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Label Class Conductor Discriminant Rank* Torsion $\textrm{End}^0(J_{\overline\Q})$ Igusa-Clebsch invariants Igusa invariants G2-invariants Equation
256.a.512.1 256.a \( 2^{8} \) \( - 2^{9} \) $0$ $\Z/2\Z\oplus\Z/10\Z$ \(\mathrm{M}_2(\Q)\) $[26,-2,40,2]$ $[52,118,-36,-3949,512]$ $[742586,129623/4,-1521/8]$ $y^2 + y = 2x^5 - 3x^4 + x^3 + x^2 - x$
324.a.648.1 324.a \( 2^{2} \cdot 3^{4} \) \( - 2^{3} \cdot 3^{4} \) $0$ $\Z/21\Z$ \(\mathrm{M}_2(\Q)\) $[60,945,2295,82944]$ $[15,-30,140,300,648]$ $[9375/8,-625/4,875/18]$ $y^2 + (x^3 + x + 1)y = x^5 + 2x^4 + 2x^3 + x^2$
388.a.776.1 388.a \( 2^{2} \cdot 97 \) \( 2^{3} \cdot 97 \) $0$ $\Z/21\Z$ \(\Q\) $[36,1569,-13743,99328]$ $[9,-62,356,-160,776]$ $[59049/776,-22599/388,7209/194]$ $y^2 + (x^3 + x + 1)y = -x^4 + 2x^2 + x$
472.a.944.1 472.a \( 2^{3} \cdot 59 \) \( - 2^{4} \cdot 59 \) $0$ $\Z/2\Z\oplus\Z/8\Z$ \(\Q\) $[280,760,60604,-3776]$ $[140,690,4544,40015,-944]$ $[-3361400000/59,-118335000/59,-5566400/59]$ $y^2 + (x^2 + 1)y = x^5 - x^4 - 2x^3 + x$
476.a.952.1 476.a \( 2^{2} \cdot 7 \cdot 17 \) \( - 2^{3} \cdot 7 \cdot 17 \) $0$ $\Z/3\Z\oplus\Z/6\Z$ \(\Q \times \Q\) $[7340,1042345,2905273355,121856]$ $[1835,96870,-3910340,-4139817700,952]$ $[20805604708146875/952,299272981175625/476,-27661753375/2]$ $y^2 + (x^3 + 1)y = -5x^4 + 7x^3 + 25x^2 - 75x + 54$
523.a.523.1 523.a \( 523 \) \( -523 \) $0$ $\Z/10\Z$ \(\Q\) $[120,-540,-29169,-2092]$ $[60,240,2241,19215,-523]$ $[-777600000/523,-51840000/523,-8067600/523]$ $y^2 + (x + 1)y = x^5 - x^4 - x^3$
523.a.523.2 523.a \( 523 \) \( -523 \) $0$ $\Z/2\Z$ \(\Q\) $[332400,10084860,1107044456391,-2092]$ $[166200,1149254190,10581558955401,109467476288772525,-523]$ $[-126810465636208320000000000/523,-5276053055713522320000000/523,-292288477352026798440000/523]$ $y^2 + xy = x^5 - 31x^4 - 110x^3 + 21x^2 - x$
529.a.529.1 529.a \( 23^{2} \) \( 23^{2} \) $0$ $\Z/11\Z$ \(\mathsf{RM}\) $[284,2401,246639,-67712]$ $[71,110,-624,-14101,-529]$ $[-1804229351/529,-39370210/529,3145584/529]$ $y^2 + (x^3 + x + 1)y = -x^5$
576.a.576.1 576.a \( 2^{6} \cdot 3^{2} \) \( - 2^{6} \cdot 3^{2} \) $0$ $\Z/10\Z$ \(\mathrm{M}_2(\Q)\) $[68,124,2616,72]$ $[68,110,-36,-3637,576]$ $[22717712/9,540430/9,-289]$ $y^2 + (x^3 + x^2 + x + 1)y = -x^3 - x$
587.a.587.1 587.a \( 587 \) \( 587 \) $1$ $\mathsf{trivial}$ \(\Q\) $[60,1401,54147,-75136]$ $[15,-49,-501,-2479,-587]$ $[-759375/587,165375/587,112725/587]$ $y^2 + (x^3 + x + 1)y = -x^2 - x$
597.a.597.1 597.a \( 3 \cdot 199 \) \( 3 \cdot 199 \) $0$ $\Z/7\Z$ \(\Q\) $[120,192,9912,2388]$ $[60,118,-68,-4501,597]$ $[259200000/199,8496000/199,-81600/199]$ $y^2 + y = x^5 + 2x^4 + 3x^3 + 2x^2 + x$
603.a.603.1 603.a \( 3^{2} \cdot 67 \) \( - 3^{2} \cdot 67 \) $0$ $\Z/10\Z$ \(\Q\) $[1672,75628,49887881,2412]$ $[836,16516,-1263521,-332270453,603]$ $[408348897330176/603,9649919856896/603,-883069772816/603]$ $y^2 + (x^2 + 1)y = x^5 + 8x^4 + 4x^3 + 4x^2 + 2x$
603.a.603.2 603.a \( 3^{2} \cdot 67 \) \( - 3^{2} \cdot 67 \) $0$ $\Z/10\Z$ \(\Q\) $[176,148,7375,-2412]$ $[88,298,1361,7741,-603]$ $[-5277319168/603,-203078656/603,-10539584/603]$ $y^2 + (x^2 + 1)y = x^5 - x^3 + x$
686.a.686.1 686.a \( 2 \cdot 7^{3} \) \( 2 \cdot 7^{3} \) $0$ $\Z/6\Z$ \(\mathsf{CM} \times \Q\) $[420,4305,640185,87808]$ $[105,280,-980,-45325,686]$ $[37209375/2,472500,-15750]$ $y^2 + (x^2 + x)y = x^5 + x^4 + 2x^3 + x^2 + x$
691.a.691.1 691.a \( 691 \) \( -691 \) $0$ $\Z/8\Z$ \(\Q\) $[104,-824,-20333,-2764]$ $[52,250,601,-7812,-691]$ $[-380204032/691,-35152000/691,-1625104/691]$ $y^2 + (x + 1)y = x^5 - x^3 - x^2$
709.a.709.1 709.a \( 709 \) \( 709 \) $0$ $\Z/8\Z$ \(\Q\) $[160,-1280,-42089,2836]$ $[80,480,1121,-35180,709]$ $[3276800000/709,245760000/709,7174400/709]$ $y^2 + xy = x^5 - 2x^2 + x$
713.a.713.1 713.a \( 23 \cdot 31 \) \( 23 \cdot 31 \) $1$ $\mathsf{trivial}$ \(\Q\) $[36,1305,-2547,91264]$ $[9,-51,173,-261,713]$ $[59049/713,-37179/713,14013/713]$ $y^2 + (x^3 + x + 1)y = -x^5 - x$
713.b.713.1 713.b \( 23 \cdot 31 \) \( 23 \cdot 31 \) $0$ $\Z/9\Z$ \(\Q\) $[92,73,6379,-91264]$ $[23,19,-41,-326,-713]$ $[-279841/31,-10051/31,943/31]$ $y^2 + (x^3 + x + 1)y = -x^4$
743.a.743.1 743.a \( 743 \) \( -743 \) $1$ $\mathsf{trivial}$ \(\Q\) $[28,1945,15219,95104]$ $[7,-79,-53,-1653,743]$ $[16807/743,-27097/743,-2597/743]$ $y^2 + (x^3 + x + 1)y = -x^4 + x^2$
745.a.745.1 745.a \( 5 \cdot 149 \) \( - 5 \cdot 149 \) $0$ $\Z/9\Z$ \(\Q\) $[124,1417,38763,95360]$ $[31,-19,39,212,745]$ $[28629151/745,-566029/745,37479/745]$ $y^2 + (x^3 + x + 1)y = -x$
763.a.763.1 763.a \( 7 \cdot 109 \) \( - 7 \cdot 109 \) $0$ $\Z/10\Z$ \(\Q\) $[216,1116,75735,-3052]$ $[108,300,81,-20313,-763]$ $[-14693280768/763,-377913600/763,-944784/763]$ $y^2 + (x^3 + x)y = -2x^4 + 2x^2 - x$
797.a.797.1 797.a \( 797 \) \( 797 \) $0$ $\Z/7\Z$ \(\Q\) $[24,528,7608,3188]$ $[12,-82,-548,-3325,797]$ $[248832/797,-141696/797,-78912/797]$ $y^2 + y = x^5 - x^4 + x^3$
832.a.832.1 832.a \( 2^{6} \cdot 13 \) \( - 2^{6} \cdot 13 \) $0$ $\Z/8\Z$ \(\Q\) $[272,-131,-12402,-104]$ $[272,3170,51008,956319,-832]$ $[-23262937088/13,-996749440/13,-58965248/13]$ $y^2 + (x^3 + x)y = x^5 - x^3 + x^2 + 2x - 1$
841.a.841.1 841.a \( 29^{2} \) \( - 29^{2} \) $0$ $\Z/7\Z$ \(\mathsf{RM}\) $[1420,4201,1973899,107648]$ $[355,5076,93408,1848516,841]$ $[5638216721875/841,227094529500/841,11771743200/841]$ $y^2 + (x^3 + x^2 + x)y = x^4 + x^3 + 3x^2 + x + 2$
847.a.847.1 847.a \( 7 \cdot 11^{2} \) \( - 7 \cdot 11^{2} \) $1$ $\Z/5\Z$ \(\Q \times \Q\) $[120,276,6864,3388]$ $[60,104,504,4856,847]$ $[777600000/847,22464000/847,259200/121]$ $y^2 + (x^3 + x^2 + x + 1)y = x^4 + x^3 + x^2$
847.d.847.1 847.d \( 7 \cdot 11^{2} \) \( - 7 \cdot 11^{2} \) $0$ $\Z/3\Z$ \(\Q \times \Q\) $[80408,402403732,8094753026048,3388]$ $[40204,281112,1967560,19956424,847]$ $[105037970421355597057024/847,18267839107785466368/847,454326923025280/121]$ $y^2 + (x^3 + x^2 + x + 1)y = -12x^6 - 15x^5 + 9x^4 + 31x^3 + 9x^2 - 15x - 12$
862.a.862.1 862.a \( 2 \cdot 431 \) \( - 2 \cdot 431 \) $0$ $\Z/8\Z$ \(\Q\) $[1940,2609665,270472593,-110336]$ $[485,-98935,11156681,-1094285985,-862]$ $[-26835438303125/862,11286912906875/862,-2624330288225/862]$ $y^2 + (x^3 + 1)y = x^5 - 2x^4 - 7x^3 + 7x^2 + 2x + 5$
862.b.862.1 862.b \( 2 \cdot 431 \) \( 2 \cdot 431 \) $0$ $\Z/9\Z$ \(\Q\) $[552,696,112755,3448]$ $[276,3058,45033,769436,862]$ $[800784050688/431,32146576704/431,1715216904/431]$ $y^2 + (x^3 + x)y = -2x^4 + 3x^2 - x - 1$
893.a.893.1 893.a \( 19 \cdot 47 \) \( 19 \cdot 47 \) $1$ $\mathsf{trivial}$ \(\Q\) $[156,-519,-11805,-114304]$ $[39,85,67,-1153,-893]$ $[-90224199/893,-5042115/893,-101907/893]$ $y^2 + (x^3 + x + 1)y = -x^4 - x^2$
909.a.909.1 909.a \( 3^{2} \cdot 101 \) \( 3^{2} \cdot 101 \) $0$ $\Z/8\Z$ \(\Q\) $[40,-200,-5469,3636]$ $[20,50,441,1580,909]$ $[3200000/909,400000/909,19600/101]$ $y^2 + (x^3 + x)y = -x^4 + x^2 - x$
925.a.925.1 925.a \( 5^{2} \cdot 37 \) \( 5^{2} \cdot 37 \) $0$ $\Z/8\Z$ \(\Q\) $[40,-944,-14117,3700]$ $[20,174,713,-4004,925]$ $[128000/37,55680/37,11408/37]$ $y^2 + (x + 1)y = -x^5 + 2x^4 - x^3 - x^2$
930.a.930.1 930.a \( 2 \cdot 3 \cdot 5 \cdot 31 \) \( 2 \cdot 3 \cdot 5 \cdot 31 \) $0$ $\Z/2\Z\oplus\Z/4\Z$ \(\Q \times \Q\) $[46596,239073,3674852529,119040]$ $[11649,5644172,3640360380,2637470125259,930]$ $[71502622649365111083/310,1487013548016809538/155,531176338621566]$ $y^2 + (x^2 + x)y = -x^5 - 7x^4 + 37x^2 - 45x + 15$
953.a.953.1 953.a \( 953 \) \( -953 \) $1$ $\mathsf{trivial}$ \(\Q\) $[92,1513,26203,121984]$ $[23,-41,67,-35,953]$ $[6436343/953,-498847/953,35443/953]$ $y^2 + (x^3 + x + 1)y = x^3 + x^2$
961.a.961.1 961.a \( 31^{2} \) \( - 31^{2} \) $0$ $\mathsf{trivial}$ \(\mathsf{RM}\) $[66980,1011437281,14016353908561,-123008]$ $[16745,-30460094,12221475912,-180792178085599,-961]$ $[-1316514841399349215625/961,143016680917998700750/961,-3426841043882137800/961]$ $y^2 + (x^3 + x + 1)y = -x^6 - x^5 - 7x^4 + 74x^3 - 145x^2 + 99x - 33$
961.a.961.2 961.a \( 31^{2} \) \( - 31^{2} \) $0$ $\Z/5\Z$ \(\mathsf{RM}\) $[11260,503521,1770579599,123008]$ $[2815,309196,43449708,6677190401,961]$ $[176763257309509375/961,6897140364776500/961,344305262376300/961]$ $y^2 + (x^3 + x + 1)y = -x^6 + 2x^5 - 8x^4 + 12x^3 - 18x^2 + 12x - 7$
961.a.961.3 961.a \( 31^{2} \) \( 31^{2} \) $0$ $\Z/5\Z$ \(\mathsf{RM}\) $[260,1681,185209,123008]$ $[65,106,-672,-13729,961]$ $[1160290625/961,29110250/961,-2839200/961]$ $y^2 + (x^3 + x + 1)y = x^5 + x^4 + x^3 - x - 1$
971.a.971.1 971.a \( 971 \) \( -971 \) $1$ $\mathsf{trivial}$ \(\Q\) $[256,1024,80304,-3884]$ $[128,512,2000,-1536,-971]$ $[-34359738368/971,-1073741824/971,-32768000/971]$ $y^2 + y = x^5 - 2x^3 + x$
997.a.997.1 997.a \( 997 \) \( 997 \) $0$ $\Z/2\Z\oplus\Z/4\Z$ \(\Q\) $[6112,48064,98113399,3988]$ $[3056,381120,61964417,11027700988,997]$ $[266542673508171776/997,10877317101649920/997,578694117523712/997]$ $y^2 + xy = x^5 - 8x^4 + 16x^3 - x$
997.a.997.2 997.a \( 997 \) \( 997 \) $0$ $\Z/8\Z$ \(\Q\) $[64,184,391,3988]$ $[32,12,305,2404,997]$ $[33554432/997,393216/997,312320/997]$ $y^2 + (x + 1)y = x^5 + x^4$
997.b.997.1 997.b \( 997 \) \( 997 \) $1$ $\Z/3\Z$ \(\Q\) $[32,16,-1680,-3988]$ $[16,8,208,816,-997]$ $[-1048576/997,-32768/997,-53248/997]$ $y^2 + y = x^5 - 2x^4 + 2x^3 - x^2$
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