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Label Class Conductor Rank* Torsion $\textrm{End}^0(J_{\overline\Q})$ Igusa-Clebsch invariants Igusa invariants G2-invariants Equation
256.a.512.1 256.a \( 2^{8} \) $0$ $\Z/2\Z\oplus\Z/10\Z$ \(\mathrm{M}_2(\Q)\) $[26,-2,40,2]$ $[52,118,-36,-3949,512]$ $[742586,129623/4,-1521/8]$ $y^2 + y = 2x^5 - 3x^4 + x^3 + x^2 - x$
400.a.409600.1 400.a \( 2^{4} \cdot 5^{2} \) $0$ $\Z/3\Z\oplus\Z/6\Z$ \(\mathrm{M}_2(\Q)\) $[248,181,14873,50]$ $[992,39072,1945600,100853504,409600]$ $[58632501248/25,2327987904/25,4674304]$ $y^2 = x^6 + 4x^4 + 4x^2 + 1$
576.a.576.1 576.a \( 2^{6} \cdot 3^{2} \) $0$ $\Z/10\Z$ \(\mathrm{M}_2(\Q)\) $[68,124,2616,72]$ $[68,110,-36,-3637,576]$ $[22717712/9,540430/9,-289]$ $y^2 + (x^3 + x^2 + x + 1)y = -x^3 - x$
576.b.147456.1 576.b \( 2^{6} \cdot 3^{2} \) $0$ $\Z/4\Z\oplus\Z/4\Z$ \(\mathrm{M}_2(\Q)\) $[152,109,5469,18]$ $[608,14240,405504,10942208,147456]$ $[5071050752/9,195344320/9,1016576]$ $y^2 = x^6 + 2x^4 + 2x^2 + 1$
1152.a.147456.1 1152.a \( 2^{7} \cdot 3^{2} \) $0$ $\Z/8\Z$ \(\mathrm{M}_2(\Q)\) $[152,109,5469,18]$ $[608,14240,405504,10942208,147456]$ $[5071050752/9,195344320/9,1016576]$ $y^2 = x^6 - 2x^4 + 2x^2 - 1$
1600.b.409600.1 1600.b \( 2^{6} \cdot 5^{2} \) $0$ $\Z/2\Z\oplus\Z/6\Z$ \(\mathrm{M}_2(\Q)\) $[248,181,14873,50]$ $[992,39072,1945600,100853504,409600]$ $[58632501248/25,2327987904/25,4674304]$ $y^2 = x^6 - 4x^4 + 4x^2 - 1$
2304.b.147456.1 2304.b \( 2^{8} \cdot 3^{2} \) $0$ $\Z/2\Z\oplus\Z/2\Z$ \(\mathrm{M}_2(\Q)\) $[152,109,5469,18]$ $[608,14240,405504,10942208,147456]$ $[5071050752/9,195344320/9,1016576]$ $y^2 = -x^6 - 2x^4 - 2x^2 - 1$
4096.e.524288.1 4096.e \( 2^{12} \) $0$ $\Z/2\Z\oplus\Z/2\Z$ \(\mathrm{M}_2(\Q)\) $[26,-2,40,2]$ $[208,1888,-2304,-1010944,524288]$ $[742586,129623/4,-1521/8]$ $y^2 = x^5 - 2x^4 - 2x^2 - x$
4608.a.4608.1 4608.a \( 2^{9} \cdot 3^{2} \) $0$ $\Z/4\Z$ \(\mathrm{M}_2(\Q)\) $[152,109,5469,18]$ $[304,3560,50688,683888,4608]$ $[5071050752/9,195344320/9,1016576]$ $y^2 + x^3y = x^4 + 2x^2 + 2$
4608.b.4608.1 4608.b \( 2^{9} \cdot 3^{2} \) $0$ $\Z/4\Z$ \(\mathrm{M}_2(\Q)\) $[152,109,5469,18]$ $[304,3560,50688,683888,4608]$ $[5071050752/9,195344320/9,1016576]$ $y^2 + x^3y = -x^4 + 2x^2 - 2$
4608.c.27648.1 4608.c \( 2^{9} \cdot 3^{2} \) $0$ $\Z/2\Z\oplus\Z/2\Z\oplus\Z/2\Z$ \(\mathrm{M}_2(\Q)\) $[24,-72,-180,108]$ $[48,288,-1024,-33024,27648]$ $[9216,1152,-256/3]$ $y^2 = x^5 - x^4 + x^2 - x$
6400.b.12800.1 6400.b \( 2^{8} \cdot 5^{2} \) $0$ $\Z/6\Z$ \(\mathrm{M}_2(\Q)\) $[248,181,14873,50]$ $[496,9768,243200,6303344,12800]$ $[58632501248/25,2327987904/25,4674304]$ $y^2 + x^3y = 2x^4 + 4x^2 + 2$
6400.d.12800.1 6400.d \( 2^{8} \cdot 5^{2} \) $1$ $\Z/6\Z$ \(\mathrm{M}_2(\Q)\) $[248,181,14873,50]$ $[496,9768,243200,6303344,12800]$ $[58632501248/25,2327987904/25,4674304]$ $y^2 + x^3y = -2x^4 + 4x^2 - 2$
6400.f.64000.1 6400.f \( 2^{8} \cdot 5^{2} \) $2$ $\Z/2\Z\oplus\Z/2\Z$ \(\mathrm{M}_2(\Q)\) $[154,310,19480,250]$ $[308,3126,-164,-2455597,64000]$ $[5413568314/125,713561079/500,-243089/1000]$ $y^2 + x^3y = -2x^4 - 3x^3 + x^2 + 6x + 4$
6400.g.64000.1 6400.g \( 2^{8} \cdot 5^{2} \) $0$ $\Z/2\Z\oplus\Z/2\Z$ \(\mathrm{M}_2(\Q)\) $[154,310,19480,250]$ $[308,3126,-164,-2455597,64000]$ $[5413568314/125,713561079/500,-243089/1000]$ $y^2 + (x^3 + x^2 + x + 1)y = -x^6 - x^3 - x - 1$
6400.i.409600.1 6400.i \( 2^{8} \cdot 5^{2} \) $0$ $\Z/2\Z$ \(\mathrm{M}_2(\Q)\) $[248,181,14873,50]$ $[992,39072,1945600,100853504,409600]$ $[58632501248/25,2327987904/25,4674304]$ $y^2 = -x^6 - 4x^4 - 4x^2 - 1$
8192.a.32768.1 8192.a \( 2^{13} \) $0$ $\Z/2\Z\oplus\Z/2\Z\oplus\Z/2\Z$ \(\mathrm{M}_2(\Q)\) $[67,82,1930,4]$ $[268,2118,-124,-1129789,32768]$ $[1350125107/32,318508017/256,-139159/512]$ $y^2 = x^5 - 3x^3 + 2x$
8192.b.131072.1 8192.b \( 2^{13} \) $0$ $\Z/2\Z\oplus\Z/2\Z\oplus\Z/2\Z$ \(\mathrm{M}_2(\Q)\) $[64,76,1552,16]$ $[256,1920,8192,-397312,131072]$ $[8388608,245760,4096]$ $y^2 = x^5 - 3x^4 + 6x^2 - 4x$
9216.a.36864.1 9216.a \( 2^{10} \cdot 3^{2} \) $0$ $\Z/2\Z\oplus\Z/2\Z$ \(\mathrm{M}_2(\Q)\) $[46,-44,-72,144]$ $[92,470,-684,-70957,36864]$ $[6436343/36,2859245/288,-10051/64]$ $y^2 = x^5 + x^3 + x$
12544.d.25088.1 12544.d \( 2^{8} \cdot 7^{2} \) $2$ $\Z/2\Z$ \(\mathrm{M}_2(\Q)\) $[74,142,3272,98]$ $[148,534,-196,-78541,25088]$ $[138687914/49,13524351/196,-1369/8]$ $y^2 + (x^3 + x^2 + x + 1)y = x^4 - x^3 + x^2 - x$
12544.g.175616.1 12544.g \( 2^{8} \cdot 7^{2} \) $1$ $\Z/2\Z$ \(\mathrm{M}_2(\Q)\) $[8,-203,455,686]$ $[16,552,-5632,-98704,175616]$ $[2048/343,4416/343,-2816/343]$ $y^2 + x^3y = x^5 + x^4 - 2x^2 - 4x - 2$
12800.c.128000.1 12800.c \( 2^{9} \cdot 5^{2} \) $0$ $\Z/2\Z\oplus\Z/2\Z\oplus\Z/2\Z$ \(\mathrm{M}_2(\Q)\) $[104,280,9140,500]$ $[208,1056,-1024,-332032,128000]$ $[380204032/125,9280128/125,-43264/125]$ $y^2 = x^5 - 3x^4 + 3x^2 - x$
16384.a.32768.1 16384.a \( 2^{14} \) $0$ $\Z/2\Z\oplus\Z/2\Z$ \(\mathrm{M}_2(\Q)\) $[67,82,1930,4]$ $[268,2118,-124,-1129789,32768]$ $[1350125107/32,318508017/256,-139159/512]$ $y^2 = x^5 + 3x^3 + 2x$
25600.a.102400.1 25600.a \( 2^{10} \cdot 5^{2} \) $1$ $\Z/2\Z\oplus\Z/2\Z$ \(\mathrm{M}_2(\Q)\) $[94,244,7096,400]$ $[188,822,-1100,-220621,102400]$ $[229345007/100,42671253/800,-24299/64]$ $y^2 = x^5 - 3x^3 + x$
25600.d.128000.1 25600.d \( 2^{10} \cdot 5^{2} \) $0$ $\Z/2\Z\oplus\Z/2\Z$ \(\mathrm{M}_2(\Q)\) $[56,-80,-260,500]$ $[112,736,-1536,-178432,128000]$ $[17210368/125,1009792/125,-18816/125]$ $y^2 = x^5 + x^4 + x^2 - x$
25600.e.128000.1 25600.e \( 2^{10} \cdot 5^{2} \) $0$ $\Z/2\Z\oplus\Z/2\Z$ \(\mathrm{M}_2(\Q)\) $[56,-80,-260,500]$ $[112,736,-1536,-178432,128000]$ $[17210368/125,1009792/125,-18816/125]$ $y^2 = x^5 - x^4 - x^2 - x$
36864.b.36864.1 36864.b \( 2^{12} \cdot 3^{2} \) $1$ $\Z/2\Z$ \(\mathrm{M}_2(\Q)\) $[46,-44,-72,144]$ $[92,470,-684,-70957,36864]$ $[6436343/36,2859245/288,-10051/64]$ $y^2 = x^5 - x^3 + x$
69696.c.627264.1 69696.c \( 2^{6} \cdot 3^{2} \cdot 11^{2} \) $0$ $\Z/2\Z$ \(\mathrm{M}_2(\Q)\) $[1220,3580,1448760,78408]$ $[1220,59630,3724380,247001675,627264]$ $[42229815050000/9801,1691859628750/9801,8837375]$ $y^2 + (x^3 + x^2 + x + 1)y = x^6 + 3x^4 - x^3 + 3x^2 - x + 1$
73728.c.884736.1 73728.c \( 2^{13} \cdot 3^{2} \) $1$ $\Z/2\Z\oplus\Z/2\Z$ \(\mathrm{M}_2(\Q)\) $[195,630,44910,108]$ $[780,18630,-380,-86843325,884736]$ $[10442615625/32,2558131875/256,-401375/1536]$ $y^2 = x^5 + 5x^3 + 6x$
73728.d.884736.1 73728.d \( 2^{13} \cdot 3^{2} \) $0$ $\Z/2\Z\oplus\Z/2\Z\oplus\Z/2\Z$ \(\mathrm{M}_2(\Q)\) $[195,630,44910,108]$ $[780,18630,-380,-86843325,884736]$ $[10442615625/32,2558131875/256,-401375/1536]$ $y^2 = 2x^5 - 5x^3 + 3x$
78400.a.78400.1 78400.a \( 2^{6} \cdot 5^{2} \cdot 7^{2} \) $0$ $\Z/2\Z$ \(\mathrm{M}_2(\Q)\) $[452,1276,189752,9800]$ $[452,7662,151900,2488139,78400]$ $[294789628688/1225,11055476814/1225,395839]$ $y^2 + (x^3 + x^2 + x + 1)y = -x^6 - 3x^4 - x^3 - 3x^2 - x - 1$
102400.b.102400.1 102400.b \( 2^{12} \cdot 5^{2} \) $1$ $\Z/2\Z$ \(\mathrm{M}_2(\Q)\) $[34,-116,-424,400]$ $[68,502,-2100,-98701,102400]$ $[1419857/100,1233163/800,-6069/64]$ $y^2 = x^5 - x^3 - x$
102400.e.102400.1 102400.e \( 2^{12} \cdot 5^{2} \) $0$ $\Z/2\Z$ \(\mathrm{M}_2(\Q)\) $[94,244,7096,400]$ $[188,822,-1100,-220621,102400]$ $[229345007/100,42671253/800,-24299/64]$ $y^2 = x^5 + 3x^3 + x$
135424.l.270848.1 135424.l \( 2^{8} \cdot 23^{2} \) $0$ $\Z/2\Z$ \(\mathrm{M}_2(\Q)\) $[170,430,23560,1058]$ $[340,3670,31740,-669325,270848]$ $[8874106250/529,1126919375/2116,108375/8]$ $y^2 + (x^3 + x^2 + x + 1)y = -x^6 - 2x^4 - x^3 - 2x^2 - x - 1$
147456.c.884736.1 147456.c \( 2^{14} \cdot 3^{2} \) $0$ $\Z/2\Z\oplus\Z/2\Z$ \(\mathrm{M}_2(\Q)\) $[195,630,44910,108]$ $[780,18630,-380,-86843325,884736]$ $[10442615625/32,2558131875/256,-401375/1536]$ $y^2 = 2x^5 + 5x^3 + 3x$
147456.e.884736.1 147456.e \( 2^{14} \cdot 3^{2} \) $1$ $\Z/2\Z\oplus\Z/2\Z$ \(\mathrm{M}_2(\Q)\) $[195,630,44910,108]$ $[780,18630,-380,-86843325,884736]$ $[10442615625/32,2558131875/256,-401375/1536]$ $y^2 = x^5 - 5x^3 + 6x$
193600.d.968000.1 193600.d \( 2^{6} \cdot 5^{2} \cdot 11^{2} \) $0$ $\Z/2\Z$ \(\mathrm{M}_2(\Q)\) $[292,2380,214520,121000]$ $[292,1966,-4356,-1284277,968000]$ $[33169145488/15125,764807422/15125,-47961/125]$ $y^2 + (x^3 + x^2 + x + 1)y = -x^6 - x^4 - x^3 - x^2 - x - 1$
193600.e.968000.1 193600.e \( 2^{6} \cdot 5^{2} \cdot 11^{2} \) $2$ $\Z/2\Z$ \(\mathrm{M}_2(\Q)\) $[292,2380,214520,121000]$ $[292,1966,-4356,-1284277,968000]$ $[33169145488/15125,764807422/15125,-47961/125]$ $y^2 + (x^3 + x^2 + x + 1)y = 2x^4 - x^3 + 2x^2 - x$
262144.a.262144.1 262144.a \( 2^{18} \) $1$ $\Z/2\Z$ \(\mathrm{M}_2(\Q)\) $[4,-14,2,1]$ $[32,640,-6144,-151552,262144]$ $[128,80,-24]$ $y^2 = x^5 - 2x^3 - x$
262144.b.524288.1 262144.b \( 2^{18} \) $1$ $\Z/2\Z$ \(\mathrm{M}_2(\Q)\) $[26,-2,40,2]$ $[208,1888,-2304,-1010944,524288]$ $[742586,129623/4,-1521/8]$ $y^2 = x^5 + 2x^3 + 2x$
262144.c.524288.1 262144.c \( 2^{18} \) $1$ $\Z/2\Z$ \(\mathrm{M}_2(\Q)\) $[26,-2,40,2]$ $[208,1888,-2304,-1010944,524288]$ $[742586,129623/4,-1521/8]$ $y^2 = x^5 - 2x^3 + 2x$
278784.a.557568.1 278784.a \( 2^{8} \cdot 3^{2} \cdot 11^{2} \) $0$ $\Z/2\Z$ \(\mathrm{M}_2(\Q)\) $[1592,1189,630369,2178]$ $[3184,419240,73041408,14200416368,557568]$ $[639139022845952/1089,26430898598080/1089,1328059136]$ $y^2 + y = 6x^6 - 8x^4 + 4x^2 - 1$
278784.b.557568.1 278784.b \( 2^{8} \cdot 3^{2} \cdot 11^{2} \) $1$ $\Z/2\Z$ \(\mathrm{M}_2(\Q)\) $[1592,1189,630369,2178]$ $[3184,419240,73041408,14200416368,557568]$ $[639139022845952/1089,26430898598080/1089,1328059136]$ $y^2 + y = -6x^6 - 8x^4 - 4x^2 - 1$
331776.e.995328.1 331776.e \( 2^{12} \cdot 3^{4} \) $0$ $\Z/2\Z$ \(\mathrm{M}_2(\Q)\) $[58,28,856,16]$ $[348,4374,-1836,-4942701,995328]$ $[20511149/4,5926527/32,-14297/64]$ $y^2 = x^5 + 3x^3 + 3x$
331776.g.995328.1 331776.g \( 2^{12} \cdot 3^{4} \) $1$ $\Z/2\Z$ \(\mathrm{M}_2(\Q)\) $[58,28,856,16]$ $[348,4374,-1836,-4942701,995328]$ $[20511149/4,5926527/32,-14297/64]$ $y^2 = x^5 - 3x^3 + 3x$
589824.a.589824.1 589824.a \( 2^{16} \cdot 3^{2} \) $0$ $\Z/2\Z$ \(\mathrm{M}_2(\Q)\) $[68,124,2616,72]$ $[272,1760,-2304,-931072,589824]$ $[22717712/9,540430/9,-289]$ $y^2 = x^5 - 4x^3 + x$
589824.b.589824.1 589824.b \( 2^{16} \cdot 3^{2} \) $2$ $\Z/2\Z$ \(\mathrm{M}_2(\Q)\) $[68,124,2616,72]$ $[272,1760,-2304,-931072,589824]$ $[22717712/9,540430/9,-289]$ $y^2 = x^5 + 4x^3 + x$
692224.a.692224.1 692224.a \( 2^{12} \cdot 13^{2} \) $0$ $\Z/2\Z$ \(\mathrm{M}_2(\Q)\) $[14,-404,-3928,-2704]$ $[28,1110,19604,-170797,-692224]$ $[-16807/676,-190365/5408,-1421/64]$ $y^2 = x^5 - 3x^3 - x$
778752.b.778752.1 778752.b \( 2^{9} \cdot 3^{2} \cdot 13^{2} \) $2$ $\Z/2\Z$ \(\mathrm{M}_2(\Q)\) $[1880,1405,879765,3042]$ $[3760,585320,120706560,27814290800,778752]$ $[1467808044800000/1521,60769678360000/1521,2191328000]$ $y^2 + y = 6x^6 - 10x^4 + 5x^2 - 1$
778752.c.778752.1 778752.c \( 2^{9} \cdot 3^{2} \cdot 13^{2} \) $2$ $\Z/2\Z$ \(\mathrm{M}_2(\Q)\) $[1880,1405,879765,3042]$ $[3760,585320,120706560,27814290800,778752]$ $[1467808044800000/1521,60769678360000/1521,2191328000]$ $y^2 + y = -6x^6 - 10x^4 - 5x^2 - 1$
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