360$	✓	✓	$[1, 3, 7, 4, 8, 26, 23, 34, 39, 17, 16, 88, 88, 178, 310, 140, 155, 299, 237, 61]$
1.6.H.4.2a	$1$	$6$	$3$	$\mathrm{U}(1)^3$	$H_{ab,bc}$	$4$	$0$	$3$	$27$	$480$	$11235$	$293328$	$293328$	$3$	$12$	$66$	$522$	$5238$	$59079$	$14$	$1302$	$278240$		✓	$[1, 3, 7, 5, 9, 38, 40, 60, 87, 39, 26, 192, 216, 479, 900, 429, 444, 992, 816, 223]$
1.6.H.4.2b	$1$	$6$	$3$	$\mathrm{U}(1)^3$	$H_{a,bc}$	$4$	$1/4$	$3$	$33$	$570$	$12425$	$309078$	$309078$	$3$	$13$	$75$	$585$	$5643$	$61609$	$14$	$1398$	$284000$		✓	$[1, 3, 8, 5, 12, 44, 43, 66, 87, 40, 28, 201, 218, 479, 900, 429, 454, 994, 829, 223]$
1.6.H.4.2c	$1$	$6$	$3$	$\mathrm{U}(1)^3$	$H_{a,b}$	$4$	$0$	$4$	$42$	$670$	$13650$	$324954$	$324954$	$3$	$14$	$84$	$648$	$6048$	$64139$	$18$	$1542$	$290400$		✓	$[1, 4, 9, 6, 12, 50, 45, 60, 88, 37, 32, 210, 222, 484, 900, 434, 437, 998, 833, 228]$
1.6.I.4.2a	$1$	$6$	$6$	$\mathrm{SU}(2)\times\mathrm{SU}(2)_2$	$\mathrm{SU}(2)\times J(E_2)$	$4$	$0$	$2$	$16$	$235$	$4410$	$93744$	$93744$	$2$	$8$	$41$	$283$	$2362$	$22156$	$8$	$620$	$91760$		✓	$[1, 2, 5, 4, 6, 19, 20, 30, 36, 17, 11, 61, 69, 136, 235, 106, 122, 233, 170, 50]$
1.6.J.4.2a	$1$	$6$	$4$	$\mathrm{U}(1)\times\mathrm{SU}(2)_2$	$J(J(E_2),E_2)$	$4$	$1/2$	$2$	$23$	$420$	$9331$	$229068$	$229068$	$2$	$9$	$56$	$471$	$4642$	$49891$	$10$	$1178$	$228360$		✓	$[1, 2, 6, 6, 10, 35, 41, 58, 80, 44, 20, 145, 184, 366, 688, 340, 336, 760, 599, 198]$
1.6.J.4.2b	$1$	$6$	$4$	$\mathrm{U}(1)\times\mathrm{SU}(2)_2$	$J(J(E_2),J(E_1))$	$4$	$1/2$	$2$	$23$	$420$	$9331$	$229068$	$229068$	$2$	$9$	$56$	$471$	$4642$	$49891$	$10$	$1178$	$228360$		✓	$[1, 2, 6, 4, 8, 35, 37, 52, 76, 32, 18, 145, 166, 364, 688, 318, 326, 722, 579, 150]$
1.6.J.4.2c	$1$	$6$	$4$	$\mathrm{U}(1)\times\mathrm{SU}(2)_2$	$J_1(J(E_2))$	$4$	$0$	$3$	$26$	$430$	$9366$	$229194$	$229194$	$2$	$9$	$56$	$471$	$4642$	$49891$	$12$	$1196$	$228560$		✓	$[1, 3, 6, 7, 9, 35, 42, 54, 81, 44, 22, 145, 188, 369, 688, 345, 329, 764, 598, 203]$
1.6.J.4.2d	$1$	$6$	$4$	$\mathrm{U}(1)\times\mathrm{SU}(2)_2$	$J_2(E_2)$	$4$	$1/4$	$3$	$31$	$500$	$10227$	$239820$	$239820$	$2$	$11$	$69$	$547$	$5068$	$52285$	$14$	$1306$	$233480$		✓	$[1, 3, 8, 7, 10, 40, 43, 58, 81, 44, 24, 153, 188, 371, 688, 345, 340, 764, 609, 203]$
1.6.J.4.2e	$1$	$6$	$4$	$\mathrm{U}(1)\times\mathrm{SU}(2)_2$	$J_2(J(E_1))$	$4$	$1/4$	$3$	$31$	$500$	$10227$	$239820$	$239820$	$3$	$13$	$75$	$563$	$5113$	$52411$	$14$	$1306$	$233480$		✓	$[1, 3, 8, 5, 10, 40, 39, 58, 77, 32, 22, 153, 170, 369, 688, 323, 340, 726, 589, 155]$
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.L.4.2a	$1$	$6$	$6$	$\mathrm{U}(1)\times\mathrm{U}(1)_2$	$L(D_2,C_2)$	$4$	$1/2$	$3$	$51$	$1230$	$33635$	$978138$	$978138$	$2$	$13$	$116$	$1279$	$15362$	$192967$	$18$	$3570$	$966600$		✓	$[1, 3, 10, 9, 18, 104, 115, 166, 283, 122, 68, 611, 742, 1727, 3424, 1697, 1726, 4146, 3517, 1003]$
1.6.L.4.2b	$1$	$6$	$6$	$\mathrm{U}(1)\times\mathrm{U}(1)_2$	$L(J(C_2),J(C_1))$	$4$	$1/2$	$3$	$51$	$1230$	$33635$	$978138$	$978138$	$2$	$14$	$119$	$1290$	$15397$	$193079$	$19$	$3585$	$966820$		✓	$[1, 3, 11, 12, 21, 104, 121, 181, 293, 151, 71, 614, 776, 1731, 3424, 1742, 1763, 4250, 3588, 1139]$
1.6.L.4.2c	$1$	$6$	$6$	$\mathrm{U}(1)\times\mathrm{U}(1)_2$	$L(J(C_2),C_2)$	$4$	$1/2$	$3$	$51$	$1230$	$33635$	$978138$	$978138$	$2$	$14$	$119$	$1290$	$15397$	$193079$	$18$	$3570$	$966600$		✓	$[1, 3, 11, 9, 19, 104, 116, 172, 283, 127, 68, 614, 742, 1727, 3424, 1697, 1742, 4146, 3530, 1003]$
1.6.L.4.2d	$1$	$6$	$6$	$\mathrm{U}(1)\times\mathrm{U}(1)_2$	$L(J(C_2),C_{2,1})$	$4$	$1/2$	$3$	$51$	$1230$	$33635$	$978138$	$978138$	$2$	$14$	$119$	$1290$	$15397$	$193079$	$19$	$3585$	$966820$		✓	$[1, 3, 11, 8, 17, 104, 113, 165, 281, 119, 67, 614, 732, 1727, 3424, 1686, 1727, 4126, 3516, 979]$
1.6.L.4.2e	$1$	$6$	$6$	$\mathrm{U}(1)\times\mathrm{U}(1)_2$	$L_1(D_2)$	$4$	$0$	$4$	$54$	$1240$	$33670$	$978264$	$978264$	$2$	$13$	$116$	$1279$	$15362$	$192967$	$20$	$3588$	$966800$		✓	$[1, 4, 10, 12, 19, 104, 120, 168, 288, 134, 72, 611, 764, 1732, 3424, 1724, 1729, 4188, 3536, 1056]$
1.6.L.4.2f	$1$	$6$	$6$	$\mathrm{U}(1)\times\mathrm{U}(1)_2$	$L_1(J(C_2))$	$4$	$0$	$4$	$54$	$1240$	$33670$	$978264$	$978264$	$2$	$14$	$119$	$1290$	$15397$	$193079$	$22$	$3618$	$967240$		✓	$[1, 4, 11, 14, 20, 104, 123, 176, 296, 155, 74, 614, 788, 1736, 3424, 1758, 1751, 4272, 3593, 1168]$
1.6.L.4.2g	$1$	$6$	$6$	$\mathrm{U}(1)\times\mathrm{U}(1)_2$	$L_2(J(C_1))$	$4$	$1/4$	$5$	$75$	$1550$	$38115$	$1042650$	$1042650$	$2$	$18$	$149$	$1498$	$16767$	$202023$	$27$	$3969$	$987300$		✓	$[1, 5, 15, 14, 25, 124, 129, 181, 295, 151, 87, 662, 792, 1753, 3424, 1764, 1751, 4266, 3648, 1161]$
1.6.L.4.2h	$1$	$6$	$6$	$\mathrm{U}(1)\times\mathrm{U}(1)_2$	$L(D_{2,1},C_2)$	$4$	$1/2$	$3$	$51$	$1230$	$33635$	$978138$	$978138$	$3$	$16$	$126$	$1310$	$15458$	$193261$	$18$	$3570$	$966600$		✓	$[1, 3, 11, 9, 21, 104, 116, 180, 283, 127, 68, 614, 742, 1727, 3424, 1697, 1760, 4146, 3530, 1003]$
1.6.L.4.2i	$1$	$6$	$6$	$\mathrm{U}(1)\times\mathrm{U}(1)_2$	$L(D_{2,1},C_{2,1})$	$4$	$1/2$	$3$	$51$	$1230$	$33635$	$978138$	$978138$	$3$	$16$	$126$	$1310$	$15458$	$193261$	$19$	$3585$	$966820$		✓	$[1, 3, 11, 8, 19, 104, 113, 173, 281, 119, 67, 614, 732, 1727, 3424, 1686, 1745, 4126, 3516, 979]$
1.6.L.4.2j	$1$	$6$	$6$	$\mathrm{U}(1)\times\mathrm{U}(1)_2$	$L_1(D_{2,1})$	$4$	$0$	$4$	$54$	$1240$	$33670$	$978264$	$978264$	$3$	$16$	$126$	$1310$	$15458$	$193261$	$22$	$3618$	$967240$		✓	$[1, 4, 11, 10, 18, 104, 115, 168, 284, 123, 70, 614, 744, 1732, 3424, 1702, 1733, 4148, 3521, 1008]$
1.6.L.4.2k	$1$	$6$	$6$	$\mathrm{U}(1)\times\mathrm{U}(1)_2$	$L_2(C_2)$	$4$	$1/4$	$5$	$75$	$1550$	$38115$	$1042650$	$1042650$	$3$	$19$	$153$	$1507$	$16793$	$202093$	$26$	$3954$	$987080$		✓	$[1, 5, 14, 11, 24, 124, 123, 174, 285, 122, 84, 659, 758, 1749, 3424, 1719, 1732, 4162, 3577, 1025]$
1.6.L.4.2l	$1$	$6$	$6$	$\mathrm{U}(1)\times\mathrm{U}(1)_2$	$L_2(C_{2,1})$	$4$	$1/4$	$5$	$75$	$1550$	$38115$	$1042650$	$1042650$	$4$	$22$	$163$	$1538$	$16889$	$202387$	$27$	$3969$	$987300$		✓	$[1, 5, 15, 10, 25, 124, 121, 181, 283, 119, 83, 662, 748, 1749, 3424, 1708, 1751, 4142, 3576, 1001]$
1.6.M.4.2a	$1$	$6$	$3$	$\mathrm{SU}(2)_{3}$	$M(D_2)$	$4$	$0$	$3$	$42$	$915$	$22974$	$620046$	$620046$	$3$	$15$	$111$	$1059$	$11493$	$133425$	$17$	$2772$	$640322$		✓	$[1, 3, 10, 8, 15, 80, 88, 132, 204, 84, 44, 387, 468, 1085, 2112, 1017, 1065, 2432, 1992, 541]$
1.6.N.4.2a	$1$	$6$	$1$	$\mathrm{U}(1)_{3}$	$A(2,2)$	$4$	$0$	$6$	$126$	$3660$	$114870$	$3720276$	$3720276$	$3$	$27$	$309$	$3963$	$53073$	$727101$	$44$	$11820$	$3864140$		✓	$[1, 6, 22, 26, 45, 320, 382, 582, 1062, 492, 224, 2259, 2928, 7154, 14784, 7782, 7911, 19760, 17520, 5350]$
1.6.N.4.2b	$1$	$6$	$1$	$\mathrm{U}(1)_{3}$	$J(A(1,2))$	$4$	$1/2$	$5$	$123$	$3650$	$114835$	$3720150$	$3720150$	$4$	$30$	$319$	$3994$	$53169$	$727395$	$42$	$11798$	$3863850$		✓	$[1, 5, 23, 21, 45, 320, 371, 587, 1053, 462, 216, 2262, 2872, 7143, 14784, 7703, 7930, 19640, 17474, 5175]$