LMFDB - Sato-Tate group search results

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Weight	Degree	Include irrational	$\mathrm{ST}^0$	Maximal

Components	Component group	$\mathrm{Pr}[a_1=0]$	Second trace moment	Fourth trace moment

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Results (40 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
1.6.N.9.2a	$1$	$6$	$1$	$\mathrm{U}(1)_{3}$	$C(3,1)$	$9$	$8/9$	$2$	$54$	$1620$	$51030$	$1653372$	$1653372$	$1$	$11$	$135$	$1755$	$23571$	$323109$	$20$	$5244$	$1717220$		✓	$[1, 2, 10, 10, 17, 144, 162, 250, 466, 196, 96, 1003, 1264, 3174, 6576, 3406, 3507, 8704, 7744, 2270]$
1.6.N.12.3a	$1$	$6$	$1$	$\mathrm{U}(1)_{3}$	$C(2,2)$	$12$	$2/3$	$2$	$42$	$1220$	$38290$	$1240092$	$1240092$	$1$	$9$	$103$	$1321$	$17691$	$242367$	$16$	$3944$	$1288060$		✓	$[1, 2, 8, 10, 15, 108, 128, 194, 354, 166, 76, 753, 976, 2386, 4932, 2594, 2641, 6588, 5840, 1790]$
1.6.N.18.3a	$1$	$6$	$1$	$\mathrm{U}(1)_{3}$	$J(C(3,1))$	$18$	$17/18$	$1$	$27$	$810$	$25515$	$826686$	$826686$	$1$	$7$	$72$	$891$	$11826$	$161676$	$10$	$2622$	$858610$		✓	$[1, 1, 6, 5, 10, 72, 82, 131, 233, 101, 48, 503, 632, 1587, 3288, 1703, 1767, 4352, 3878, 1135]$
1.6.N.18.4a	$1$	$6$	$1$	$\mathrm{U}(1)_{3}$	$D(3,1)$	$18$	$4/9$	$2$	$30$	$820$	$25550$	$826812$	$826812$	$1$	$7$	$71$	$887$	$11811$	$161625$	$12$	$2644$	$858900$		✓	$[1, 2, 6, 10, 13, 72, 94, 138, 242, 136, 56, 503, 688, 1598, 3288, 1782, 1775, 4472, 3936, 1310]$
1.6.N.21.1a	$1$	$6$	$1$	$\mathrm{U}(1)_{3}$	$C(1,7)$	$21$	$2/3$	$2$	$30$	$740$	$22190$	$710892$	$710892$	$1$	$7$	$67$	$791$	$10271$	$139225$	$12$	$2316$	$737820$		✓	$[1, 2, 6, 6, 9, 64, 72, 108, 202, 86, 44, 431, 544, 1362, 2822, 1462, 1507, 3732, 3322, 978]$
1.6.N.24.12a	$1$	$6$	$1$	$\mathrm{U}(1)_{3}$	$J_s(C(2,2))$	$24$	$5/6$	$1$	$21$	$610$	$19145$	$620046$	$620046$	$1$	$7$	$58$	$681$	$8906$	$121366$	$8$	$1972$	$644030$		✓	$[1, 1, 6, 5, 10, 54, 66, 107, 177, 91, 38, 381, 488, 1193, 2466, 1297, 1343, 3294, 2938, 895]$
1.6.N.24.12b	$1$	$6$	$1$	$\mathrm{U}(1)_{3}$	$D(2,2)$	$24$	$1/3$	$2$	$24$	$620$	$19180$	$620172$	$620172$	$1$	$6$	$55$	$670$	$8871$	$121254$	$10$	$1994$	$644320$		✓	$[1, 2, 5, 8, 10, 54, 71, 104, 182, 103, 42, 378, 516, 1200, 2466, 1338, 1332, 3354, 2954, 984]$
1.6.N.24.13a	$1$	$6$	$1$	$\mathrm{U}(1)_{3}$	$J(C(2,2))$	$24$	$5/6$	$1$	$21$	$610$	$19145$	$620046$	$620046$	$1$	$6$	$56$	$674$	$8886$	$121305$	$8$	$1972$	$644030$		✓	$[1, 1, 5, 5, 9, 54, 65, 103, 177, 86, 38, 378, 488, 1193, 2466, 1297, 1334, 3294, 2926, 895]$
1.6.N.27.3a	$1$	$6$	$1$	$\mathrm{U}(1)_{3}$	$C(3,3)$	$27$	$20/27$	$2$	$30$	$660$	$18270$	$564732$	$564732$	$1$	$7$	$63$	$687$	$8451$	$111225$	$12$	$1932$	$581240$		✓	$[1, 2, 6, 6, 9, 56, 60, 88, 162, 70, 40, 343, 428, 1066, 2208, 1146, 1183, 2912, 2592, 770]$
1.6.N.36.9a	$1$	$6$	$1$	$\mathrm{U}(1)_{3}$	$E(36)$	$36$	$2/9$	$2$	$18$	$420$	$12810$	$413532$	$413532$	$1$	$5$	$39$	$453$	$5931$	$80883$	$8$	$1344$	$429740$		✓	$[1, 2, 4, 6, 7, 36, 48, 70, 122, 70, 28, 253, 344, 802, 1644, 894, 889, 2236, 1972, 658]$
1.6.N.36.10a	$1$	$6$	$1$	$\mathrm{U}(1)_{3}$	$J(D(3,1))$	$36$	$13/18$	$1$	$15$	$410$	$12775$	$413406$	$413406$	$1$	$5$	$40$	$457$	$5946$	$80934$	$6$	$1322$	$429450$		✓	$[1, 1, 4, 5, 8, 36, 48, 75, 121, 71, 28, 253, 344, 799, 1644, 891, 901, 2236, 1974, 655]$
1.6.N.36.11a	$1$	$6$	$1$	$\mathrm{U}(1)_{3}$	$C(6,2)$	$36$	$13/18$	$2$	$30$	$620$	$15750$	$456372$	$456372$	$1$	$7$	$61$	$627$	$7241$	$90645$	$12$	$1724$	$462700$		✓	$[1, 2, 6, 6, 9, 52, 54, 74, 130, 60, 32, 275, 344, 818, 1680, 878, 887, 2208, 1960, 606]$
1.6.N.42.1a	$1$	$6$	$1$	$\mathrm{U}(1)_{3}$	$J(C(1,7))$	$42$	$5/6$	$1$	$15$	$370$	$11095$	$355446$	$355446$	$1$	$5$	$38$	$409$	$5176$	$69734$	$6$	$1158$	$368910$		✓	$[1, 1, 4, 3, 6, 32, 37, 60, 101, 46, 22, 217, 272, 681, 1411, 731, 767, 1866, 1667, 489]$
1.6.N.48.3a	$1$	$6$	$1$	$\mathrm{U}(1)_{3}$	$C(4,4)$	$48$	$2/3$	$2$	$30$	$620$	$15050$	$408492$	$408492$	$1$	$7$	$61$	$617$	$6851$	$81625$	$12$	$1656$	$399480$		✓	$[1, 2, 6, 6, 9, 52, 52, 70, 118, 52, 32, 253, 296, 694, 1372, 698, 711, 1732, 1518, 466]$
1.6.N.48.48a	$1$	$6$	$1$	$\mathrm{U}(1)_{3}$	$J(D(2,2))$	$48$	$2/3$	$1$	$12$	$310$	$9590$	$310086$	$310086$	$1$	$5$	$33$	$352$	$4486$	$60779$	$5$	$997$	$322160$		✓	$[1, 1, 4, 4, 7, 27, 37, 60, 91, 57, 21, 192, 258, 600, 1233, 669, 684, 1677, 1489, 492]$
1.6.N.54.5a	$1$	$6$	$1$	$\mathrm{U}(1)_{3}$	$J(C(3,3))$	$54$	$47/54$	$1$	$15$	$330$	$9135$	$282366$	$282366$	$1$	$5$	$36$	$357$	$4266$	$55734$	$6$	$966$	$290620$		✓	$[1, 1, 4, 3, 6, 28, 31, 50, 81, 38, 20, 173, 214, 533, 1104, 573, 605, 1456, 1302, 385]$
1.6.N.54.5b	$1$	$6$	$1$	$\mathrm{U}(1)_{3}$	$D(3,3)$	$54$	$10/27$	$2$	$18$	$340$	$9170$	$282492$	$282492$	$1$	$5$	$35$	$353$	$4251$	$55683$	$8$	$984$	$290820$		✓	$[1, 2, 4, 6, 7, 28, 36, 50, 86, 50, 24, 173, 236, 538, 1104, 602, 601, 1500, 1320, 446]$
1.6.N.54.8a	$1$	$6$	$1$	$\mathrm{U}(1)_{3}$	$J_s(C(3,3))$	$54$	$47/54$	$1$	$15$	$330$	$9135$	$282366$	$282366$	$1$	$5$	$36$	$357$	$4266$	$55734$	$6$	$966$	$290620$		✓	$[1, 1, 4, 3, 6, 28, 31, 50, 81, 38, 20, 173, 214, 533, 1104, 573, 605, 1456, 1302, 385]$
1.6.N.72.39a	$1$	$6$	$1$	$\mathrm{U}(1)_{3}$	$J_n(E(36))$	$72$	$11/18$	$1$	$9$	$210$	$6405$	$206766$	$206766$	$1$	$3$	$20$	$227$	$2966$	$40442$	$4$	$672$	$214870$		✓	$[1, 1, 2, 3, 4, 18, 24, 35, 61, 35, 14, 127, 172, 401, 822, 447, 445, 1118, 986, 329]$
1.6.N.72.40a	$1$	$6$	$1$	$\mathrm{U}(1)_{3}$	$J(E(36))$	$72$	$11/18$	$1$	$9$	$210$	$6405$	$206766$	$206766$	$1$	$4$	$24$	$240$	$3006$	$40563$	$4$	$672$	$214870$		✓	$[1, 1, 3, 3, 5, 18, 25, 41, 61, 38, 14, 128, 172, 401, 822, 447, 458, 1118, 992, 329]$
1.6.N.72.41a	$1$	$6$	$1$	$\mathrm{U}(1)_{3}$	$E(72)$	$72$	$1/9$	$2$	$12$	$220$	$6440$	$206892$	$206892$	$1$	$4$	$23$	$236$	$2991$	$40512$	$6$	$694$	$215160$		✓	$[1, 2, 3, 4, 4, 18, 25, 36, 62, 37, 14, 128, 172, 404, 822, 450, 446, 1118, 990, 332]$
1.6.N.72.42a	$1$	$6$	$1$	$\mathrm{U}(1)_{3}$	$J_s(C(6,2))$	$72$	$31/36$	$1$	$15$	$310$	$7875$	$228186$	$228186$	$1$	$5$	$34$	$323$	$3646$	$45394$	$6$	$862$	$231350$		✓	$[1, 1, 4, 3, 6, 26, 28, 41, 65, 33, 16, 139, 172, 409, 840, 439, 451, 1104, 986, 303]$
1.6.N.72.43a	$1$	$6$	$1$	$\mathrm{U}(1)_{3}$	$D(6,2)$	$72$	$13/36$	$2$	$18$	$320$	$7910$	$228312$	$228312$	$1$	$5$	$34$	$323$	$3646$	$45393$	$8$	$884$	$231640$		✓	$[1, 2, 4, 6, 7, 26, 34, 44, 70, 50, 20, 139, 200, 416, 840, 480, 455, 1164, 1014, 392]$
1.6.N.72.44a	$1$	$6$	$1$	$\mathrm{U}(1)_{3}$	$J(C(6,2))$	$72$	$31/36$	$1$	$15$	$310$	$7875$	$228186$	$228186$	$1$	$5$	$35$	$327$	$3661$	$45444$	$6$	$862$	$231350$		✓	$[1, 1, 4, 3, 6, 26, 28, 43, 65, 33, 16, 139, 172, 409, 840, 439, 457, 1104, 986, 303]$
1.6.N.96.64a	$1$	$6$	$1$	$\mathrm{U}(1)_{3}$	$J_s(C(4,4))$	$96$	$5/6$	$1$	$15$	$310$	$7525$	$204246$	$204246$	$1$	$5$	$34$	$319$	$3456$	$40904$	$6$	$828$	$199740$		✓	$[1, 1, 4, 3, 6, 26, 27, 40, 59, 30, 16, 129, 148, 347, 686, 349, 367, 866, 768, 233]$
1.6.N.96.64b	$1$	$6$	$1$	$\mathrm{U}(1)_{3}$	$D(4,4)$	$96$	$1/3$	$2$	$18$	$320$	$7560$	$204372$	$204372$	$1$	$5$	$34$	$318$	$3451$	$40883$	$8$	$846$	$199940$		✓	$[1, 2, 4, 6, 7, 26, 32, 41, 64, 41, 20, 128, 170, 352, 686, 376, 365, 908, 783, 286]$
1.6.N.96.72a	$1$	$6$	$1$	$\mathrm{U}(1)_{3}$	$J(C(4,4))$	$96$	$5/6$	$1$	$15$	$310$	$7525$	$204246$	$204246$	$1$	$5$	$35$	$322$	$3466$	$40934$	$6$	$828$	$199740$		✓	$[1, 1, 4, 3, 6, 26, 27, 41, 59, 29, 16, 128, 148, 347, 686, 349, 369, 866, 765, 233]$
1.6.N.108.17a	$1$	$6$	$1$	$\mathrm{U}(1)_{3}$	$J(D(3,3))$	$108$	$37/54$	$1$	$9$	$170$	$4585$	$141246$	$141246$	$1$	$4$	$22$	$190$	$2166$	$27963$	$4$	$492$	$145410$		✓	$[1, 1, 3, 3, 5, 14, 19, 31, 43, 28, 12, 88, 118, 269, 552, 301, 314, 750, 666, 223]$
1.6.N.108.22a	$1$	$6$	$1$	$\mathrm{U}(1)_{3}$	$C(6,6)$	$108$	$37/54$	$2$	$30$	$620$	$14910$	$390852$	$390852$	$1$	$7$	$61$	$615$	$6741$	$78045$	$12$	$1644$	$369760$		✓	$[1, 2, 6, 6, 9, 52, 52, 68, 114, 46, 32, 247, 284, 630, 1204, 562, 571, 1324, 1076, 302]$
1.6.N.144.182a	$1$	$6$	$1$	$\mathrm{U}(1)_{3}$	$J(E(72))$	$144$	$5/9$	$1$	$6$	$110$	$3220$	$103446$	$103446$	$1$	$3$	$14$	$125$	$1516$	$20317$	$3$	$347$	$107580$		✓	$[1, 1, 2, 2, 3, 9, 13, 21, 31, 20, 7, 65, 86, 202, 411, 225, 230, 559, 498, 166]$
1.6.N.144.183a	$1$	$6$	$1$	$\mathrm{U}(1)_{3}$	$J(D(6,2))$	$144$	$49/72$	$1$	$9$	$160$	$3955$	$114156$	$114156$	$1$	$4$	$21$	$173$	$1856$	$22793$	$4$	$442$	$115820$		✓	$[1, 1, 3, 3, 5, 13, 18, 27, 35, 28, 10, 71, 100, 208, 420, 240, 238, 582, 513, 196]$
1.6.N.168.42a	$1$	$6$	$1$	$\mathrm{U}(1)_{3}$	$E(168)$	$168$	$1/3$	$2$	$12$	$140$	$3080$	$90972$	$90972$	$1$	$4$	$19$	$140$	$1451$	$18112$	$6$	$366$	$94080$		✓	$[1, 2, 3, 4, 4, 10, 15, 18, 30, 23, 10, 56, 84, 176, 356, 206, 198, 498, 436, 172]$
1.6.N.192.956a	$1$	$6$	$1$	$\mathrm{U}(1)_{3}$	$J(D(4,4))$	$192$	$2/3$	$1$	$9$	$160$	$3780$	$102186$	$102186$	$1$	$4$	$21$	$171$	$1761$	$20548$	$4$	$423$	$99970$	✓	✓	$[1, 1, 3, 3, 5, 13, 17, 26, 32, 24, 10, 66, 85, 176, 343, 188, 195, 454, 399, 143]$
1.6.N.216.92a	$1$	$6$	$1$	$\mathrm{U}(1)_{3}$	$D(6,6)$	$216$	$37/108$	$2$	$18$	$320$	$7490$	$195552$	$195552$	$1$	$5$	$34$	$317$	$3396$	$39093$	$8$	$840$	$185080$		✓	$[1, 2, 4, 6, 7, 26, 32, 40, 62, 38, 20, 125, 164, 320, 602, 308, 295, 704, 562, 204]$
1.6.N.216.95a	$1$	$6$	$1$	$\mathrm{U}(1)_{3}$	$J_s(C(6,6))$	$216$	$91/108$	$1$	$15$	$310$	$7455$	$195426$	$195426$	$1$	$5$	$34$	$317$	$3396$	$39094$	$6$	$822$	$184880$		✓	$[1, 1, 4, 3, 6, 26, 27, 38, 57, 26, 16, 125, 142, 315, 602, 281, 293, 662, 544, 151]$
1.6.N.216.99a	$1$	$6$	$1$	$\mathrm{U}(1)_{3}$	$J(C(6,6))$	$216$	$91/108$	$1$	$15$	$310$	$7455$	$195426$	$195426$	$1$	$5$	$35$	$321$	$3411$	$39144$	$6$	$822$	$184880$		✓	$[1, 1, 4, 3, 6, 26, 27, 40, 57, 26, 16, 125, 142, 315, 602, 281, 299, 662, 544, 151]$
1.6.N.216.153a	$1$	$6$	$1$	$\mathrm{U}(1)_{3}$	$E(216)$	$216$	$7/27$	$2$	$12$	$140$	$2800$	$75852$	$75852$	$1$	$4$	$19$	$136$	$1311$	$15312$	$6$	$334$	$76240$		✓	$[1, 2, 3, 4, 4, 10, 13, 16, 26, 17, 10, 48, 64, 140, 282, 158, 158, 382, 338, 120]$
1.6.N.336.208a	$1$	$6$	$1$	$\mathrm{U}(1)_{3}$	$J(E(168))$	$336$	$2/3$	$1$	$6$	$70$	$1540$	$45486$	$45486$	$1$	$3$	$12$	$77$	$746$	$9117$	$3$	$183$	$47040$	✓	✓	$[1, 1, 2, 2, 3, 5, 8, 12, 15, 13, 5, 29, 42, 88, 178, 103, 106, 249, 221, 86]$
1.6.N.432.523a	$1$	$6$	$1$	$\mathrm{U}(1)_{3}$	$J(D(6,6))$	$432$	$145/216$	$1$	$9$	$160$	$3745$	$97776$	$97776$	$1$	$4$	$21$	$170$	$1731$	$19643$	$4$	$420$	$92540$	✓	✓	$[1, 1, 3, 3, 5, 13, 17, 25, 31, 22, 10, 64, 82, 160, 301, 154, 158, 352, 287, 102]$
1.6.N.432.734a	$1$	$6$	$1$	$\mathrm{U}(1)_{3}$	$J(E(216))$	$432$	$17/27$	$1$	$6$	$70$	$1400$	$37926$	$37926$	$1$	$3$	$12$	$75$	$676$	$7717$	$3$	$167$	$38120$	✓	✓	$[1, 1, 2, 2, 3, 5, 7, 11, 13, 10, 5, 25, 32, 70, 141, 79, 86, 191, 172, 60]$

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This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.