Sato-Tate group search results

Results (26 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.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	$1$	$6$	$4$	$\mathrm{U}(1)\times\mathrm{SU}(2)_2$	$J_2(E_4)$	$8$	$1/8$	$3$	$27$	$380$	$6923$	$148260$	$148260$	$2$	$9$	$51$	$371$	$3198$	$31103$	$12$	$858$	$132960$		✓	$[1, 3, 6, 5, 8, 28, 27, 34, 47, 26, 18, 97, 106, 207, 368, 187, 178, 394, 321, 109]$
1.6.J.8.3a	$1$	$6$	$4$	$\mathrm{U}(1)\times\mathrm{SU}(2)_2$	$J(J(E_4),J(E_2))$	$8$	$1/4$	$2$	$15$	$225$	$4739$	$114933$	$114933$	$2$	$7$	$35$	$257$	$2392$	$25195$	$8$	$630$	$114920$		✓	$[1, 2, 4, 4, 6, 18, 22, 31, 41, 25, 11, 74, 94, 187, 344, 175, 171, 382, 304, 104]$
1.6.J.8.3b	$1$	$6$	$4$	$\mathrm{U}(1)\times\mathrm{SU}(2)_2$	$J(J(E_4),E_4)$	$8$	$1/2$	$2$	$21$	$330$	$6419$	$142548$	$142548$	$2$	$8$	$44$	$329$	$2962$	$29790$	$8$	$762$	$129760$		✓	$[1, 2, 5, 4, 9, 25, 26, 37, 46, 26, 16, 93, 104, 202, 368, 182, 181, 392, 316, 104]$
1.6.J.8.3c	$1$	$6$	$4$	$\mathrm{U}(1)\times\mathrm{SU}(2)_2$	$J_1(J(E_4))$	$8$	$0$	$3$	$24$	$340$	$6454$	$142674$	$142674$	$2$	$8$	$44$	$329$	$2962$	$29790$	$10$	$780$	$129960$		✓	$[1, 3, 5, 5, 8, 25, 27, 33, 47, 26, 18, 93, 108, 205, 368, 187, 174, 396, 315, 109]$
1.6.J.8.5a	$1$	$6$	$4$	$\mathrm{U}(1)\times\mathrm{SU}(2)_2$	$J_2(J(E_2))$	$8$	$3/8$	$2$	$17$	$255$	$5131$	$119973$	$119973$	$2$	$8$	$41$	$291$	$2582$	$26276$	$8$	$662$	$116840$		✓	$[1, 2, 5, 4, 7, 20, 23, 34, 41, 25, 13, 78, 96, 187, 344, 175, 178, 384, 309, 104]$
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.J.12.4b	$1$	$6$	$4$	$\mathrm{U}(1)\times\mathrm{SU}(2)_2$	$J_2(J(E_3))$	$12$	$1/4$	$2$	$15$	$200$	$3717$	$83223$	$83223$	$2$	$7$	$33$	$216$	$1822$	$18040$	$7$	$471$	$79070$		✓	$[1, 2, 4, 3, 6, 15, 16, 24, 28, 15, 11, 55, 62, 126, 233, 114, 121, 246, 204, 57]$
1.6.J.12.4c	$1$	$6$	$4$	$\mathrm{U}(1)\times\mathrm{SU}(2)_2$	$J(J(E_6),E_6)$	$12$	$1/2$	$2$	$21$	$330$	$6405$	$140868$	$140868$	$2$	$8$	$44$	$328$	$2932$	$29110$	$8$	$756$	$124500$		✓	$[1, 2, 5, 4, 9, 25, 26, 36, 44, 23, 16, 92, 102, 192, 340, 156, 161, 332, 257, 80]$
1.6.J.12.4d	$1$	$6$	$4$	$\mathrm{U}(1)\times\mathrm{SU}(2)_2$	$J_1(J(E_6))$	$12$	$0$	$3$	$24$	$340$	$6440$	$140994$	$140994$	$2$	$8$	$44$	$328$	$2932$	$29110$	$10$	$774$	$124700$		✓	$[1, 3, 5, 5, 8, 25, 27, 32, 45, 23, 18, 92, 106, 195, 340, 161, 154, 336, 256, 85]$
1.6.J.12.5a	$1$	$6$	$4$	$\mathrm{U}(1)\times\mathrm{SU}(2)_2$	$J_2(E_6)$	$12$	$1/12$	$3$	$27$	$380$	$6895$	$146160$	$146160$	$2$	$9$	$51$	$369$	$3158$	$30343$	$12$	$852$	$127700$		✓	$[1, 3, 6, 5, 8, 28, 27, 32, 45, 22, 18, 95, 104, 195, 340, 159, 156, 334, 259, 83]$
1.6.J.16.11a	$1$	$6$	$4$	$\mathrm{U}(1)\times\mathrm{SU}(2)_2$	$J_2(J(E_4))$	$16$	$5/16$	$2$	$15$	$195$	$3479$	$74193$	$74193$	$2$	$7$	$32$	$203$	$1647$	$15685$	$7$	$438$	$66580$	✓	✓	$[1, 2, 4, 3, 6, 14, 15, 22, 24, 16, 10, 50, 55, 105, 184, 96, 97, 199, 165, 57]$
1.6.J.24.14a	$1$	$6$	$4$	$\mathrm{U}(1)\times\mathrm{SU}(2)_2$	$J_2(J(E_6))$	$24$	$7/24$	$2$	$15$	$195$	$3465$	$73143$	$73143$	$2$	$7$	$32$	$202$	$1627$	$15305$	$7$	$435$	$63950$	✓	✓	$[1, 2, 4, 3, 6, 14, 15, 21, 23, 14, 10, 49, 54, 99, 170, 82, 86, 169, 134, 44]$