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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.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 \( 3 \cdot 83 \) $0$ $\Z/28\Z$ \(\Q\) $[1932,87897,65765571,860544]$ $[483,6058,-161212,-28641190,6723]$ $[324526850403/83,25281736298/249,-4178776252/747]$ $y^2 + (x^3 + 1)y = -x^5 + x^3 + x^2 + 3x + 2$
256.a.512.1 256.a \( 2^{8} \) $0$ $\Z/2\Z\oplus\Z/10\Z$ \(\mathrm{M}_2(\Q)\) $[26,-2,40,2]$ $[52,118,-36,-3949,512]$ $[742586,129623/4,-1521/8]$ $y^2 + y = 2x^5 - 3x^4 + x^3 + x^2 - x$
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 \( 277 \) $0$ $\Z/5\Z$ \(\Q\) $[4480,1370512,1511819744,-1108]$ $[2240,-19352,164384,-1569936,-277]$ $[-56394933862400000/277,217505333248000/277,-824813158400/277]$ $y^2 + y = x^5 - 9x^4 + 14x^3 - 19x^2 + 11x - 6$
294.a.294.1 294.a \( 2 \cdot 3 \cdot 7^{2} \) $0$ $\Z/12\Z$ \(\Q \times \Q\) $[236,505,18451,37632]$ $[59,124,564,4475,294]$ $[714924299/294,12733498/147,327214/49]$ $y^2 + (x^3 + 1)y = x^4 + x^2$
294.a.8232.1 294.a \( 2 \cdot 3 \cdot 7^{2} \) $0$ $\Z/12\Z$ \(\Q \times \Q\) $[7636,11785,29745701,1053696]$ $[1909,151354,15951264,1885732415,8232]$ $[25353016669288549/8232,75211396489919/588,49431027484/7]$ $y^2 + (x^3 + 1)y = -2x^4 + 4x^2 - 9x - 14$
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 \( 5 \cdot 59 \) $0$ $\Z/2\Z$ \(\Q\) $[198804,305807001,18482629056189,-37760]$ $[49701,90182600,203402032096,494095763610824,-295]$ $[-303267334973269931148501/295,-2214359494206283568520/59,-502441543825401014496/295]$ $y^2 + (x^2 + x + 1)y = x^5 - 40x^3 + 22x^2 + 389x - 608$
324.a.648.1 324.a \( 2^{2} \cdot 3^{4} \) $0$ $\Z/21\Z$ \(\mathrm{M}_2(\Q)\) $[60,945,2295,82944]$ $[15,-30,140,300,648]$ $[9375/8,-625/4,875/18]$ $y^2 + (x^3 + x + 1)y = x^5 + 2x^4 + 2x^3 + x^2$
336.a.172032.1 336.a \( 2^{4} \cdot 3 \cdot 7 \) $0$ $\Z/2\Z$ \(\Q \times \Q\) $[16916,151117825,232872423961,-21504]$ $[16916,-88822256,277597802496,-798387183476800,-172032]$ $[-1352659309173012149/168,419870026410625699/168,-461744933079368]$ $y^2 + (x^3 + x)y = -x^6 + 15x^4 - 75x^2 - 56$
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 \( 353 \) $0$ $\Z/11\Z$ \(\Q\) $[188,817,30871,45184]$ $[47,58,256,2167,353]$ $[229345007/353,6021734/353,565504/353]$ $y^2 + (x^3 + x + 1)y = x^2$
360.a.6480.1 360.a \( 2^{3} \cdot 3^{2} \cdot 5 \) $0$ $\Z/2\Z\oplus\Z/2\Z\oplus\Z/8\Z$ \(\Q \times \Q\) $[2360,11992,9047820,25920]$ $[1180,56018,3453120,234166319,6480]$ $[28596971960000/81,1150492082200/81,6677950400/9]$ $y^2 + (x^3 + x)y = -3x^4 + 7x^2 - 5$
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 \( 2 \cdot 197 \) $0$ $\Z/20\Z$ \(\Q\) $[80,-20,649,-12608]$ $[40,70,39,-835,-3152]$ $[-6400000/197,-280000/197,-3900/197]$ $y^2 + (x + 1)y = -x^5$
400.a.409600.1 400.a \( 2^{4} \cdot 5^{2} \) $0$ $\Z/3\Z\oplus\Z/6\Z$ \(\mathrm{M}_2(\Q)\) $[248,181,14873,50]$ $[992,39072,1945600,100853504,409600]$ $[58632501248/25,2327987904/25,4674304]$ $y^2 = x^6 + 4x^4 + 4x^2 + 1$
427.a.2989.1 427.a \( 7 \cdot 61 \) $0$ $\Z/14\Z$ \(\Q\) $[4564,-22439,-35962915,-382592]$ $[1141,55180,3641688,277583402,-2989]$ $[-39466820645749/61,-1672794336220/61,-96756008472/61]$ $y^2 + (x^3 + 1)y = x^5 - x^4 - 5x^3 + 4x^2 + 4x - 4$
448.a.448.2 448.a \( 2^{6} \cdot 7 \) $0$ $\Z/12\Z$ \(\mathsf{CM} \times \Q\) $[828,16635,5308452,56]$ $[828,17476,-853888,-253107460,448]$ $[6080953884912/7,155007628668/7,-1306723104]$ $y^2 + (x^3 + x)y = -2x^4 + 7$
448.a.448.1 448.a \( 2^{6} \cdot 7 \) $0$ $\Z/6\Z$ \(\mathsf{CM} \times \Q\) $[828,16635,5308452,56]$ $[828,17476,-853888,-253107460,448]$ $[6080953884912/7,155007628668/7,-1306723104]$ $y^2 + (x^3 + x)y = x^4 - 7$
450.a.2700.1 450.a \( 2 \cdot 3^{2} \cdot 5^{2} \) $0$ $\Z/24\Z$ \(\Q \times \Q\) $[364,3529,393211,345600]$ $[91,198,0,-9801,2700]$ $[6240321451/2700,8289281/150,0]$ $y^2 + (x^3 + 1)y = x^5 + 3x^4 + 3x^3 + 3x^2 + x$
450.a.36450.1 450.a \( 2 \cdot 3^{2} \cdot 5^{2} \) $0$ $\Z/2\Z\oplus\Z/12\Z$ \(\Q \times \Q\) $[23444,212089,1627179821,4665600]$ $[5861,1422468,457836300,164990835819,36450]$ $[6916057684302385301/36450,5303516319500302/675,1294426477922/3]$ $y^2 + (x^3 + 1)y = x^5 - 4x^4 - 9x^3 + 28x^2 - 6x - 16$
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 \( 2^{3} \cdot 59 \) $0$ $\Z/8\Z$ \(\Q\) $[152,17065,1592025,7552]$ $[152,-10414,-926656,-62325777,60416]$ $[79235168/59,-35714813/59,-20907676/59]$ $y^2 + (x + 1)y = 8x^5 + 5x^4 + 4x^3 + 2x^2$
476.a.952.1 476.a \( 2^{2} \cdot 7 \cdot 17 \) $0$ $\Z/3\Z\oplus\Z/6\Z$ \(\Q \times \Q\) $[7340,1042345,2905273355,121856]$ $[1835,96870,-3910340,-4139817700,952]$ $[20805604708146875/952,299272981175625/476,-27661753375/2]$ $y^2 + (x^3 + 1)y = -5x^4 + 7x^3 + 25x^2 - 75x + 54$
484.a.1936.1 484.a \( 2^{2} \cdot 11^{2} \) $0$ $\Z/15\Z$ \(\Q \times \Q\) $[184,37,721,242]$ $[184,1386,15040,211591,1936]$ $[13181630464/121,49057344/11,31824640/121]$ $y^2 + y = x^6 + 2x^4 + x^2$
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