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Label Class Conductor Rank* Torsion $\textrm{End}^0(J_{\overline\Q})$ Igusa-Clebsch invariants Igusa invariants G2-invariants Equation
169.a.169.1 169.a \( 13^{2} \) $0$ $\Z/19\Z$ \(\mathrm{M}_2(\Q)\) $[4,793,3757,-21632]$ $[1,-33,-43,-283,-169]$ $[-1/169,33/169,43/169]$ $y^2 + (x^3 + x + 1)y = x^5 + x^4$
196.a.21952.1 196.a \( 2^{2} \cdot 7^{2} \) $0$ $\Z/6\Z\oplus\Z/6\Z$ \(\mathrm{M}_2(\Q)\) $[1340,1345,149855,2809856]$ $[335,4620,90160,2214800,21952]$ $[4219140959375/21952,6203236875/784,12905875/28]$ $y^2 + (x^2 + x)y = x^6 + 3x^5 + 6x^4 + 7x^3 + 6x^2 + 3x + 1$
249.a.6723.1 249.a \( 3 \cdot 83 \) $0$ $\Z/28\Z$ \(\Q\) $[1932,87897,65765571,860544]$ $[483,6058,-161212,-28641190,6723]$ $[324526850403/83,25281736298/249,-4178776252/747]$ $y^2 + (x^3 + 1)y = -x^5 + x^3 + x^2 + 3x + 2$
256.a.512.1 256.a \( 2^{8} \) $0$ $\Z/2\Z\oplus\Z/10\Z$ \(\mathrm{M}_2(\Q)\) $[26,-2,40,2]$ $[52,118,-36,-3949,512]$ $[742586,129623/4,-1521/8]$ $y^2 + y = 2x^5 - 3x^4 + x^3 + x^2 - x$
324.a.648.1 324.a \( 2^{2} \cdot 3^{4} \) $0$ $\Z/21\Z$ \(\mathrm{M}_2(\Q)\) $[60,945,2295,82944]$ $[15,-30,140,300,648]$ $[9375/8,-625/4,875/18]$ $y^2 + (x^3 + x + 1)y = x^5 + 2x^4 + 2x^3 + x^2$
360.a.6480.1 360.a \( 2^{3} \cdot 3^{2} \cdot 5 \) $0$ $\Z/2\Z\oplus\Z/2\Z\oplus\Z/8\Z$ \(\Q \times \Q\) $[2360,11992,9047820,25920]$ $[1180,56018,3453120,234166319,6480]$ $[28596971960000/81,1150492082200/81,6677950400/9]$ $y^2 + (x^3 + x)y = -3x^4 + 7x^2 - 5$
388.a.776.1 388.a \( 2^{2} \cdot 97 \) $0$ $\Z/21\Z$ \(\Q\) $[36,1569,-13743,99328]$ $[9,-62,356,-160,776]$ $[59049/776,-22599/388,7209/194]$ $y^2 + (x^3 + x + 1)y = -x^4 + 2x^2 + x$
394.a.3152.1 394.a \( 2 \cdot 197 \) $0$ $\Z/20\Z$ \(\Q\) $[80,-20,649,-12608]$ $[40,70,39,-835,-3152]$ $[-6400000/197,-280000/197,-3900/197]$ $y^2 + (x + 1)y = -x^5$
450.a.2700.1 450.a \( 2 \cdot 3^{2} \cdot 5^{2} \) $0$ $\Z/24\Z$ \(\Q \times \Q\) $[364,3529,393211,345600]$ $[91,198,0,-9801,2700]$ $[6240321451/2700,8289281/150,0]$ $y^2 + (x^3 + 1)y = x^5 + 3x^4 + 3x^3 + 3x^2 + x$
574.a.293888.1 574.a \( 2 \cdot 7 \cdot 41 \) $0$ $\Z/2\Z\oplus\Z/10\Z$ \(\Q\) $[68,-55823,-955895,-37617664]$ $[17,2338,2304,-1356769,-293888]$ $[-1419857/293888,-820471/20992,-2601/1148]$ $y^2 + (x^2 + x)y = x^5 - x^4 - 3x^2 + x + 1$
588.a.18816.1 588.a \( 2^{2} \cdot 3 \cdot 7^{2} \) $0$ $\Z/24\Z$ \(\Q \times \Q\) $[748,11545,2902787,2408448]$ $[187,976,-192,-247120,18816]$ $[228669389707/18816,398891383/1176,-34969/98]$ $y^2 + (x^3 + 1)y = x^5 + x^4 + 5x^2 + 12x + 8$
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.b.450000.1 600.b \( 2^{3} \cdot 3 \cdot 5^{2} \) $0$ $\Z/2\Z\oplus\Z/2\Z\oplus\Z/8\Z$ \(\Q \times \Q\) $[18072,38904,233095932,1800000]$ $[9036,3395570,1698206400,953774351375,450000]$ $[418329622965299904/3125,3479436045234936/625,38515932506304/125]$ $y^2 + (x^3 + x)y = -5x^4 + 25x^2 - 45$
676.a.5408.1 676.a \( 2^{2} \cdot 13^{2} \) $0$ $\Z/21\Z$ \(\Q \times \Q\) $[204,3273,161211,692224]$ $[51,-28,0,-196,5408]$ $[345025251/5408,-928557/1352,0]$ $y^2 + (x^3 + x^2 + x)y = x^3 + 3x^2 + 3x + 1$
688.a.2752.1 688.a \( 2^{4} \cdot 43 \) $0$ $\Z/20\Z$ \(\Q\) $[32,112,-680,-344]$ $[32,-32,1344,10496,-2752]$ $[-524288/43,16384/43,-21504/43]$ $y^2 + y = 2x^5 - 5x^4 + 4x^3 - x$
800.a.409600.1 800.a \( 2^{5} \cdot 5^{2} \) $0$ $\Z/24\Z$ \(\Q \times \Q\) $[120,309,14889,50]$ $[480,6304,-151552,-28121344,409600]$ $[62208000,1702080,-85248]$ $y^2 = x^6 - 2x^2 + 1$
816.a.39168.1 816.a \( 2^{4} \cdot 3 \cdot 17 \) $0$ $\Z/2\Z\oplus\Z/2\Z\oplus\Z/6\Z$ \(\Q\) $[436,3373,434667,4896]$ $[436,5672,77824,439920,39168]$ $[61544958196/153,1836351122/153,57789184/153]$ $y^2 + (x^2 + 1)y = 3x^5 - 4x^3 - x^2 + x$
847.a.847.1 847.a \( 7 \cdot 11^{2} \) $1$ $\Z/5\Z$ \(\Q \times \Q\) $[120,276,6864,3388]$ $[60,104,504,4856,847]$ $[777600000/847,22464000/847,259200/121]$ $y^2 + (x^3 + x^2 + x + 1)y = x^4 + x^3 + x^2$
966.a.834624.1 966.a \( 2 \cdot 3 \cdot 7 \cdot 23 \) $0$ $\Z/2\Z\oplus\Z/12\Z$ \(\Q\) $[92,24673,-557265,-106831872]$ $[23,-1006,14336,-170577,-834624]$ $[-279841/36288,266087/18144,-736/81]$ $y^2 + (x^2 + x)y = x^5 - x^4 + x^3 + x^2 - x + 1$
1083.a.1083.1 1083.a \( 3 \cdot 19^{2} \) $1$ $\Z/3\Z$ \(\Q \times \Q\) $[56,244,928,4332]$ $[28,-8,264,1832,1083]$ $[17210368/1083,-175616/1083,68992/361]$ $y^2 + (x^3 + x^2 + x + 1)y = -x^3$
1145.a.143125.1 1145.a \( 5 \cdot 229 \) $1$ $\Z/2\Z$ \(\Q\) $[5004,191097,289856403,18320000]$ $[1251,57246,3273124,204393402,143125]$ $[3063984390631251/143125,112077149104746/143125,5122442333124/143125]$ $y^2 + (x^3 + x^2 + x)y = 2x^4 + 4x^3 + 9x^2 + 10x + 9$
1192.a.19072.1 1192.a \( 2^{3} \cdot 149 \) $0$ $\Z/22\Z$ \(\Q\) $[160,3184,271780,76288]$ $[80,-264,-17220,-361824,19072]$ $[25600000/149,-1056000/149,-861000/149]$ $y^2 + (x^3 + x)y = x^3 - 2x^2 - x + 1$
1253.b.1253.1 1253.b \( 7 \cdot 179 \) $1$ $\mathsf{trivial}$ \(\Q\) $[348,2409,250779,160384]$ $[87,215,467,-1399,1253]$ $[4984209207/1253,141578145/1253,3534723/1253]$ $y^2 + (x^3 + x + 1)y = x^4 + x^2$
1300.a.130000.1 1300.a \( 2^{2} \cdot 5^{2} \cdot 13 \) $1$ $\Z/6\Z$ \(\Q \times \Q\) $[4600,9904,15140164,520000]$ $[2300,218766,27536704,3868964111,130000]$ $[6436343000000/13,266172592200/13,1120532032]$ $y^2 + (x^3 + x)y = 2x^4 + 9x^2 + 13$
1312.a.2624.1 1312.a \( 2^{5} \cdot 41 \) $1$ $\Z/2\Z$ \(\Q\) $[112,91,1912,328]$ $[112,462,3440,42959,2624]$ $[275365888/41,10141824/41,674240/41]$ $y^2 + (x + 1)y = x^6 + 2x^5 + 3x^4 + 2x^3 + x^2$
1312.c.671744.1 1312.c \( 2^{5} \cdot 41 \) $0$ $\Z/22\Z$ \(\Q\) $[164,1441,58489,83968]$ $[164,160,1984,74944,671744]$ $[2825761/16,8405/8,1271/16]$ $y^2 + (x + 1)y = x^6 + 4x^5 + 7x^4 + 5x^3 + 2x^2$
1331.a.1331.1 1331.a \( 11^{3} \) $1$ $\Z/5\Z$ \(\mathsf{CM} \times \Q\) $[88,2068,83248,5324]$ $[44,-264,-4840,-70664,1331]$ $[123904,-16896,-7040]$ $y^2 + x^3y = -x^4 - x^3 + 2x^2 + 3x + 1$
1338.a.2676.1 1338.a \( 2 \cdot 3 \cdot 223 \) $1$ $\Z/2\Z$ \(\Q\) $[716,985,119011,342528]$ $[179,1294,13664,192855,2676]$ $[183765996899/2676,3710764333/1338,109452056/669]$ $y^2 + (x^3 + x^2 + x)y = x^4 + x^3 + 2x^2 + x + 1$
1369.a.1369.1 1369.a \( 37^{2} \) $1$ $\Z/3\Z$ \(\Q \times \Q\) $[24,-300,-2976,-5476]$ $[12,56,168,-280,-1369]$ $[-248832/1369,-96768/1369,-24192/1369]$ $y^2 + (x^3 + x^2 + x + 1)y = -x^4 - x^3 - x^2$
1490.a.1490.1 1490.a \( 2 \cdot 5 \cdot 149 \) $1$ $\Z/2\Z$ \(\Q\) $[1108,2617,932621,-190720]$ $[277,3088,44636,707107,-1490]$ $[-1630793025157/1490,-32816072552/745,-1712437822/745]$ $y^2 + (x^3 + 1)y = x^5 - 4x^3 - 2x^2 + 2x$
1519.a.1519.1 1519.a \( 7^{2} \cdot 31 \) $1$ $\mathsf{trivial}$ \(\Q\) $[804,1953,517041,-194432]$ $[201,1602,16160,170439,-1519]$ $[-328080401001/1519,-13009202802/1519,-652880160/1519]$ $y^2 + (x^3 + x + 1)y = -2x^4 + 2x^2 - x - 1$
1573.a.190333.1 1573.a \( 11^{2} \cdot 13 \) $1$ $\Z/5\Z$ \(\Q \times \Q\) $[38120,8596,107715056,761332]$ $[19060,15135384,16023823816,19083558276376,190333]$ $[2515443004991977600000/190333,9527291378032704000/17303,336426770019200/11]$ $y^2 + x^3y = -7x^4 - 7x^3 + 38x^2 + 21x - 83$
1647.a.1647.1 1647.a \( 3^{3} \cdot 61 \) $1$ $\mathsf{trivial}$ \(\Q\) $[36,-639,16641,210816]$ $[9,30,-296,-891,1647]$ $[2187/61,810/61,-888/61]$ $y^2 + (x^3 + x + 1)y = x^5$
1655.a.206875.1 1655.a \( 5 \cdot 331 \) $1$ $\Z/2\Z$ \(\Q\) $[11444,-79223,-306097691,-26480000]$ $[2861,344356,55836816,10292018960,-206875]$ $[-191685511916770301/206875,-8064198843467636/206875,-457042262577936/206875]$ $y^2 + (x^3 + 1)y = x^5 - x^4 - 7x^3 + 2x^2 + 14x - 10$
1689.a.45603.1 1689.a \( 3 \cdot 563 \) $1$ $\Z/2\Z$ \(\Q\) $[34900,-37799,-434488675,-5837184]$ $[8725,3173476,1539708400,840751466856,-45603]$ $[-50562341569814453125/45603,-2107810313223812500/45603,-117211264267750000/45603]$ $y^2 + (x^2 + x + 1)y = x^5 - 6x^4 + 21x^3 + 15x^2 + 3x$
1753.a.1753.1 1753.a \( 1753 \) $1$ $\mathsf{trivial}$ \(\Q\) $[108,1497,18531,224384]$ $[27,-32,256,1472,1753]$ $[14348907/1753,-629856/1753,186624/1753]$ $y^2 + (x^3 + 1)y = x^2$
1776.b.191808.1 1776.b \( 2^{4} \cdot 3 \cdot 37 \) $0$ $\Z/20\Z$ \(\Q\) $[32,-1136,-7560,23976]$ $[32,800,64,-159488,191808]$ $[524288/2997,409600/2997,1024/2997]$ $y^2 + y = 2x^5 + x^4 - x^2$
1777.a.1777.1 1777.a \( 1777 \) $1$ $\mathsf{trivial}$ \(\Q\) $[6052,-1391,-2704039,227456]$ $[1513,95440,8030588,760371511,1777]$ $[7928565897078793/1777,330557651801680/1777,18383373101372/1777]$ $y^2 + (x^3 + x + 1)y = -3x^4 + 7x^2 - x - 8$
1861.a.1861.1 1861.a \( 1861 \) $1$ $\mathsf{trivial}$ \(\Q\) $[60,3057,16311,-238208]$ $[15,-118,312,-2311,-1861]$ $[-759375/1861,398250/1861,-70200/1861]$ $y^2 + (x^3 + x + 1)y = -x^4 + x^3 - x^2$
1863.a.1863.1 1863.a \( 3^{4} \cdot 23 \) $1$ $\mathsf{trivial}$ \(\Q\) $[3588,6921,8059509,-238464]$ $[897,33237,1630597,89486835,-1863]$ $[-311709013239,-12876157827,-6338130539/9]$ $y^2 + (x^3 + x + 1)y = 2x^5 + 4x^4 - 5x^2 + x$
1904.a.487424.1 1904.a \( 2^{4} \cdot 7 \cdot 17 \) $0$ $\Z/2\Z\oplus\Z/10\Z$ \(\Q\) $[172,-1091,-23251,60928]$ $[172,1960,-2304,-1059472,487424]$ $[147008443/476,2782745/136,-16641/119]$ $y^2 + (x^3 + x)y = x^5 - 2x^2 - x + 1$
1908.a.183168.1 1908.a \( 2^{2} \cdot 3^{2} \cdot 53 \) $0$ $\Z/24\Z$ \(\Q\) $[556,8089,1394947,-23445504]$ $[139,468,-144,-59760,-183168]$ $[-51888844699/183168,-34913047/5088,19321/1272]$ $y^2 + (x^3 + 1)y = 2x^4 + 3x^3 + 4x^2 + 2x$
1923.b.17307.1 1923.b \( 3 \cdot 641 \) $1$ $\mathsf{trivial}$ \(\Q\) $[1692,10929,5898807,2215296]$ $[423,7000,146780,3271985,17307]$ $[501577530309/641,19622547000/641,972711060/641]$ $y^2 + (x^3 + x + 1)y = x^4 + 3x^2 + x + 2$
1936.a.1936.1 1936.a \( 2^{4} \cdot 11^{2} \) $1$ $\Z/5\Z$ \(\Q \times \Q\) $[184,37,721,242]$ $[184,1386,15040,211591,1936]$ $[13181630464/121,49057344/11,31824640/121]$ $y^2 + y = -x^6 + 2x^4 - x^2$
1973.a.1973.1 1973.a \( 1973 \) $1$ $\mathsf{trivial}$ \(\Q\) $[80,148,7256,-7892]$ $[40,42,-384,-4281,-1973]$ $[-102400000/1973,-2688000/1973,614400/1973]$ $y^2 + y = x^6 - x^5 + x^2 - x$
1985.a.1985.1 1985.a \( 5 \cdot 397 \) $1$ $\Z/2\Z$ \(\Q\) $[428,1705,359371,254080]$ $[107,406,-44,-42386,1985]$ $[14025517307/1985,497367458/1985,-503756/1985]$ $y^2 + (x^3 + 1)y = x^5 + x^4 - x$
1987.a.1987.1 1987.a \( 1987 \) $1$ $\mathsf{trivial}$ \(\Q\) $[452,1129,100197,254336]$ $[113,485,3425,37950,1987]$ $[18424351793/1987,699805045/1987,43733825/1987]$ $y^2 + (x^3 + x + 1)y = -x^4 + x^2 - x - 1$
2001.a.2001.1 2001.a \( 3 \cdot 23 \cdot 29 \) $1$ $\mathsf{trivial}$ \(\Q\) $[100,97,10385,256128]$ $[25,22,-80,-621,2001]$ $[9765625/2001,343750/2001,-50000/2001]$ $y^2 + (x^3 + x + 1)y = x^5 + x^4 + x^3$
2007.a.6021.1 2007.a \( 3^{2} \cdot 223 \) $1$ $\Z/2\Z$ \(\Q\) $[588,6777,1216467,770688]$ $[147,618,1988,-22422,6021]$ $[2542277241/223,72707082/223,4773188/669]$ $y^2 + (x^2 + x + 1)y = x^6 + x^4$
2020.a.646400.1 2020.a \( 2^{2} \cdot 5 \cdot 101 \) $1$ $\Z/2\Z$ \(\Q\) $[394,1648,195485,2525]$ $[788,21478,704476,23455651,646400]$ $[1186837123028/2525,82103660647/5050,6835002271/10100]$ $y^2 + x^3y = 2x^4 - x^3 + 5x^2 - 4x + 4$
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