Sato-Tate group search results

Results (36 matches)

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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.E.12.4a	$1$	$4$	$3$	$\mathrm{SU}(2)_{2}$	$J(E_6)$	$12$	$7/12$	$1$	$6$	$50$	$490$	$5292$	$5292$	$1$	$3$	$7$	$25$	$91$	$387$				✓	✓	$[1, 1, 2, 3, 3, 4, 3, 7, 6, 7]$
1.4.F.12.4a	$1$	$4$	$1$	$\mathrm{U}(1)_{2}$	$J(D_3)$	$12$	$3/4$	$1$	$9$	$110$	$1505$	$21546$	$21546$	$1$	$4$	$10$	$48$	$216$	$1153$					✓	$[1, 1, 3, 5, 7, 11, 9, 29, 31, 30]$
1.4.F.12.4b	$1$	$4$	$1$	$\mathrm{U}(1)_{2}$	$D_{6,1}$	$12$	$3/4$	$1$	$9$	$110$	$1505$	$21546$	$21546$	$1$	$4$	$11$	$48$	$221$	$1153$					✓	$[1, 1, 3, 5, 7, 9, 9, 27, 31, 22]$
1.4.F.12.4c	$1$	$4$	$1$	$\mathrm{U}(1)_{2}$	$D_6$	$12$	$7/12$	$2$	$18$	$200$	$2450$	$31752$	$31752$	$1$	$5$	$16$	$77$	$356$	$1803$					✓	$[1, 2, 4, 7, 12, 12, 14, 39, 40, 29]$
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.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.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.K.12.4a	$1$	$6$	$4$	$\mathrm{SU}(2)\times\mathrm{U}(1)_2$	$\mathrm{SU}(2)\times J(D_3)$	$12$	$0$	$2$	$17$	$280$	$5999$	$145593$	$145593$	$2$	$8$	$41$	$303$	$2812$	$29636$	$8$	$696$	$131965$		✓	$[1, 2, 5, 4, 7, 22, 23, 36, 46, 23, 16, 97, 108, 222, 400, 186, 205, 429, 336, 99]$
1.6.K.12.4b	$1$	$6$	$4$	$\mathrm{SU}(2)\times\mathrm{U}(1)_2$	$\mathrm{SU}(2)\times D_{6,1}$	$12$	$0$	$2$	$17$	$280$	$5999$	$145593$	$145593$	$2$	$8$	$42$	$307$	$2827$	$29686$	$8$	$696$	$131965$		✓	$[1, 2, 5, 4, 7, 22, 23, 36, 44, 21, 16, 97, 106, 222, 400, 184, 205, 419, 330, 89]$
1.6.K.12.4c	$1$	$6$	$4$	$\mathrm{SU}(2)\times\mathrm{U}(1)_2$	$\mathrm{SU}(2)\times D_6$	$12$	$0$	$3$	$32$	$535$	$10864$	$246204$	$246204$	$2$	$10$	$65$	$536$	$5037$	$51346$	$13$	$1306$	$223415$		✓	$[1, 3, 7, 6, 10, 42, 41, 52, 77, 31, 24, 158, 172, 346, 620, 274, 276, 600, 456, 122]$
1.6.K.12.4d	$1$	$6$	$4$	$\mathrm{SU}(2)\times\mathrm{U}(1)_2$	$\mathrm{SU}(2)\times D_{6,2}$	$12$	$0$	$3$	$32$	$535$	$10864$	$246204$	$246204$	$3$	$13$	$75$	$567$	$5133$	$51640$	$14$	$1316$	$223525$		✓	$[1, 3, 8, 5, 11, 42, 40, 58, 75, 30, 25, 161, 169, 347, 620, 271, 292, 592, 457, 114]$
1.6.L.12.4a	$1$	$6$	$6$	$\mathrm{U}(1)\times\mathrm{U}(1)_2$	$L(J(D_3),J(C_3))$	$12$	$1/2$	$2$	$24$	$480$	$12040$	$336672$	$336672$	$2$	$9$	$56$	$507$	$5562$	$67046$	$9$	$1311$	$330040$		✓	$[1, 2, 6, 5, 11, 39, 45, 71, 102, 56, 27, 213, 264, 583, 1150, 586, 607, 1422, 1209, 383]$
1.6.L.12.4b	$1$	$6$	$6$	$\mathrm{U}(1)\times\mathrm{U}(1)_2$	$L(J(D_3),D_3)$	$12$	$1/2$	$2$	$24$	$480$	$12040$	$336672$	$336672$	$2$	$9$	$56$	$507$	$5562$	$67046$	$9$	$1311$	$330030$		✓	$[1, 2, 6, 5, 11, 39, 45, 69, 100, 52, 27, 213, 260, 583, 1150, 580, 601, 1401, 1196, 355]$
1.6.L.12.4c	$1$	$6$	$6$	$\mathrm{U}(1)\times\mathrm{U}(1)_2$	$L(D_{6,1},D_3)$	$12$	$1/2$	$2$	$24$	$480$	$12040$	$336672$	$336672$	$2$	$9$	$57$	$511$	$5577$	$67096$	$9$	$1311$	$330030$		✓	$[1, 2, 6, 5, 11, 39, 45, 71, 100, 52, 27, 213, 260, 583, 1150, 580, 607, 1401, 1196, 355]$
1.6.L.12.4d	$1$	$6$	$6$	$\mathrm{U}(1)\times\mathrm{U}(1)_2$	$L(D_{6,1},C_{6,1})$	$12$	$1/2$	$2$	$24$	$480$	$12040$	$336672$	$336672$	$2$	$9$	$57$	$511$	$5577$	$67096$	$9$	$1311$	$330040$		✓	$[1, 2, 6, 5, 11, 39, 45, 69, 98, 48, 27, 213, 256, 583, 1150, 574, 601, 1382, 1185, 331]$
1.6.L.12.4e	$1$	$6$	$6$	$\mathrm{U}(1)\times\mathrm{U}(1)_2$	$L(J(D_3),D_{3,2})$	$12$	$1/2$	$2$	$24$	$480$	$12040$	$336672$	$336672$	$2$	$9$	$56$	$507$	$5562$	$67046$	$10$	$1326$	$330250$		✓	$[1, 2, 6, 4, 9, 39, 42, 62, 98, 44, 26, 213, 250, 583, 1150, 569, 586, 1381, 1182, 331]$
1.6.L.12.4f	$1$	$6$	$6$	$\mathrm{U}(1)\times\mathrm{U}(1)_2$	$L(D_{6,1},D_{3,2})$	$12$	$1/2$	$2$	$24$	$480$	$12040$	$336672$	$336672$	$2$	$9$	$57$	$511$	$5577$	$67096$	$10$	$1326$	$330250$		✓	$[1, 2, 6, 4, 9, 39, 42, 64, 98, 44, 26, 213, 250, 583, 1150, 569, 592, 1381, 1182, 331]$
1.6.L.12.4g	$1$	$6$	$6$	$\mathrm{U}(1)\times\mathrm{U}(1)_2$	$L_1(J(D_3))$	$12$	$0$	$3$	$27$	$490$	$12075$	$336798$	$336798$	$2$	$9$	$56$	$507$	$5562$	$67046$	$12$	$1344$	$330460$		✓	$[1, 3, 6, 7, 10, 39, 47, 66, 105, 60, 30, 213, 276, 588, 1150, 602, 595, 1444, 1214, 412]$
1.6.L.12.4h	$1$	$6$	$6$	$\mathrm{U}(1)\times\mathrm{U}(1)_2$	$L_1(D_{6,1})$	$12$	$0$	$3$	$27$	$490$	$12075$	$336798$	$336798$	$2$	$9$	$57$	$511$	$5577$	$67096$	$12$	$1344$	$330460$		✓	$[1, 3, 6, 7, 10, 39, 47, 64, 101, 52, 30, 213, 268, 588, 1150, 590, 589, 1404, 1190, 360]$
1.6.L.12.4i	$1$	$6$	$6$	$\mathrm{U}(1)\times\mathrm{U}(1)_2$	$L(D_6,D_3)$	$12$	$1/3$	$3$	$33$	$570$	$12985$	$346878$	$346878$	$2$	$10$	$65$	$566$	$5917$	$69106$	$13$	$1455$	$335790$		✓	$[1, 3, 7, 6, 11, 44, 47, 63, 101, 49, 29, 216, 262, 585, 1150, 582, 586, 1403, 1192, 357]$
1.6.L.12.4j	$1$	$6$	$6$	$\mathrm{U}(1)\times\mathrm{U}(1)_2$	$L_2(D_3)$	$12$	$1/4$	$3$	$33$	$590$	$13545$	$358218$	$358218$	$2$	$10$	$66$	$578$	$6032$	$70096$	$13$	$1455$	$337070$		✓	$[1, 3, 7, 6, 11, 46, 47, 65, 101, 49, 33, 228, 266, 591, 1150, 588, 588, 1407, 1208, 363]$
1.6.L.12.4k	$1$	$6$	$6$	$\mathrm{U}(1)\times\mathrm{U}(1)_2$	$L(D_6,C_6)$	$12$	$1/2$	$3$	$45$	$930$	$22365$	$586278$	$586278$	$2$	$12$	$95$	$932$	$10137$	$117136$	$16$	$2460$	$554580$		✓	$[1, 3, 9, 7, 15, 76, 78, 106, 171, 69, 46, 372, 426, 943, 1800, 843, 855, 1980, 1613, 435]$
1.6.L.12.4l	$1$	$6$	$6$	$\mathrm{U}(1)\times\mathrm{U}(1)_2$	$L_1(D_6)$	$12$	$0$	$4$	$48$	$940$	$22400$	$586404$	$586404$	$2$	$12$	$95$	$932$	$10137$	$117136$	$18$	$2478$	$554780$		✓	$[1, 4, 9, 10, 16, 76, 83, 108, 176, 81, 50, 372, 448, 948, 1800, 870, 858, 2022, 1632, 488]$
1.6.L.12.4m	$1$	$6$	$6$	$\mathrm{U}(1)\times\mathrm{U}(1)_2$	$L(D_{6,2},D_{3,2})$	$12$	$1/3$	$3$	$33$	$570$	$12985$	$346878$	$346878$	$3$	$13$	$75$	$597$	$6013$	$69400$	$14$	$1470$	$336010$		✓	$[1, 3, 8, 5, 12, 44, 45, 70, 99, 46, 28, 219, 252, 585, 1150, 571, 605, 1383, 1191, 333]$
1.6.L.12.4n	$1$	$6$	$6$	$\mathrm{U}(1)\times\mathrm{U}(1)_2$	$L_2(D_{3,2})$	$12$	$1/4$	$3$	$33$	$590$	$13545$	$358218$	$358218$	$3$	$13$	$76$	$609$	$6128$	$70390$	$14$	$1470$	$337290$		✓	$[1, 3, 8, 5, 12, 46, 45, 72, 99, 46, 32, 231, 256, 591, 1150, 577, 607, 1387, 1207, 339]$
1.6.L.12.4o	$1$	$6$	$6$	$\mathrm{U}(1)\times\mathrm{U}(1)_2$	$L(D_{6,2},C_6)$	$12$	$1/2$	$3$	$45$	$930$	$22365$	$586278$	$586278$	$3$	$15$	$105$	$963$	$10233$	$117430$	$16$	$2460$	$554580$		✓	$[1, 3, 10, 7, 18, 76, 79, 120, 171, 74, 46, 375, 426, 943, 1800, 843, 889, 1980, 1626, 435]$
1.6.L.12.4p	$1$	$6$	$6$	$\mathrm{U}(1)\times\mathrm{U}(1)_2$	$L_1(D_{6,2})$	$12$	$0$	$4$	$48$	$940$	$22400$	$586404$	$586404$	$3$	$15$	$105$	$963$	$10233$	$117430$	$20$	$2508$	$555220$		✓	$[1, 4, 10, 8, 15, 76, 78, 108, 172, 70, 48, 375, 428, 948, 1800, 848, 862, 1982, 1617, 440]$
1.6.M.12.4a	$1$	$6$	$3$	$\mathrm{SU}(2)_{3}$	$M(D_6)$	$12$	$1/6$	$2$	$20$	$360$	$8260$	$213864$	$213864$	$2$	$8$	$48$	$402$	$4087$	$45972$	$8$	$994$	$217328$	✓	✓	$[1, 2, 5, 4, 8, 30, 33, 50, 70, 33, 18, 134, 162, 366, 708, 346, 364, 818, 672, 190]$
1.6.N.12.4a	$1$	$6$	$1$	$\mathrm{U}(1)_{3}$	$J(B(3,1))$	$12$	$2/3$	$2$	$42$	$1220$	$38290$	$1240092$	$1240092$	$2$	$12$	$112$	$1348$	$17772$	$242610$	$15$	$3941$	$1288050$		✓	$[1, 2, 9, 9, 18, 107, 129, 206, 354, 170, 75, 756, 976, 2385, 4929, 2594, 2665, 6587, 5852, 1785]$
1.6.N.12.4b	$1$	$6$	$1$	$\mathrm{U}(1)_{3}$	$B(3,2)$	$12$	$1/6$	$4$	$60$	$1440$	$41300$	$1283184$	$1283184$	$2$	$14$	$132$	$1514$	$19052$	$252270$	$22$	$4362$	$1321580$		✓	$[1, 4, 11, 14, 22, 122, 147, 212, 372, 193, 86, 778, 1032, 2414, 4962, 2660, 2656, 6678, 5896, 1906]$
1.6.N.12.4c	$1$	$6$	$1$	$\mathrm{U}(1)_{3}$	$J(A(1,6)_2)$	$12$	$1/2$	$3$	$51$	$1310$	$39235$	$1250298$	$1250298$	$3$	$16$	$130$	$1438$	$18258$	$245373$	$18$	$4074$	$1294620$		✓	$[1, 3, 11, 9, 21, 112, 130, 212, 357, 163, 78, 764, 964, 2387, 4938, 2577, 2680, 6556, 5846, 1733]$
1.6.N.12.4d	$1$	$6$	$1$	$\mathrm{U}(1)_{3}$	$J(A(3,2))$	$12$	$2/3$	$3$	$57$	$1430$	$41265$	$1283058$	$1283058$	$3$	$17$	$142$	$1545$	$19148$	$252564$	$20$	$4340$	$1321290$		✓	$[1, 3, 12, 9, 22, 122, 136, 217, 363, 163, 78, 781, 976, 2403, 4962, 2581, 2675, 6558, 5850, 1731]$
1.6.N.12.4e	$1$	$6$	$1$	$\mathrm{U}(1)_{3}$	$J(A(1,6)_1)$	$12$	$1/2$	$5$	$99$	$2450$	$67235$	$1956150$	$1956150$	$4$	$26$	$235$	$2570$	$30769$	$386151$	$34$	$7122$	$1934400$		✓	$[1, 5, 19, 15, 35, 208, 224, 336, 561, 231, 132, 1222, 1462, 3449, 6852, 3373, 3486, 8304, 7102, 2009]$

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