Sato-Tate group search results

Results (1-50 of 267 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.B.1.1a	$1$	$4$	$6$	$\mathrm{SU}(2)\times\mathrm{SU}(2)$	$\mathrm{SU}(2)\times\mathrm{SU}(2)$	$1$	$0$	$2$	$10$	$70$	$588$	$5544$	$5544$	$2$	$5$	$14$	$44$	$152$	$569$					✓	$[1, 2, 2, 3, 4, 3, 4, 6, 6, 4]$
1.4.C.1.1a	$1$	$4$	$4$	$\mathrm{U}(1)\times\mathrm{SU}(2)$	$\mathrm{U}(1)\times\mathrm{SU}(2)$	$1$	$0$	$3$	$20$	$175$	$1764$	$19404$	$19404$	$2$	$6$	$20$	$76$	$312$	$1364$					✓	$[1, 3, 3, 6, 10, 6, 10, 21, 21, 10]$
1.4.C.2.1a	$1$	$4$	$4$	$\mathrm{U}(1)\times\mathrm{SU}(2)$	$N(\mathrm{U}(1)\times\mathrm{SU}(2))$	$2$	$0$	$2$	$11$	$90$	$889$	$9723$	$9723$	$2$	$5$	$14$	$46$	$172$	$714$				✓	✓	$[1, 2, 2, 4, 5, 4, 6, 11, 11, 6]$
1.4.D.1.1a	$1$	$4$	$2$	$\mathrm{U}(1)\times\mathrm{U}(1)$	$F$	$1$	$0$	$4$	$36$	$400$	$4900$	$63504$	$63504$	$2$	$8$	$32$	$148$	$712$	$3584$				✓	✓	$[1, 4, 5, 12, 24, 16, 28, 73, 80, 40]$
1.4.D.2.1a	$1$	$4$	$2$	$\mathrm{U}(1)\times\mathrm{U}(1)$	$F_{ab}$	$2$	$1/2$	$2$	$18$	$200$	$2450$	$31752$	$31752$	$2$	$6$	$20$	$82$	$372$	$1824$					✓	$[1, 2, 3, 8, 12, 10, 14, 37, 40, 22]$
1.4.D.2.1b	$1$	$4$	$2$	$\mathrm{U}(1)\times\mathrm{U}(1)$	$F_a$	$2$	$0$	$3$	$21$	$210$	$2485$	$31878$	$31878$	$2$	$6$	$20$	$82$	$372$	$1824$					✓	$[1, 3, 3, 7, 12, 9, 15, 37, 42, 21]$
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.2.1b	$1$	$4$	$3$	$\mathrm{SU}(2)_{2}$	$J(E_1)$	$2$	$1/2$	$2$	$16$	$160$	$1792$	$21504$	$21504$	$2$	$6$	$20$	$78$	$332$	$1516$					✓	$[1, 2, 3, 6, 10, 8, 10, 25, 28, 16]$
1.4.F.2.1b	$1$	$4$	$1$	$\mathrm{U}(1)_{2}$	$C_2$	$2$	$1/2$	$4$	$48$	$640$	$8960$	$129024$	$129024$	$2$	$10$	$44$	$230$	$1212$	$6628$					✓	$[1, 4, 7, 18, 40, 32, 52, 153, 184, 104]$
1.4.F.3.1a	$1$	$4$	$1$	$\mathrm{U}(1)_{2}$	$C_3$	$3$	$0$	$4$	$36$	$440$	$6020$	$86184$	$86184$	$2$	$8$	$34$	$164$	$842$	$4506$					✓	$[1, 4, 5, 12, 28, 20, 36, 101, 124, 66]$
1.4.F.4.1b	$1$	$4$	$1$	$\mathrm{U}(1)_{2}$	$C_4$	$4$	$1/4$	$4$	$36$	$400$	$5040$	$68544$	$68544$	$2$	$8$	$32$	$150$	$732$	$3776$					✓	$[1, 4, 5, 12, 24, 18, 28, 79, 96, 54]$
1.4.F.4.2c	$1$	$4$	$1$	$\mathrm{U}(1)_{2}$	$D_{2,1}$	$4$	$3/4$	$2$	$24$	$320$	$4480$	$64512$	$64512$	$2$	$7$	$26$	$123$	$622$	$3346$					✓	$[1, 2, 4, 11, 20, 18, 26, 77, 92, 54]$
1.4.F.6.1b	$1$	$4$	$1$	$\mathrm{U}(1)_{2}$	$D_{3,2}$	$6$	$1/2$	$2$	$18$	$220$	$3010$	$43092$	$43092$	$2$	$6$	$21$	$90$	$437$	$2285$					✓	$[1, 2, 3, 8, 14, 12, 18, 51, 62, 35]$
1.4.F.6.2c	$1$	$4$	$1$	$\mathrm{U}(1)_{2}$	$C_6$	$6$	$1/6$	$4$	$36$	$400$	$4900$	$63504$	$63504$	$2$	$8$	$32$	$148$	$712$	$3586$					✓	$[1, 4, 5, 12, 24, 16, 28, 73, 80, 42]$
1.4.F.8.3c	$1$	$4$	$1$	$\mathrm{U}(1)_{2}$	$D_{4,2}$	$8$	$5/8$	$2$	$18$	$200$	$2520$	$34272$	$34272$	$2$	$6$	$20$	$83$	$382$	$1920$					✓	$[1, 2, 3, 8, 12, 11, 14, 40, 48, 29]$
1.4.F.12.4d	$1$	$4$	$1$	$\mathrm{U}(1)_{2}$	$D_{6,2}$	$12$	$7/12$	$2$	$18$	$200$	$2450$	$31752$	$31752$	$2$	$6$	$20$	$82$	$372$	$1825$					✓	$[1, 2, 3, 8, 12, 10, 14, 37, 40, 23]$
1.6.C.1.1a	$1$	$6$	$13$	$\mathrm{SU}(2)\times\mathrm{USp}(4)$	$\mathrm{SU}(2)\times \mathrm{USp}(4)$	$1$	$0$	$2$	$11$	$94$	$1050$	$14076$	$14076$	$2$	$6$	$23$	$109$	$613$	$3941$	$6$	$188$	$12226$	✓	✓	$[1, 2, 3, 2, 3, 6, 5, 6, 6, 3, 4, 9, 8, 12, 16, 8, 10, 12, 9, 4]$
1.6.D.1.1a	$1$	$6$	$11$	$\mathrm{U}(1)\times\mathrm{USp}(4)$	$\mathrm{U}(1)\times \mathrm{USp}(4)$	$1$	$0$	$3$	$21$	$214$	$2758$	$41796$	$41796$	$2$	$7$	$32$	$181$	$1193$	$8801$	$8$	$348$	$29536$		✓	$[1, 3, 4, 3, 6, 13, 11, 10, 13, 6, 10, 27, 24, 34, 50, 24, 20, 34, 27, 10]$
1.6.D.2.1a	$1$	$6$	$11$	$\mathrm{U}(1)\times\mathrm{USp}(4)$	$N(\mathrm{U}(1)\times \mathrm{USp}(4))$	$2$	$0$	$2$	$12$	$114$	$1421$	$21195$	$21195$	$2$	$6$	$23$	$112$	$668$	$4656$	$6$	$198$	$15216$	✓	✓	$[1, 2, 3, 2, 4, 7, 6, 7, 7, 4, 6, 15, 13, 18, 25, 13, 13, 18, 15, 6]$
1.6.E.2.1a	$1$	$6$	$9$	$\mathrm{SU}(2)^3$	$E_{t}$	$2$	$0$	$2$	$13$	$145$	$2128$	$36624$	$36624$	$2$	$7$	$32$	$186$	$1287$	$10080$	$7$	$366$	$36795$		✓	$[1, 2, 4, 3, 4, 11, 11, 15, 16, 7, 6, 23, 25, 45, 70, 31, 40, 62, 41, 13]$
1.6.F.2.1a	$1$	$6$	$7$	$\mathrm{U}(1)\times\mathrm{SU}(2)^2$	$F_{at}$	$2$	$1/2$	$2$	$20$	$285$	$4949$	$97608$	$97608$	$2$	$8$	$44$	$308$	$2507$	$22530$	$9$	$692$	$90730$		✓	$[1, 2, 5, 3, 6, 22, 20, 25, 33, 12, 10, 61, 62, 122, 210, 87, 91, 179, 130, 31]$
1.6.F.2.1b	$1$	$6$	$7$	$\mathrm{U}(1)\times\mathrm{SU}(2)^2$	$F_{t}$	$2$	$0$	$3$	$23$	$295$	$4984$	$97734$	$97734$	$2$	$8$	$44$	$308$	$2507$	$22530$	$10$	$698$	$90780$		✓	$[1, 3, 5, 5, 7, 22, 24, 26, 35, 17, 13, 61, 73, 125, 210, 99, 92, 191, 135, 45]$
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.4.1a	$1$	$6$	$5$	$\mathrm{U}(1)^2\times\mathrm{SU}(2)$	$F_{ac}\times \mathrm{SU}(2)$	$4$	$0$	$2$	$17$	$270$	$5439$	$123123$	$123123$	$2$	$7$	$38$	$284$	$2567$	$25820$	$7$	$658$	$111760$	✓	✓	$[1, 2, 4, 3, 6, 21, 21, 29, 38, 15, 13, 81, 85, 174, 310, 136, 146, 296, 229, 57]$
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.H.8.2a	$1$	$6$	$3$	$\mathrm{U}(1)^3$	$H_{c,at}$	$8$	$3/8$	$2$	$18$	$290$	$6230$	$154602$	$154602$	$2$	$7$	$38$	$293$	$2822$	$30805$	$7$	$699$	$142000$	✓	✓	$[1, 2, 4, 3, 7, 22, 23, 33, 44, 20, 15, 101, 110, 240, 450, 215, 228, 498, 416, 112]$
1.6.I.2.1a	$1$	$6$	$6$	$\mathrm{SU}(2)\times\mathrm{SU}(2)_2$	$\mathrm{SU}(2)\times E_2$	$2$	$0$	$3$	$30$	$465$	$8806$	$187446$	$187446$	$2$	$11$	$69$	$531$	$4628$	$44045$	$14$	$1228$	$183420$		✓	$[1, 3, 8, 7, 9, 38, 38, 52, 71, 30, 19, 119, 135, 269, 470, 209, 231, 463, 334, 97]$
1.6.I.3.1a	$1$	$6$	$6$	$\mathrm{SU}(2)\times\mathrm{SU}(2)_2$	$\mathrm{SU}(2)\times E_3$	$3$	$0$	$3$	$26$	$355$	$6258$	$128646$	$128646$	$2$	$9$	$53$	$385$	$3238$	$30163$	$12$	$872$	$124190$		✓	$[1, 3, 6, 5, 7, 28, 26, 34, 47, 18, 15, 81, 87, 181, 318, 137, 153, 299, 218, 57]$
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.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.I.6.1a	$1$	$6$	$6$	$\mathrm{SU}(2)\times\mathrm{SU}(2)_2$	$\mathrm{SU}(2)\times J(E_3)$	$6$	$0$	$2$	$14$	$180$	$3136$	$64344$	$64344$	$2$	$7$	$33$	$210$	$1667$	$15215$	$7$	$442$	$62145$		✓	$[1, 2, 4, 3, 5, 14, 14, 21, 24, 11, 9, 42, 45, 92, 159, 70, 83, 151, 112, 30]$
1.6.I.6.2a	$1$	$6$	$6$	$\mathrm{SU}(2)\times\mathrm{SU}(2)_2$	$\mathrm{SU}(2)\times E_6$	$6$	$0$	$3$	$26$	$345$	$5754$	$110586$	$110586$	$2$	$9$	$51$	$357$	$2868$	$25403$	$12$	$808$	$101370$		✓	$[1, 3, 6, 5, 7, 26, 24, 28, 39, 16, 13, 69, 73, 135, 230, 99, 101, 201, 146, 43]$
1.6.I.8.3a	$1$	$6$	$6$	$\mathrm{SU}(2)\times\mathrm{SU}(2)_2$	$\mathrm{SU}(2)\times J(E_4)$	$8$	$0$	$2$	$14$	$175$	$2898$	$56364$	$56364$	$2$	$7$	$32$	$197$	$1502$	$13185$	$7$	$412$	$52590$	✓	✓	$[1, 2, 4, 3, 5, 13, 13, 19, 21, 11, 8, 37, 39, 75, 125, 58, 67, 121, 91, 28]$
1.6.I.12.4a	$1$	$6$	$6$	$\mathrm{SU}(2)\times\mathrm{SU}(2)_2$	$\mathrm{SU}(2)\times J(E_6)$	$12$	$0$	$2$	$14$	$175$	$2884$	$55314$	$55314$	$2$	$7$	$32$	$196$	$1482$	$12835$	$7$	$410$	$50735$	✓	✓	$[1, 2, 4, 3, 5, 13, 13, 18, 20, 10, 8, 36, 38, 69, 115, 51, 57, 102, 76, 23]$
1.6.J.2.1a	$1$	$6$	$4$	$\mathrm{U}(1)\times\mathrm{SU}(2)_2$	$J(E_2,E_1)$	$2$	$1/2$	$3$	$43$	$830$	$18627$	$458010$	$458010$	$2$	$13$	$99$	$907$	$9188$	$99515$	$18$	$2338$	$456520$		✓	$[1, 3, 10, 7, 12, 70, 71, 94, 151, 58, 34, 287, 328, 725, 1376, 631, 636, 1440, 1149, 295]$
1.6.J.2.1b	$1$	$6$	$4$	$\mathrm{U}(1)\times\mathrm{SU}(2)_2$	$J_1(E_2)$	$2$	$0$	$4$	$46$	$840$	$18662$	$458136$	$458136$	$2$	$13$	$99$	$907$	$9188$	$99515$	$20$	$2356$	$456720$		✓	$[1, 4, 10, 12, 15, 70, 80, 102, 160, 82, 40, 287, 368, 732, 1376, 680, 649, 1520, 1188, 396]$
1.6.J.3.1a	$1$	$6$	$4$	$\mathrm{U}(1)\times\mathrm{SU}(2)_2$	$J_1(E_3)$	$3$	$0$	$4$	$42$	$670$	$13594$	$318276$	$318276$	$2$	$11$	$77$	$661$	$6438$	$68173$	$16$	$1656$	$308840$		✓	$[1, 4, 8, 8, 13, 52, 54, 66, 108, 44, 34, 201, 234, 490, 932, 438, 431, 970, 780, 210]$
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.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.6.1a	$1$	$6$	$4$	$\mathrm{U}(1)\times\mathrm{SU}(2)_2$	$J(J(E_3),E_3)$	$6$	$1/2$	$2$	$21$	$335$	$6797$	$159138$	$159138$	$2$	$8$	$45$	$348$	$3267$	$34220$	$8$	$828$	$154420$		✓	$[1, 2, 5, 4, 9, 26, 28, 40, 54, 25, 17, 102, 117, 245, 466, 219, 227, 485, 395, 105]$
1.6.J.6.1b	$1$	$6$	$4$	$\mathrm{U}(1)\times\mathrm{SU}(2)_2$	$J_1(J(E_3))$	$6$	$0$	$3$	$24$	$345$	$6832$	$159264$	$159264$	$2$	$8$	$45$	$348$	$3267$	$34220$	$10$	$846$	$154620$		✓	$[1, 3, 5, 5, 8, 26, 29, 36, 55, 25, 19, 102, 121, 248, 466, 224, 220, 489, 394, 110]$
1.6.J.6.2a	$1$	$6$	$4$	$\mathrm{U}(1)\times\mathrm{SU}(2)_2$	$J(E_6,E_3)$	$6$	$1/6$	$3$	$27$	$380$	$7175$	$162540$	$162540$	$2$	$9$	$51$	$381$	$3438$	$35093$	$12$	$924$	$157300$		✓	$[1, 3, 6, 5, 8, 28, 29, 34, 55, 24, 18, 103, 118, 247, 466, 221, 218, 486, 395, 107]$
1.6.J.6.2b	$1$	$6$	$4$	$\mathrm{U}(1)\times\mathrm{SU}(2)_2$	$J_2(E_3)$	$6$	$0$	$3$	$27$	$390$	$7399$	$166320$	$166320$	$2$	$9$	$53$	$397$	$3548$	$35813$	$12$	$924$	$157940$		✓	$[1, 3, 6, 5, 8, 30, 29, 38, 55, 24, 20, 107, 120, 249, 466, 223, 226, 488, 399, 109]$
1.6.J.6.2c	$1$	$6$	$4$	$\mathrm{U}(1)\times\mathrm{SU}(2)_2$	$J_1(E_6)$	$6$	$0$	$4$	$42$	$660$	$12810$	$281736$	$281736$	$2$	$11$	$75$	$621$	$5768$	$57953$	$16$	$1512$	$249000$		✓	$[1, 4, 8, 8, 13, 50, 50, 58, 88, 40, 32, 181, 204, 384, 680, 312, 299, 664, 504, 160]$
1.6.J.8.2a	$1$	$6$	$4$	$\mathrm{U}(1)\times\mathrm{SU}(2)_2$	$J_2(E_4)$	$8$	$1/8$	$3$	$27$	$380$	$6923$	$148260$	$148260$	$2$	$9$	$51$	$371$	$3198$	$31103$	$12$	$858$	$132960$		✓	$[1, 3, 6, 5, 8, 28, 27, 34, 47, 26, 18, 97, 106, 207, 368, 187, 178, 394, 321, 109]$