Sato-Tate group search results

Results (10 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.I.1.1a	$1$	$6$	$6$	$\mathrm{SU}(2)\times\mathrm{SU}(2)_2$	$\mathrm{SU}(2)\times E_1$	$1$	$0$	$5$	$58$	$925$	$17598$	$374850$	$374850$	$4$	$21$	$137$	$1059$	$9250$	$88075$	$26$	$2444$	$366740$		✓	$[1, 5, 14, 9, 15, 76, 70, 96, 133, 44, 35, 235, 251, 535, 940, 399, 449, 887, 642, 155]$
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.2.1b	$1$	$6$	$6$	$\mathrm{SU}(2)\times\mathrm{SU}(2)_2$	$\mathrm{SU}(2)\times J(E_1)$	$2$	$0$	$3$	$30$	$465$	$8806$	$187446$	$187446$	$3$	$13$	$75$	$547$	$4673$	$44171$	$14$	$1228$	$183420$		✓	$[1, 3, 8, 5, 9, 38, 36, 52, 67, 24, 19, 119, 127, 269, 470, 201, 231, 445, 324, 79]$
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	$1$	$6$	$6$	$\mathrm{SU}(2)\times\mathrm{SU}(2)_2$	$\mathrm{SU}(2)\times J(E_6)$	$12$	$0$	$2$	$14$	$175$	$2884$	$55314$	$55314$	$2$	$7$	$32$	$196$	$1482$	$12835$	$7$	$410$	$50735$	✓	✓	$[1, 2, 4, 3, 5, 13, 13, 18, 20, 10, 8, 36, 38, 69, 115, 51, 57, 102, 76, 23]$