Sato-Tate group search results

Results (20 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.4.1a	$1$	$4$	$2$	$\mathrm{U}(1)\times\mathrm{U}(1)$	$F_{ac}$	$4$	$3/4$	$1$	$9$	$100$	$1225$	$15876$	$15876$	$1$	$3$	$10$	$41$	$186$	$912$				✓	✓	$[1, 1, 2, 4, 6, 5, 7, 19, 20, 11]$
1.4.E.4.1a	$1$	$4$	$3$	$\mathrm{SU}(2)_{2}$	$E_4$	$4$	$1/4$	$2$	$12$	$100$	$1008$	$11424$	$11424$	$1$	$4$	$11$	$46$	$182$	$824$					✓	$[1, 2, 3, 4, 6, 8, 6, 15, 16, 16]$
1.4.F.4.1a	$1$	$4$	$1$	$\mathrm{U}(1)_{2}$	$C_{4,1}$	$4$	$3/4$	$2$	$24$	$320$	$4480$	$64512$	$64512$	$1$	$5$	$22$	$115$	$606$	$3314$					✓	$[1, 2, 4, 9, 20, 16, 26, 77, 92, 52]$
1.4.F.4.1b	$1$	$4$	$1$	$\mathrm{U}(1)_{2}$	$C_4$	$4$	$1/4$	$4$	$36$	$400$	$5040$	$68544$	$68544$	$2$	$8$	$32$	$150$	$732$	$3776$					✓	$[1, 4, 5, 12, 24, 18, 28, 79, 96, 54]$
1.6.G.4.1a	$1$	$6$	$5$	$\mathrm{U}(1)^2\times\mathrm{SU}(2)$	$F_{ac}\times \mathrm{SU}(2)$	$4$	$0$	$2$	$17$	$270$	$5439$	$123123$	$123123$	$2$	$7$	$38$	$284$	$2567$	$25820$	$7$	$658$	$111760$	✓	✓	$[1, 2, 4, 3, 6, 21, 21, 29, 38, 15, 13, 81, 85, 174, 310, 136, 146, 296, 229, 57]$
1.6.H.4.1a	$1$	$6$	$3$	$\mathrm{U}(1)^3$	$H_{act}$	$4$	$1/2$	$2$	$24$	$470$	$11200$	$293202$	$293202$	$2$	$8$	$53$	$482$	$5117$	$58715$	$10$	$1254$	$277600$		✓	$[1, 2, 5, 4, 8, 38, 39, 54, 86, 35, 24, 188, 214, 474, 900, 424, 431, 990, 807, 218]$
1.6.H.4.1b	$1$	$6$	$3$	$\mathrm{U}(1)^3$	$H_{at}$	$4$	$0$	$3$	$27$	$480$	$11235$	$293328$	$293328$	$2$	$8$	$53$	$482$	$5117$	$58715$	$10$	$1254$	$277600$		✓	$[1, 3, 5, 5, 9, 38, 42, 54, 87, 35, 26, 188, 216, 475, 900, 425, 432, 992, 810, 219]$
1.6.I.4.1a	$1$	$6$	$6$	$\mathrm{SU}(2)\times\mathrm{SU}(2)_2$	$\mathrm{SU}(2)\times E_4$	$4$	$0$	$3$	$26$	$345$	$5782$	$112686$	$112686$	$2$	$9$	$51$	$359$	$2908$	$26103$	$12$	$812$	$105080$		✓	$[1, 3, 6, 5, 7, 26, 24, 30, 41, 18, 13, 71, 75, 147, 250, 113, 121, 239, 176, 53]$
1.6.J.4.1a	$1$	$6$	$4$	$\mathrm{U}(1)\times\mathrm{SU}(2)_2$	$J(E_4,E_2)$	$4$	$0$	$3$	$27$	$440$	$9443$	$229740$	$229740$	$2$	$9$	$57$	$479$	$4688$	$50123$	$14$	$1242$	$229640$		✓	$[1, 3, 6, 7, 8, 36, 41, 52, 81, 44, 20, 145, 184, 371, 688, 345, 326, 760, 599, 203]$
1.6.J.4.1b	$1$	$6$	$4$	$\mathrm{U}(1)\times\mathrm{SU}(2)_2$	$J_1(E_4)$	$4$	$0$	$4$	$42$	$660$	$12838$	$285096$	$285096$	$2$	$11$	$75$	$623$	$5828$	$59313$	$16$	$1524$	$259520$		✓	$[1, 4, 8, 8, 13, 50, 50, 60, 92, 46, 32, 183, 208, 404, 736, 364, 339, 784, 622, 208]$
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.L.4.1a	$1$	$6$	$6$	$\mathrm{U}(1)\times\mathrm{U}(1)_2$	$L(C_{4,1},C_2)$	$4$	$1/2$	$3$	$51$	$1230$	$33635$	$978138$	$978138$	$2$	$12$	$113$	$1270$	$15337$	$192897$	$18$	$3570$	$966600$		✓	$[1, 3, 9, 9, 17, 104, 114, 162, 283, 119, 68, 610, 742, 1727, 3424, 1697, 1720, 4146, 3512, 1003]$
1.6.L.4.1b	$1$	$6$	$6$	$\mathrm{U}(1)\times\mathrm{U}(1)_2$	$L_1(C_{4,1})$	$4$	$0$	$4$	$54$	$1240$	$33670$	$978264$	$978264$	$2$	$12$	$113$	$1270$	$15337$	$192897$	$18$	$3570$	$966600$		✓	$[1, 4, 9, 10, 18, 104, 117, 162, 284, 119, 70, 610, 744, 1728, 3424, 1698, 1721, 4148, 3515, 1004]$
1.6.L.4.1c	$1$	$6$	$6$	$\mathrm{U}(1)\times\mathrm{U}(1)_2$	$L(C_4,C_2)$	$4$	$0$	$5$	$63$	$1310$	$34195$	$982170$	$982170$	$3$	$17$	$135$	$1367$	$15773$	$194891$	$26$	$3762$	$971720$		✓	$[1, 5, 12, 11, 18, 108, 117, 164, 285, 122, 68, 611, 742, 1733, 3424, 1703, 1722, 4146, 3519, 1009]$
1.6.L.4.1d	$1$	$6$	$6$	$\mathrm{U}(1)\times\mathrm{U}(1)_2$	$L_1(C_4)$	$4$	$0$	$6$	$90$	$1860$	$44870$	$1190196$	$1190196$	$3$	$21$	$183$	$1847$	$20333$	$237711$	$32$	$4932$	$1138880$		✓	$[1, 6, 16, 14, 27, 152, 154, 206, 346, 138, 92, 747, 864, 1950, 3768, 1822, 1837, 4368, 3658, 1034]$
1.6.M.4.1a	$1$	$6$	$3$	$\mathrm{SU}(2)_{3}$	$M(C_4)$	$4$	$0$	$3$	$42$	$915$	$22974$	$620046$	$620046$	$2$	$13$	$105$	$1043$	$11448$	$133299$	$17$	$2772$	$640322$		✓	$[1, 3, 10, 8, 13, 80, 86, 126, 204, 80, 42, 387, 462, 1083, 2112, 1011, 1055, 2424, 1988, 533]$
1.6.N.4.1a	$1$	$6$	$1$	$\mathrm{U}(1)_{3}$	$J_n(A(1,2))$	$4$	$1/2$	$5$	$123$	$3650$	$114835$	$3720150$	$3720150$	$2$	$26$	$305$	$3954$	$53047$	$727031$	$42$	$11798$	$3863850$		✓	$[1, 5, 23, 21, 41, 320, 371, 571, 1053, 462, 216, 2262, 2872, 7143, 14784, 7703, 7894, 19640, 17474, 5175]$
1.6.N.4.1b	$1$	$6$	$1$	$\mathrm{U}(1)_{3}$	$A(1,4)_2$	$4$	$0$	$6$	$126$	$3660$	$114870$	$3720276$	$3720276$	$3$	$27$	$309$	$3963$	$53073$	$727101$	$44$	$11820$	$3864140$		✓	$[1, 6, 22, 22, 41, 320, 370, 570, 1054, 456, 216, 2259, 2872, 7146, 14784, 7706, 7891, 19640, 17460, 5178]$
1.6.N.4.1c	$1$	$6$	$1$	$\mathrm{U}(1)_{3}$	$A(1,4)_1$	$4$	$0$	$10$	$198$	$4900$	$136710$	$4113900$	$4113900$	$5$	$43$	$443$	$5091$	$62735$	$811093$	$68$	$14444$	$4173380$		✓	$[1, 10, 34, 30, 61, 416, 446, 654, 1170, 488, 264, 2515, 3080, 7526, 15328, 7898, 8079, 19976, 17684, 5226]$