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Label Class Conductor Rank* Torsion $\textrm{End}^0(J_{\overline\Q})$ Igusa-Clebsch invariants Igusa invariants G2-invariants Equation
249.a.249.1 249.a \( 3 \cdot 83 \) $0$ $\Z/14\Z$ \(\Q\) $[108,57,2259,-31872]$ $[27,28,32,20,-249]$ $[-4782969/83,-183708/83,-7776/83]$ $y^2 + (x^3 + 1)y = x^2 + x$
249.a.6723.1 249.a \( 3 \cdot 83 \) $0$ $\Z/28\Z$ \(\Q\) $[1932,87897,65765571,860544]$ $[483,6058,-161212,-28641190,6723]$ $[324526850403/83,25281736298/249,-4178776252/747]$ $y^2 + (x^3 + 1)y = -x^5 + x^3 + x^2 + 3x + 2$
277.a.277.1 277.a \( 277 \) $0$ $\Z/15\Z$ \(\Q\) $[64,352,9552,-1108]$ $[32,-16,-464,-3776,-277]$ $[-33554432/277,524288/277,475136/277]$ $y^2 + (x^3 + x^2 + x + 1)y = -x^2 - x$
277.a.277.2 277.a \( 277 \) $0$ $\Z/5\Z$ \(\Q\) $[4480,1370512,1511819744,-1108]$ $[2240,-19352,164384,-1569936,-277]$ $[-56394933862400000/277,217505333248000/277,-824813158400/277]$ $y^2 + y = x^5 - 9x^4 + 14x^3 - 19x^2 + 11x - 6$
295.a.295.1 295.a \( 5 \cdot 59 \) $0$ $\Z/14\Z$ \(\Q\) $[108,-39,20835,37760]$ $[27,32,-256,-1984,295]$ $[14348907/295,629856/295,-186624/295]$ $y^2 + (x^3 + 1)y = -x^2$
295.a.295.2 295.a \( 5 \cdot 59 \) $0$ $\Z/2\Z$ \(\Q\) $[198804,305807001,18482629056189,-37760]$ $[49701,90182600,203402032096,494095763610824,-295]$ $[-303267334973269931148501/295,-2214359494206283568520/59,-502441543825401014496/295]$ $y^2 + (x^2 + x + 1)y = x^5 - 40x^3 + 22x^2 + 389x - 608$
349.a.349.1 349.a \( 349 \) $0$ $\Z/13\Z$ \(\Q\) $[8,208,1464,-1396]$ $[4,-34,-124,-413,-349]$ $[-1024/349,2176/349,1984/349]$ $y^2 + (x^3 + x^2 + x + 1)y = -x^3 - x^2$
353.a.353.1 353.a \( 353 \) $0$ $\Z/11\Z$ \(\Q\) $[188,817,30871,45184]$ $[47,58,256,2167,353]$ $[229345007/353,6021734/353,565504/353]$ $y^2 + (x^3 + x + 1)y = x^2$
363.a.11979.1 363.a \( 3 \cdot 11^{2} \) $0$ $\Z/2\Z\oplus\Z/10\Z$ \(\Q \times \Q\) $[344,-3068,-526433,-47916]$ $[172,1744,45841,1210779,-11979]$ $[-150536645632/11979,-8874253312/11979,-1356160144/11979]$ $y^2 + (x^2 + 1)y = x^5 + 2x^3 + 4x^2 + 2x$
363.a.43923.1 363.a \( 3 \cdot 11^{2} \) $0$ $\Z/10\Z$ \(\Q \times \Q\) $[11096,25612,88274095,-175692]$ $[5548,1278244,392069161,135322995423,-43923]$ $[-5256325630316243968/43923,-1804005053317888/363,-99735603013264/363]$ $y^2 + x^2y = 11x^5 - 13x^4 - 7x^3 + 10x^2 + x - 2$
388.a.776.1 388.a \( 2^{2} \cdot 97 \) $0$ $\Z/21\Z$ \(\Q\) $[36,1569,-13743,99328]$ $[9,-62,356,-160,776]$ $[59049/776,-22599/388,7209/194]$ $y^2 + (x^3 + x + 1)y = -x^4 + 2x^2 + x$
389.a.389.1 389.a \( 389 \) $0$ $\Z/10\Z$ \(\Q\) $[2440,51100,45041351,1556]$ $[1220,53500,2084961,-79649395,389]$ $[2702708163200000/389,97147868000000/389,3103255952400/389]$ $y^2 + (x^3 + x)y = x^5 - 2x^4 - 8x^3 + 16x + 7$
389.a.389.2 389.a \( 389 \) $0$ $\Z/10\Z$ \(\Q\) $[16,100,1775,1556]$ $[8,-14,-159,-367,389]$ $[32768/389,-7168/389,-10176/389]$ $y^2 + (x + 1)y = x^5 + 2x^4 + 2x^3 + x^2$
394.a.394.1 394.a \( 2 \cdot 197 \) $0$ $\Z/10\Z$ \(\Q\) $[11032,106300,393913607,1576]$ $[5516,1250044,371875905,122164372511,394]$ $[12960598758485504,532478222573696,28717744887720]$ $y^2 + (x^3 + x)y = 2x^5 + x^4 - 12x^3 + 17x - 9$
394.a.3152.1 394.a \( 2 \cdot 197 \) $0$ $\Z/20\Z$ \(\Q\) $[80,-20,649,-12608]$ $[40,70,39,-835,-3152]$ $[-6400000/197,-280000/197,-3900/197]$ $y^2 + (x + 1)y = -x^5$
427.a.2989.1 427.a \( 7 \cdot 61 \) $0$ $\Z/14\Z$ \(\Q\) $[4564,-22439,-35962915,-382592]$ $[1141,55180,3641688,277583402,-2989]$ $[-39466820645749/61,-1672794336220/61,-96756008472/61]$ $y^2 + (x^3 + 1)y = x^5 - x^4 - 5x^3 + 4x^2 + 4x - 4$
461.a.461.1 461.a \( 461 \) $0$ $\Z/7\Z$ \(\Q\) $[1176,144,66456,1844]$ $[588,14382,467132,16957923,461]$ $[70288881159168/461,2923824242304/461,161508086208/461]$ $y^2 + x^3y = x^5 - 3x^3 + 3x - 2$
461.a.461.2 461.a \( 461 \) $0$ $\mathsf{trivial}$ \(\Q\) $[80664,166117104,3752725952952,1844]$ $[40332,40091742,45075737276,52661714805267,461]$ $[106720731303787612818432/461,2630293443843585469056/461,73323359651716069824/461]$ $y^2 + y = x^5 - x^4 - 39x^3 + 10x^2 + 272x - 306$
464.a.464.1 464.a \( 2^{4} \cdot 29 \) $0$ $\Z/8\Z$ \(\Q\) $[136,280,15060,1856]$ $[68,146,-64,-6417,464]$ $[90870848/29,2869192/29,-18496/29]$ $y^2 + (x + 1)y = -x^6 - 2x^5 - 2x^4 - x^3$
464.a.29696.1 464.a \( 2^{4} \cdot 29 \) $0$ $\Z/2\Z\oplus\Z/8\Z$ \(\Q\) $[680,-5255,-1253953,-3712]$ $[680,22770,1180736,71106895,-29696]$ $[-141985700000/29,-6991813125/29,-533176100/29]$ $y^2 + (x + 1)y = 8x^5 + 3x^4 - 4x^3 - 2x^2$
464.a.29696.2 464.a \( 2^{4} \cdot 29 \) $0$ $\Z/2\Z\oplus\Z/2\Z$ \(\Q\) $[45368,202225,3012190355,-3712]$ $[45368,85625826,215176422416,607585463496703,-29696]$ $[-187693059992988715232/29,-7808250185554819143/29,-432507850151022641/29]$ $y^2 + xy = 4x^5 + 33x^4 + 72x^3 + 16x^2 + x$
472.a.944.1 472.a \( 2^{3} \cdot 59 \) $0$ $\Z/2\Z\oplus\Z/8\Z$ \(\Q\) $[280,760,60604,-3776]$ $[140,690,4544,40015,-944]$ $[-3361400000/59,-118335000/59,-5566400/59]$ $y^2 + (x^2 + 1)y = x^5 - x^4 - 2x^3 + x$
472.a.60416.1 472.a \( 2^{3} \cdot 59 \) $0$ $\Z/8\Z$ \(\Q\) $[152,17065,1592025,7552]$ $[152,-10414,-926656,-62325777,60416]$ $[79235168/59,-35714813/59,-20907676/59]$ $y^2 + (x + 1)y = 8x^5 + 5x^4 + 4x^3 + 2x^2$
523.a.523.1 523.a \( 523 \) $0$ $\Z/10\Z$ \(\Q\) $[120,-540,-29169,-2092]$ $[60,240,2241,19215,-523]$ $[-777600000/523,-51840000/523,-8067600/523]$ $y^2 + (x + 1)y = x^5 - x^4 - x^3$
523.a.523.2 523.a \( 523 \) $0$ $\Z/2\Z$ \(\Q\) $[332400,10084860,1107044456391,-2092]$ $[166200,1149254190,10581558955401,109467476288772525,-523]$ $[-126810465636208320000000000/523,-5276053055713522320000000/523,-292288477352026798440000/523]$ $y^2 + xy = x^5 - 31x^4 - 110x^3 + 21x^2 - x$
529.a.529.1 529.a \( 23^{2} \) $0$ $\Z/11\Z$ \(\mathsf{RM}\) $[284,2401,246639,-67712]$ $[71,110,-624,-14101,-529]$ $[-1804229351/529,-39370210/529,3145584/529]$ $y^2 + (x^3 + x + 1)y = -x^5$
555.a.8325.1 555.a \( 3 \cdot 5 \cdot 37 \) $0$ $\Z/2\Z\oplus\Z/10\Z$ \(\Q\) $[1264,18124,6869487,33300]$ $[632,13622,351361,9125317,8325]$ $[100828984082432/8325,3438682756096/8325,140342016064/8325]$ $y^2 + (x + 1)y = 3x^5 - 2x^4 - 4x^3 + x^2 + x$
574.a.293888.1 574.a \( 2 \cdot 7 \cdot 41 \) $0$ $\Z/2\Z\oplus\Z/10\Z$ \(\Q\) $[68,-55823,-955895,-37617664]$ $[17,2338,2304,-1356769,-293888]$ $[-1419857/293888,-820471/20992,-2601/1148]$ $y^2 + (x^2 + x)y = x^5 - x^4 - 3x^2 + x + 1$
587.a.587.1 587.a \( 587 \) $1$ $\mathsf{trivial}$ \(\Q\) $[60,1401,54147,-75136]$ $[15,-49,-501,-2479,-587]$ $[-759375/587,165375/587,112725/587]$ $y^2 + (x^3 + x + 1)y = -x^2 - x$
597.a.597.1 597.a \( 3 \cdot 199 \) $0$ $\Z/7\Z$ \(\Q\) $[120,192,9912,2388]$ $[60,118,-68,-4501,597]$ $[259200000/199,8496000/199,-81600/199]$ $y^2 + y = x^5 + 2x^4 + 3x^3 + 2x^2 + x$
600.a.18000.1 600.a \( 2^{3} \cdot 3 \cdot 5^{2} \) $0$ $\Z/2\Z\oplus\Z/2\Z\oplus\Z/6\Z$ \(\Q \times \Q\) $[1376,23824,11410044,72000]$ $[688,15752,244900,-19908576,18000]$ $[9634345320448/1125,320612931584/1125,289804864/45]$ $y^2 + xy = 10x^5 - 18x^4 + 8x^3 + x^2 - x$
600.a.96000.1 600.a \( 2^{3} \cdot 3 \cdot 5^{2} \) $0$ $\Z/2\Z\oplus\Z/6\Z$ \(\Q \times \Q\) $[92,4981,43947,-12000]$ $[92,-2968,47600,-1107456,-96000]$ $[-25745372/375,9027914/375,-62951/15]$ $y^2 + (x + 1)y = 4x^5 + 5x^4 + 3x^3 + 2x^2$
603.a.603.1 603.a \( 3^{2} \cdot 67 \) $0$ $\Z/10\Z$ \(\Q\) $[1672,75628,49887881,2412]$ $[836,16516,-1263521,-332270453,603]$ $[408348897330176/603,9649919856896/603,-883069772816/603]$ $y^2 + (x^2 + 1)y = x^5 + 8x^4 + 4x^3 + 4x^2 + 2x$
603.a.603.2 603.a \( 3^{2} \cdot 67 \) $0$ $\Z/10\Z$ \(\Q\) $[176,148,7375,-2412]$ $[88,298,1361,7741,-603]$ $[-5277319168/603,-203078656/603,-10539584/603]$ $y^2 + (x^2 + 1)y = x^5 - x^3 + x$
604.a.9664.1 604.a \( 2^{2} \cdot 151 \) $0$ $\mathsf{trivial}$ \(\Q\) $[49556,-797087975,-23996873337603,1236992]$ $[12389,39607304,223396249616,299729401586052,9664]$ $[291864493641401980949/9664,9414430497536890397/1208,2143030742187944921/604]$ $y^2 + (x^2 + x + 1)y = 4x^5 + 9x^4 + 48x^3 - 4x^2 - 53x - 21$
604.a.9664.2 604.a \( 2^{2} \cdot 151 \) $0$ $\Z/27\Z$ \(\Q\) $[116,6265,95277,1236992]$ $[29,-226,836,-6708,9664]$ $[20511149/9664,-2755957/4832,175769/2416]$ $y^2 + (x^3 + 1)y = -x^4 + x^3 + x^2 - x$
644.b.14812.1 644.b \( 2^{2} \cdot 7 \cdot 23 \) $0$ $\Z/10\Z$ \(\Q\) $[1268,-40511,-17688719,-1895936]$ $[317,5875,170781,4905488,-14812]$ $[-3201078401357/14812,-187148201375/14812,-17161611909/14812]$ $y^2 + (x^3 + 1)y = x^5 - x^4 - 4x^3 + 5x^2 - x - 1$
688.a.2752.1 688.a \( 2^{4} \cdot 43 \) $0$ $\Z/20\Z$ \(\Q\) $[32,112,-680,-344]$ $[32,-32,1344,10496,-2752]$ $[-524288/43,16384/43,-21504/43]$ $y^2 + y = 2x^5 - 5x^4 + 4x^3 - x$
688.a.704512.2 688.a \( 2^{4} \cdot 43 \) $0$ $\Z/10\Z$ \(\Q\) $[464,-248,-39602,-86]$ $[1856,146176,15688704,1937702912,-704512]$ $[-1344218660864/43,-57041383424/43,-3298550016/43]$ $y^2 = 2x^5 - 7x^4 - 8x^3 + 2x^2 + 4x + 1$
688.a.704512.1 688.a \( 2^{4} \cdot 43 \) $0$ $\Z/10\Z$ \(\Q\) $[128,532,26830,86]$ $[512,5248,-408576,-59183104,704512]$ $[2147483648/43,42991616/43,-6537216/43]$ $y^2 = 2x^5 + 4x^3 + x^2 + 2x + 1$
691.a.691.1 691.a \( 691 \) $0$ $\Z/8\Z$ \(\Q\) $[104,-824,-20333,-2764]$ $[52,250,601,-7812,-691]$ $[-380204032/691,-35152000/691,-1625104/691]$ $y^2 + (x + 1)y = x^5 - x^3 - x^2$
704.a.45056.1 704.a \( 2^{6} \cdot 11 \) $0$ $\Z/2\Z\oplus\Z/6\Z$ \(\Q\) $[134,-464,-15328,-176]$ $[268,4230,61444,-356477,-45056]$ $[-1350125107/44,-636113745/352,-68955529/704]$ $y^2 + y = 4x^5 + 4x^4 - x^3 - 2x^2$
708.a.2832.1 708.a \( 2^{2} \cdot 3 \cdot 59 \) $0$ $\Z/10\Z$ \(\Q\) $[148,2065,76361,362496]$ $[37,-29,-59,-756,2832]$ $[69343957/2832,-1468937/2832,-1369/48]$ $y^2 + (x^2 + x + 1)y = x^5$
708.a.19116.1 708.a \( 2^{2} \cdot 3 \cdot 59 \) $0$ $\Z/10\Z$ \(\Q\) $[908,-132815,8426215,2446848]$ $[227,7681,-438901,-39657072,19116]$ $[602738989907/19116,89845294523/19116,-383324231/324]$ $y^2 + (x^3 + 1)y = -x^5 + 4x^2 + 4x - 1$
708.a.181248.1 708.a \( 2^{2} \cdot 3 \cdot 59 \) $0$ $\Z/2\Z$ \(\Q\) $[234100,3468879025,202585466081177,-23199744]$ $[58525,-1820975,60952909,62829762150,-181248]$ $[-686605237334059580078125/181248,365029741228054296875/181248,-208774418179643125/181248]$ $y^2 + (x^3 + 1)y = -x^6 - 4x^5 + 9x^4 + 48x^3 - 41x^2 - 98x - 36$
709.a.709.1 709.a \( 709 \) $0$ $\Z/8\Z$ \(\Q\) $[160,-1280,-42089,2836]$ $[80,480,1121,-35180,709]$ $[3276800000/709,245760000/709,7174400/709]$ $y^2 + xy = x^5 - 2x^2 + x$
713.a.713.1 713.a \( 23 \cdot 31 \) $1$ $\mathsf{trivial}$ \(\Q\) $[36,1305,-2547,91264]$ $[9,-51,173,-261,713]$ $[59049/713,-37179/713,14013/713]$ $y^2 + (x^3 + x + 1)y = -x^5 - x$
713.b.713.1 713.b \( 23 \cdot 31 \) $0$ $\Z/9\Z$ \(\Q\) $[92,73,6379,-91264]$ $[23,19,-41,-326,-713]$ $[-279841/31,-10051/31,943/31]$ $y^2 + (x^3 + x + 1)y = -x^4$
726.a.1452.1 726.a \( 2 \cdot 3 \cdot 11^{2} \) $0$ $\Z/10\Z$ \(\Q \times \Q\) $[760,-69236,-16142609,-5808]$ $[380,17556,702601,-10306189,-1452]$ $[-1980879200000/363,-7297976000/11,-25363896100/363]$ $y^2 + (x^2 + 1)y = 2x^5 + 2x^4 + 6x^3 - 2x^2 - x$
731.a.12427.1 731.a \( 17 \cdot 43 \) $0$ $\Z/10\Z$ \(\Q\) $[480,-21564,-3373785,-49708]$ $[240,5994,167265,1053891,-12427]$ $[-796262400000/12427,-82861056000/12427,-9634464000/12427]$ $y^2 + (x^3 + x^2)y = x^5 + 2x^4 - x - 3$
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