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Label Class Conductor Rank* Torsion $\textrm{End}^0(J_{\overline\Q})$ Igusa-Clebsch invariants Igusa invariants G2-invariants Equation
464.a.464.1 464.a \( 2^{4} \cdot 29 \) $0$ $\Z/8\Z$ \(\Q\) $[136,280,15060,1856]$ $[68,146,-64,-6417,464]$ $[90870848/29,2869192/29,-18496/29]$ $y^2 + (x + 1)y = -x^6 - 2x^5 - 2x^4 - x^3$
472.a.60416.1 472.a \( 2^{3} \cdot 59 \) $0$ $\Z/8\Z$ \(\Q\) $[152,17065,1592025,7552]$ $[152,-10414,-926656,-62325777,60416]$ $[79235168/59,-35714813/59,-20907676/59]$ $y^2 + (x + 1)y = 8x^5 + 5x^4 + 4x^3 + 2x^2$
691.a.691.1 691.a \( 691 \) $0$ $\Z/8\Z$ \(\Q\) $[104,-824,-20333,-2764]$ $[52,250,601,-7812,-691]$ $[-380204032/691,-35152000/691,-1625104/691]$ $y^2 + (x + 1)y = x^5 - x^3 - x^2$
709.a.709.1 709.a \( 709 \) $0$ $\Z/8\Z$ \(\Q\) $[160,-1280,-42089,2836]$ $[80,480,1121,-35180,709]$ $[3276800000/709,245760000/709,7174400/709]$ $y^2 + xy = x^5 - 2x^2 + x$
720.a.6480.1 720.a \( 2^{4} \cdot 3^{2} \cdot 5 \) $0$ $\Z/2\Z\oplus\Z/4\Z$ \(\Q \times \Q\) $[2360,11992,9047820,25920]$ $[1180,56018,3453120,234166319,6480]$ $[28596971960000/81,1150492082200/81,6677950400/9]$ $y^2 + (x^3 + x)y = 2x^4 + 7x^2 + 5$
807.a.2421.1 807.a \( 3 \cdot 269 \) $0$ $\Z/8\Z$ \(\Q\) $[680,640,153059,9684]$ $[340,4710,84049,1598140,2421]$ $[4543542400000/2421,61707280000/807,9716064400/2421]$ $y^2 + (x^3 + x)y = x^5 - 2x^3 - x^2 + 2x - 1$
832.a.832.1 832.a \( 2^{6} \cdot 13 \) $0$ $\Z/8\Z$ \(\Q\) $[272,-131,-12402,-104]$ $[272,3170,51008,956319,-832]$ $[-23262937088/13,-996749440/13,-58965248/13]$ $y^2 + (x^3 + x)y = x^5 - x^3 + x^2 + 2x - 1$
834.a.1668.1 834.a \( 2 \cdot 3 \cdot 139 \) $0$ $\Z/8\Z$ \(\Q\) $[372,3345,401289,213504]$ $[93,221,-111,-14791,1668]$ $[2318961231/556,59254299/556,-320013/556]$ $y^2 + (x^3 + 1)y = -x^2 + x - 1$
847.c.9317.1 847.c \( 7 \cdot 11^{2} \) $0$ $\Z/8\Z$ \(\Q\) $[424,3520,581427,37268]$ $[212,1286,-7999,-837396,9317]$ $[428232184832/9317,12253172608/9317,-359507056/9317]$ $y^2 + (x^3 + x^2)y = x^4 + x^3 - x - 2$
862.a.862.1 862.a \( 2 \cdot 431 \) $0$ $\Z/8\Z$ \(\Q\) $[1940,2609665,270472593,-110336]$ $[485,-98935,11156681,-1094285985,-862]$ $[-26835438303125/862,11286912906875/862,-2624330288225/862]$ $y^2 + (x^3 + 1)y = x^5 - 2x^4 - 7x^3 + 7x^2 + 2x + 5$
882.a.302526.1 882.a \( 2 \cdot 3^{2} \cdot 7^{2} \) $0$ $\Z/2\Z\oplus\Z/4\Z$ \(\Q \times \Q\) $[2572,-283391,165464399,38723328]$ $[643,29035,-3791761,-820283387,302526]$ $[109914468611443/302526,7718888172745/302526,-1567699793689/302526]$ $y^2 + (x^3 + 1)y = x^5 - 2x^4 - 5x^3 + 11x^2 - 12x + 5$
909.a.909.1 909.a \( 3^{2} \cdot 101 \) $0$ $\Z/8\Z$ \(\Q\) $[40,-200,-5469,3636]$ $[20,50,441,1580,909]$ $[3200000/909,400000/909,19600/101]$ $y^2 + (x^3 + x)y = -x^4 + x^2 - x$
925.a.925.1 925.a \( 5^{2} \cdot 37 \) $0$ $\Z/8\Z$ \(\Q\) $[40,-944,-14117,3700]$ $[20,174,713,-4004,925]$ $[128000/37,55680/37,11408/37]$ $y^2 + (x + 1)y = -x^5 + 2x^4 - x^3 - x^2$
930.a.930.1 930.a \( 2 \cdot 3 \cdot 5 \cdot 31 \) $0$ $\Z/2\Z\oplus\Z/4\Z$ \(\Q \times \Q\) $[46596,239073,3674852529,119040]$ $[11649,5644172,3640360380,2637470125259,930]$ $[71502622649365111083/310,1487013548016809538/155,531176338621566]$ $y^2 + (x^2 + x)y = -x^5 - 7x^4 + 37x^2 - 45x + 15$
936.a.1872.1 936.a \( 2^{3} \cdot 3^{2} \cdot 13 \) $0$ $\Z/2\Z\oplus\Z/4\Z$ \(\Q \times \Q\) $[45352,11224,169415364,7488]$ $[22676,21423170,26983749312,38232821637503,1872]$ $[374724646811252438336/117,15612163699641478120/117,7411896491650496]$ $y^2 + (x^3 + x)y = -x^6 - 9x^4 - 32x^2 - 39$
960.a.245760.1 960.a \( 2^{6} \cdot 3 \cdot 5 \) $0$ $\Z/2\Z\oplus\Z/4\Z$ \(\Q \times \Q\) $[120,213,10095,30]$ $[480,7328,-15360,-15268096,245760]$ $[103680000,3297600,-14400]$ $y^2 = 2x^5 + x^4 + 4x^3 + x^2 + 2x$
960.a.368640.1 960.a \( 2^{6} \cdot 3 \cdot 5 \) $0$ $\Z/2\Z\oplus\Z/4\Z$ \(\Q \times \Q\) $[8952,6072,17987052,1440]$ $[17904,13340192,13237770240,14762078945024,368640]$ $[24952719973569408/5,1038436236963696/5,11510985848256]$ $y^2 = x^5 + 13x^4 + 44x^3 + 13x^2 + x$
960.a.983040.1 960.a \( 2^{6} \cdot 3 \cdot 5 \) $0$ $\Z/2\Z\oplus\Z/4\Z$ \(\Q \times \Q\) $[9,33,666,120]$ $[36,-298,-34260,-330541,983040]$ $[19683/320,-36207/2560,-46251/1024]$ $y^2 = x^5 - 2x^4 - x^3 - 2x^2 + x$
990.a.8910.1 990.a \( 2 \cdot 3^{2} \cdot 5 \cdot 11 \) $0$ $\Z/2\Z\oplus\Z/4\Z$ \(\Q \times \Q\) $[3268,252577,318023313,1140480]$ $[817,17288,-766260,-231227341,8910]$ $[364007458703857/8910,4713906106372/4455,-57404054]$ $y^2 + (x^2 + x)y = 3x^5 + 4x^4 + 7x^3 + 4x^2 + 3x$
997.a.997.1 997.a \( 997 \) $0$ $\Z/2\Z\oplus\Z/4\Z$ \(\Q\) $[6112,48064,98113399,3988]$ $[3056,381120,61964417,11027700988,997]$ $[266542673508171776/997,10877317101649920/997,578694117523712/997]$ $y^2 + xy = x^5 - 8x^4 + 16x^3 - x$
997.a.997.2 997.a \( 997 \) $0$ $\Z/8\Z$ \(\Q\) $[64,184,391,3988]$ $[32,12,305,2404,997]$ $[33554432/997,393216/997,312320/997]$ $y^2 + (x + 1)y = x^5 + x^4$
1050.a.131250.1 1050.a \( 2 \cdot 3 \cdot 5^{2} \cdot 7 \) $0$ $\Z/2\Z\oplus\Z/4\Z$ \(\Q \times \Q\) $[11868,198609,759217863,16800000]$ $[2967,358520,56735700,9949557875,131250]$ $[76641937806559869/43750,312136655012892/4375,475666111026/125]$ $y^2 + (x^2 + x)y = 3x^6 + 8x^5 + 15x^4 + 17x^3 + 15x^2 + 8x + 3$
1051.b.1051.1 1051.b \( 1051 \) $0$ $\Z/8\Z$ \(\Q\) $[64,-200,185,4204]$ $[32,76,-241,-3372,1051]$ $[33554432/1051,2490368/1051,-246784/1051]$ $y^2 + (x + 1)y = -x^5 - x^4$
1123.a.1123.1 1123.a \( 1123 \) $0$ $\Z/8\Z$ \(\Q\) $[24,-672,-75,4492]$ $[12,118,-361,-4564,1123]$ $[248832/1123,203904/1123,-51984/1123]$ $y^2 + (x^3 + x)y = -x^4 - x^2 - x$
1147.a.35557.1 1147.a \( 31 \cdot 37 \) $0$ $\Z/2\Z\oplus\Z/4\Z$ \(\Q\) $[3712,11944,14677639,142228]$ $[1856,141540,14195057,1578113548,35557]$ $[22023678539595776/35557,904926084464640/35557,48898223869952/35557]$ $y^2 + xy = x^5 + 8x^4 + 18x^3 + 8x^2 + x$
1152.a.147456.1 1152.a \( 2^{7} \cdot 3^{2} \) $0$ $\Z/8\Z$ \(\mathrm{M}_2(\Q)\) $[152,109,5469,18]$ $[608,14240,405504,10942208,147456]$ $[5071050752/9,195344320/9,1016576]$ $y^2 = x^6 - 2x^4 + 2x^2 - 1$
1176.a.2352.1 1176.a \( 2^{3} \cdot 3 \cdot 7^{2} \) $0$ $\Z/2\Z\oplus\Z/4\Z$ \(\Q \times \Q\) $[1032,984,324564,9408]$ $[516,10930,305472,9539663,2352]$ $[762091768512/49,31284414360/49,1694453184/49]$ $y^2 + (x^3 + x)y = x^4 + 3x^2 + 3$
1184.a.2368.1 1184.a \( 2^{5} \cdot 37 \) $0$ $\Z/8\Z$ \(\Q\) $[128,16,1208,296]$ $[128,672,4160,20224,2368]$ $[536870912/37,22020096/37,1064960/37]$ $y^2 + y = 2x^5 + x^4 + x^2 + x$
1184.a.606208.2 1184.a \( 2^{5} \cdot 37 \) $0$ $\Z/8\Z$ \(\Q\) $[352,316,34242,74]$ $[1408,79232,5831680,483323904,606208]$ $[337748426752/37,13498597376/37,705633280/37]$ $y^2 = x^6 - 2x^5 + 5x^4 - 4x^3 + 6x^2 - 2x + 2$
1225.a.6125.1 1225.a \( 5^{2} \cdot 7^{2} \) $0$ $\Z/8\Z$ \(\mathsf{RM}\) $[320,14344,962481,-24500]$ $[160,-1324,8791,-86604,-6125]$ $[-838860800/49,43384832/49,-9001984/245]$ $y^2 + (x^3 + x^2)y = 2x^3 + x^2 + x + 2$
1309.a.9163.1 1309.a \( 7 \cdot 11 \cdot 17 \) $0$ $\Z/8\Z$ \(\Q\) $[1696,-7904,-4279929,-36652]$ $[848,31280,1576817,89675604,-9163]$ $[-438509757267968/9163,-1122032353280/539,-103081401088/833]$ $y^2 + (x^2 + 1)y = 7x^5 - x^4 - 5x^3 - x^2 + x$
1320.a.2640.1 1320.a \( 2^{3} \cdot 3 \cdot 5 \cdot 11 \) $0$ $\Z/2\Z\oplus\Z/4\Z$ \(\Q \times \Q\) $[63768,10392,220729308,10560]$ $[31884,42356162,75020763840,149479393726079,2640]$ $[686471900571962215488/55,28601826290311163976/55,28888377841215936]$ $y^2 + (x^3 + x)y = -x^6 + 9x^4 - 40x^2 + 55$
1344.a.4032.1 1344.a \( 2^{6} \cdot 3 \cdot 7 \) $0$ $\Z/2\Z\oplus\Z/4\Z$ \(\mathsf{CM} \times \Q\) $[48576,2301,37257288,504]$ $[48576,98316290,265314615552,805457471422463,4032]$ $[469554780013829554176/7,19564477241823191040/7,155268783788507136]$ $y^2 + xy = -x^6 - 12x^4 - 48x^2 - 63$
1344.a.4032.2 1344.a \( 2^{6} \cdot 3 \cdot 7 \) $0$ $\Z/2\Z\oplus\Z/4\Z$ \(\mathsf{CM} \times \Q\) $[48576,2301,37257288,504]$ $[48576,98316290,265314615552,805457471422463,4032]$ $[469554780013829554176/7,19564477241823191040/7,155268783788507136]$ $y^2 + xy = -x^6 + 12x^4 - 48x^2 + 63$
1344.b.172032.1 1344.b \( 2^{6} \cdot 3 \cdot 7 \) $0$ $\Z/2\Z\oplus\Z/4\Z$ \(\Q \times \Q\) $[4248,2904,4071996,672]$ $[8496,2999840,1408899072,742741622528,172032]$ $[1801197437083776/7,74856652932240/7,591152665536]$ $y^2 = x^5 - 11x^4 + 32x^3 - 11x^2 + x$
1376.a.2752.1 1376.a \( 2^{5} \cdot 43 \) $0$ $\Z/8\Z$ \(\Q\) $[192,-528,-2760,-344]$ $[192,1888,64,-888064,-2752]$ $[-4076863488/43,-208797696/43,-36864/43]$ $y^2 + y = 2x^5 + 3x^4 - 2x^2$
1408.b.180224.1 1408.b \( 2^{7} \cdot 11 \) $0$ $\Z/8\Z$ \(\Q\) $[80,280,8718,22]$ $[320,1280,-154624,-12779520,180224]$ $[204800000/11,2560000/11,-966400/11]$ $y^2 = 2x^5 + 2x^4 + 4x^3 + 3x^2 + 2x + 1$
1408.b.720896.1 1408.b \( 2^{7} \cdot 11 \) $0$ $\Z/8\Z$ \(\Q\) $[680,32140,5350958,-88]$ $[2720,-34560,1197056,515399680,-720896]$ $[-2271771200000/11,10612080000/11,-135136400/11]$ $y^2 + y = 4x^5 + 17x^4 - 8x^3 - 3x^2 + x$
1408.b.720896.2 1408.b \( 2^{7} \cdot 11 \) $0$ $\Z/2\Z\oplus\Z/4\Z$ \(\Q\) $[32,-80,-1240,-88]$ $[128,1536,45056,851968,-720896]$ $[-524288/11,-49152/11,-1024]$ $y^2 = x^5 + 2x^3 - 4x^2 + x$
1470.a.2940.1 1470.a \( 2 \cdot 3 \cdot 5 \cdot 7^{2} \) $0$ $\Z/2\Z\oplus\Z/4\Z$ \(\Q \times \Q\) $[2556,6897,5825079,376320]$ $[639,16726,574080,21769511,2940]$ $[35512646315733/980,727349955399/490,3906815328/49]$ $y^2 + (x^2 + x)y = -x^6 + 2x^5 - 5x^4 + 4x^3 - 5x^2 + 2x - 1$
1472.a.5888.1 1472.a \( 2^{6} \cdot 23 \) $0$ $\Z/2\Z\oplus\Z/4\Z$ \(\Q\) $[2,-56,74,23]$ $[4,150,-692,-6317,5888]$ $[4/23,75/46,-173/92]$ $y^2 = x^5 + x^4 - x^3 - 2x^2 - x$
1472.a.94208.2 1472.a \( 2^{6} \cdot 23 \) $0$ $\Z/8\Z$ \(\Q\) $[256,-116,-128996,-368]$ $[512,11232,1184000,120012544,-94208]$ $[-8589934592/23,-368050176/23,-75776000/23]$ $y^2 + y = 4x^5 + x^4 + 4x^2 + 2x$
1534.a.3068.1 1534.a \( 2 \cdot 13 \cdot 59 \) $0$ $\Z/8\Z$ \(\Q\) $[2228,-11087,-8234503,-392704]$ $[557,13389,442913,16859305,-3068]$ $[-53613724194557/3068,-2313735590577/3068,-2329039243/52]$ $y^2 + (x^3 + 1)y = x^5 - 4x^3 - x^2 + 4x - 1$
1536.b.49152.2 1536.b \( 2^{9} \cdot 3 \) $0$ $\Z/2\Z\oplus\Z/4\Z$ \(\mathsf{CM} \times \Q\) $[624,141,29202,6]$ $[2496,258080,35377152,5424021248,49152]$ $[1970977701888,81648253440,4484054016]$ $y^2 + x^3y = 3x^4 + 11x^2 + 12$
1536.c.98304.1 1536.c \( 2^{9} \cdot 3 \) $0$ $\Z/2\Z\oplus\Z/4\Z$ \(\mathsf{CM} \times \Q\) $[1068,38019,11064156,12]$ $[4272,354880,32280576,2990701568,98304]$ $[14473882091808,281451823560,5992838496]$ $y^2 + y = 4x^6 - 12x^5 + 3x^4 + 14x^3 - 5x^2 - 4x + 1$
1573.b.224939.1 1573.b \( 11^{2} \cdot 13 \) $0$ $\Z/2\Z\oplus\Z/4\Z$ \(\Q\) $[472,-4796,-683705,-899756]$ $[236,3120,53993,751987,-224939]$ $[-732082482176/224939,-3154621440/17303,-3007194128/224939]$ $y^2 + (x + 1)y = x^5 + x^4 - 5x^3 + 3x^2 - 1$
1584.a.684288.1 1584.a \( 2^{4} \cdot 3^{2} \cdot 11 \) $0$ $\Z/2\Z\oplus\Z/2\Z\oplus\Z/2\Z$ \(\Q \times \Q\) $[7444,76621,183223627,85536]$ $[7444,2257800,897608448,396034111728,684288]$ $[89287745446261204/2673,1212671977685150/891,1962567037712/27]$ $y^2 + (x^3 + x)y = -x^6 + 6x^4 - 17x^2 + 11$
1656.a.804816.1 1656.a \( 2^{3} \cdot 3^{2} \cdot 23 \) $0$ $\Z/2\Z\oplus\Z/4\Z$ \(\Q\) $[680,19992,5459780,13248]$ $[1020,13362,-5426240,-1428326961,804816]$ $[283971400000/207,10941251000/621,-39204584000/5589]$ $y^2 + xy = 2x^5 - 6x^4 + 13x^3 - 13x^2 + 9x$
1680.a.16800.1 1680.a \( 2^{4} \cdot 3 \cdot 5 \cdot 7 \) $0$ $\Z/2\Z\oplus\Z/4\Z$ \(\Q \times \Q\) $[404040,44088,5935895700,67200]$ $[202020,1700496002,19085068732800,240969733145567999,16800]$ $[20029151526577171524000,834544374130868293620,46363176164438078400]$ $y^2 + (x^3 + x)y = -x^6 - 18x^4 - 136x^2 - 350$
1800.a.3600.1 1800.a \( 2^{3} \cdot 3^{2} \cdot 5^{2} \) $0$ $\Z/8\Z$ \(\Q \times \Q\) $[280,856,70812,14400]$ $[140,674,4032,27551,3600]$ $[134456000/9,4623640/9,21952]$ $y^2 + (x^3 + x)y = -x^4 + x^2 - 1$
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