| Label |
Class |
Conductor |
Discriminant |
Rank* |
2-Selmer rank |
Torsion |
$\textrm{End}^0(J_{\overline\Q})$ |
$\textrm{End}^0(J)$ |
$\GL_2\textsf{-type}$ |
Sato-Tate |
Nonmaximal primes |
$\Q$-simple |
\(\overline{\Q}\)-simple |
\(\Aut(X)\) |
\(\Aut(X_{\overline{\Q}})\) |
$\Q$-points |
$\Q$-Weierstrass points |
mod-$\ell$ images |
Locally solvable |
Square Ш* |
Analytic Ш* |
Tamagawa |
Regulator |
Real period |
Leading coefficient |
Igusa-Clebsch invariants |
Igusa invariants |
G2-invariants |
Equation |
| 1152.a.147456.1 |
1152.a |
\( 2^{7} \cdot 3^{2} \) |
\( 2^{14} \cdot 3^{2} \) |
$0$ |
$1$ |
$\Z/8\Z$ |
\(\mathrm{M}_2(\Q)\) |
\(\Q \times \Q\) |
✓ |
$J(E_1)$ |
|
|
|
$C_2^2$ |
$D_4$ |
$4$ |
$2$ |
2.180.5, 3.1080.10 |
✓ |
✓ |
$1$ |
\( 2^{2} \) |
\(1.000000\) |
\(7.270694\) |
\(0.454418\) |
$[152,109,5469,18]$ |
$[608,14240,405504,10942208,147456]$ |
$[5071050752/9,195344320/9,1016576]$ |
$y^2 = x^6 - 2x^4 + 2x^2 - 1$ |
| 1600.b.409600.1 |
1600.b |
\( 2^{6} \cdot 5^{2} \) |
\( 2^{14} \cdot 5^{2} \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/6\Z$ |
\(\mathrm{M}_2(\Q)\) |
\(\Q \times \Q\) |
✓ |
$J(E_1)$ |
|
|
|
$C_2^2$ |
$D_4$ |
$4$ |
$2$ |
2.360.1, 3.8640.8 |
✓ |
✓ |
$1$ |
\( 2 \cdot 3 \) |
\(1.000000\) |
\(12.846191\) |
\(0.535258\) |
$[248,181,14873,50]$ |
$[992,39072,1945600,100853504,409600]$ |
$[58632501248/25,2327987904/25,4674304]$ |
$y^2 = x^6 - 4x^4 + 4x^2 - 1$ |
| 2500.a.50000.1 |
2500.a |
\( 2^{2} \cdot 5^{4} \) |
\( 2^{4} \cdot 5^{5} \) |
$0$ |
$0$ |
$\Z/15\Z$ |
\(\mathrm{M}_2(\Q)\) |
\(\Q \times \Q\) |
✓ |
$J(E_1)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$4$ |
$0$ |
2.60.2, 3.8640.9 |
✓ |
✓ |
$1$ |
\( 3 \cdot 5 \) |
\(1.000000\) |
\(10.235464\) |
\(0.682364\) |
$[100,625,21385,2048]$ |
$[125,0,-10000,-312500,50000]$ |
$[9765625/16,0,-3125]$ |
$y^2 + (x^3 + 1)y = x^5 + 2x^3 + x$ |
| 2500.a.400000.1 |
2500.a |
\( 2^{2} \cdot 5^{4} \) |
\( - 2^{7} \cdot 5^{5} \) |
$0$ |
$0$ |
$\Z/5\Z$ |
\(\mathrm{M}_2(\Q)\) |
\(\Q \times \Q\) |
✓ |
$J(E_1)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$0$ |
$0$ |
2.60.2, 3.2880.2 |
|
✓ |
$1$ |
\( 5 \) |
\(1.000000\) |
\(3.411821\) |
\(0.682364\) |
$[860,36865,8199455,16384]$ |
$[1075,9750,107500,5125000,400000]$ |
$[459401384375/128,1937983125/64,9938375/32]$ |
$y^2 + (x^3 + 1)y = -2x^6 - 2x^5 + 2x^3 - 2x - 2$ |
| 2916.a.5832.1 |
2916.a |
\( 2^{2} \cdot 3^{6} \) |
\( 2^{3} \cdot 3^{6} \) |
$0$ |
$0$ |
$\Z/3\Z\oplus\Z/3\Z$ |
\(\mathrm{M}_2(\Q)\) |
\(\Q \times \Q\) |
✓ |
$J(E_1)$ |
|
|
|
$C_2^2$ |
$D_6$ |
$4$ |
$0$ |
2.60.2, 3.17280.1 |
✓ |
✓ |
$1$ |
\( 3 \) |
\(1.000000\) |
\(19.520681\) |
\(0.722988\) |
$[4,369,1257,-3072]$ |
$[3,-138,-356,-5028,-5832]$ |
$[-1/24,23/36,89/162]$ |
$y^2 + (x^3 + 1)y = x^3$ |
| 2916.a.139968.1 |
2916.a |
\( 2^{2} \cdot 3^{6} \) |
\( - 2^{6} \cdot 3^{7} \) |
$0$ |
$0$ |
$\Z/3\Z\oplus\Z/9\Z$ |
\(\mathrm{M}_2(\Q)\) |
\(\Q \times \Q\) |
✓ |
$J(E_1)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$6$ |
$0$ |
2.60.2, 3.5760.3 |
✓ |
✓ |
$1$ |
\( 3^{3} \) |
\(1.000000\) |
\(19.520681\) |
\(0.722988\) |
$[324,12609,1778337,73728]$ |
$[243,-2268,-314496,-20391588,139968]$ |
$[387420489/64,-3720087/16,-132678]$ |
$y^2 + (x^2 + x + 1)y = x^6 - 3x^5 + 5x^4 - 6x^3 + x$ |
| 3969.d.250047.1 |
3969.d |
\( 3^{4} \cdot 7^{2} \) |
\( - 3^{6} \cdot 7^{3} \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/6\Z$ |
\(\mathrm{M}_2(\Q)\) |
\(\mathsf{RM}\) |
✓ |
$J(E_1)$ |
|
✓ |
|
$C_2$ |
$C_2$ |
$4$ |
$2$ |
2.180.3, 3.1920.1 |
✓ |
✓ |
$1$ |
\( 2^{3} \) |
\(1.000000\) |
\(13.559050\) |
\(0.753281\) |
$[452,-15543,-660459,131712]$ |
$[339,10617,-211009,-46063185,250047]$ |
$[18424351793/1029,5106412483/3087,-2694373921/27783]$ |
$y^2 + (x^2 + x + 1)y = -3x^5 + 5x^4 - 4x^3 + x$ |
| 4608.a.4608.1 |
4608.a |
\( 2^{9} \cdot 3^{2} \) |
\( - 2^{9} \cdot 3^{2} \) |
$0$ |
$1$ |
$\Z/4\Z$ |
\(\mathrm{M}_2(\Q)\) |
\(\Q \times \Q\) |
✓ |
$J(E_1)$ |
|
|
|
$C_2^2$ |
$D_4$ |
$2$ |
$0$ |
2.90.5, 3.1080.10 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(13.153769\) |
\(0.822111\) |
$[152,109,5469,18]$ |
$[304,3560,50688,683888,4608]$ |
$[5071050752/9,195344320/9,1016576]$ |
$y^2 + x^3y = x^4 + 2x^2 + 2$ |
| 4608.b.4608.1 |
4608.b |
\( 2^{9} \cdot 3^{2} \) |
\( 2^{9} \cdot 3^{2} \) |
$0$ |
$1$ |
$\Z/4\Z$ |
\(\mathrm{M}_2(\Q)\) |
\(\Q \times \Q\) |
✓ |
$J(E_1)$ |
|
|
|
$C_2^2$ |
$D_4$ |
$2$ |
$0$ |
2.90.5, 3.1080.10 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(10.282314\) |
\(0.642645\) |
$[152,109,5469,18]$ |
$[304,3560,50688,683888,4608]$ |
$[5071050752/9,195344320/9,1016576]$ |
$y^2 + x^3y = -x^4 + 2x^2 - 2$ |
| 6400.b.12800.1 |
6400.b |
\( 2^{8} \cdot 5^{2} \) |
\( - 2^{9} \cdot 5^{2} \) |
$0$ |
$1$ |
$\Z/6\Z$ |
\(\mathrm{M}_2(\Q)\) |
\(\Q \times \Q\) |
✓ |
$J(E_1)$ |
|
|
|
$C_2^2$ |
$D_4$ |
$2$ |
$0$ |
2.180.4, 3.8640.8 |
✓ |
✓ |
$1$ |
\( 3 \) |
\(1.000000\) |
\(11.281316\) |
\(0.940110\) |
$[248,181,14873,50]$ |
$[496,9768,243200,6303344,12800]$ |
$[58632501248/25,2327987904/25,4674304]$ |
$y^2 + x^3y = 2x^4 + 4x^2 + 2$ |
| 6400.d.12800.1 |
6400.d |
\( 2^{8} \cdot 5^{2} \) |
\( 2^{9} \cdot 5^{2} \) |
$1$ |
$2$ |
$\Z/6\Z$ |
\(\mathrm{M}_2(\Q)\) |
\(\Q \times \Q\) |
✓ |
$J(E_1)$ |
|
|
|
$C_2^2$ |
$D_4$ |
$6$ |
$0$ |
2.180.4, 3.8640.8 |
✓ |
✓ |
$1$ |
\( 3 \) |
\(0.413437\) |
\(18.167258\) |
\(0.625918\) |
$[248,181,14873,50]$ |
$[496,9768,243200,6303344,12800]$ |
$[58632501248/25,2327987904/25,4674304]$ |
$y^2 + x^3y = -2x^4 + 4x^2 - 2$ |
| 9216.a.36864.1 |
9216.a |
\( 2^{10} \cdot 3^{2} \) |
\( 2^{12} \cdot 3^{2} \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/2\Z$ |
\(\mathrm{M}_2(\Q)\) |
\(\Q \times \Q\) |
✓ |
$J(E_1)$ |
|
|
|
$C_2^2$ |
$D_4$ |
$2$ |
$2$ |
2.360.1, 3.1080.10 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(1.000000\) |
\(9.381457\) |
\(1.172682\) |
$[46,-44,-72,144]$ |
$[92,470,-684,-70957,36864]$ |
$[6436343/36,2859245/288,-10051/64]$ |
$y^2 = x^5 + x^3 + x$ |
| 25600.a.102400.1 |
25600.a |
\( 2^{10} \cdot 5^{2} \) |
\( 2^{12} \cdot 5^{2} \) |
$1$ |
$3$ |
$\Z/2\Z\oplus\Z/2\Z$ |
\(\mathrm{M}_2(\Q)\) |
\(\Q \times \Q\) |
✓ |
$J(E_1)$ |
|
|
|
$C_2^2$ |
$D_4$ |
$4$ |
$2$ |
2.360.1, 3.1080.10 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(0.717386\) |
\(16.418098\) |
\(1.472264\) |
$[94,244,7096,400]$ |
$[188,822,-1100,-220621,102400]$ |
$[229345007/100,42671253/800,-24299/64]$ |
$y^2 = x^5 - 3x^3 + x$ |
| 25600.f.512000.1 |
25600.f |
\( 2^{10} \cdot 5^{2} \) |
\( 2^{12} \cdot 5^{3} \) |
$0$ |
$3$ |
$\Z/2\Z\oplus\Z/2\Z\oplus\Z/2\Z$ |
\(\mathrm{M}_2(\Q)\) |
\(\mathsf{RM}\) |
✓ |
$J(E_1)$ |
|
✓ |
|
$C_2$ |
$C_2^2$ |
$4$ |
$4$ |
2.360.2, 3.1080.4 |
✓ |
✓ |
$1$ |
\( 2^{3} \) |
\(1.000000\) |
\(11.501498\) |
\(1.437687\) |
$[566,2164,432824,2000]$ |
$[1132,47622,2094500,25779779,512000]$ |
$[1815232161643/500,539680767657/4000,335492821/64]$ |
$y^2 = 2x^5 - 5x^4 - x^3 + 5x^2 + 2x$ |
| 26244.c.157464.1 |
26244.c |
\( 2^{2} \cdot 3^{8} \) |
\( 2^{3} \cdot 3^{9} \) |
$0$ |
$0$ |
$\Z/3\Z\oplus\Z/3\Z$ |
\(\mathrm{M}_2(\Q)\) |
\(\Q \times \Q\) |
✓ |
$J(E_1)$ |
|
|
|
$C_2^2$ |
$D_6$ |
$4$ |
$0$ |
2.60.2, 3.5760.3 |
✓ |
✓ |
$1$ |
\( 3^{2} \) |
\(1.000000\) |
\(14.148765\) |
\(1.572085\) |
$[60,945,2295,82944]$ |
$[45,-270,3780,24300,157464]$ |
$[9375/8,-625/4,875/18]$ |
$y^2 + (x^3 + 1)y = 2x^3$ |
| 36864.b.36864.1 |
36864.b |
\( 2^{12} \cdot 3^{2} \) |
\( 2^{12} \cdot 3^{2} \) |
$1$ |
$2$ |
$\Z/2\Z$ |
\(\mathrm{M}_2(\Q)\) |
\(\Q \times \Q\) |
✓ |
$J(E_1)$ |
|
|
|
$C_2^2$ |
$D_4$ |
$4$ |
$2$ |
2.180.5, 3.1080.10 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.675802\) |
\(9.381457\) |
\(1.585002\) |
$[46,-44,-72,144]$ |
$[92,470,-684,-70957,36864]$ |
$[6436343/36,2859245/288,-10051/64]$ |
$y^2 = x^5 - x^3 + x$ |
| 102400.e.102400.1 |
102400.e |
\( 2^{12} \cdot 5^{2} \) |
\( 2^{12} \cdot 5^{2} \) |
$0$ |
$1$ |
$\Z/2\Z$ |
\(\mathrm{M}_2(\Q)\) |
\(\Q \times \Q\) |
✓ |
$J(E_1)$ |
|
|
|
$C_2^2$ |
$D_4$ |
$2$ |
$2$ |
2.180.5, 3.1080.10 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(8.209049\) |
\(2.052262\) |
$[94,244,7096,400]$ |
$[188,822,-1100,-220621,102400]$ |
$[229345007/100,42671253/800,-24299/64]$ |
$y^2 = x^5 + 3x^3 + x$ |
| 236196.a.472392.1 |
236196.a |
\( 2^{2} \cdot 3^{10} \) |
\( - 2^{3} \cdot 3^{10} \) |
$1$ |
$1$ |
$\mathsf{trivial}$ |
\(\mathrm{M}_2(\Q)\) |
\(\Q \times \Q\) |
✓ |
$J(E_1)$ |
|
|
|
$C_2^2$ |
$D_6$ |
$0$ |
$0$ |
2.60.2, 3.5760.11 |
|
✓ |
$1$ |
\( 1 \) |
\(0.909555\) |
\(4.016028\) |
\(3.652798\) |
$[356,3969,419553,248832]$ |
$[267,1482,-2884,-741588,472392]$ |
$[5584059449/1944,174127343/2916,-5711041/13122]$ |
$y^2 + (x^3 + 1)y = -x^6 - 1$ |
| 278784.a.557568.1 |
278784.a |
\( 2^{8} \cdot 3^{2} \cdot 11^{2} \) |
\( 2^{9} \cdot 3^{2} \cdot 11^{2} \) |
$0$ |
$2$ |
$\Z/2\Z$ |
\(\mathrm{M}_2(\Q)\) |
\(\Q \times \Q\) |
✓ |
$J(E_1)$ |
|
|
|
$C_2^2$ |
$D_4$ |
$0$ |
$0$ |
2.90.5, 3.1080.10 |
|
|
$2$ |
\( 1 \) |
\(1.000000\) |
\(5.710508\) |
\(2.855254\) |
$[1592,1189,630369,2178]$ |
$[3184,419240,73041408,14200416368,557568]$ |
$[639139022845952/1089,26430898598080/1089,1328059136]$ |
$y^2 + y = 6x^6 - 8x^4 + 4x^2 - 1$ |
| 278784.b.557568.1 |
278784.b |
\( 2^{8} \cdot 3^{2} \cdot 11^{2} \) |
\( - 2^{9} \cdot 3^{2} \cdot 11^{2} \) |
$1$ |
$2$ |
$\Z/2\Z$ |
\(\mathrm{M}_2(\Q)\) |
\(\Q \times \Q\) |
✓ |
$J(E_1)$ |
|
|
|
$C_2^2$ |
$D_4$ |
$0$ |
$0$ |
2.90.5, 3.1080.10 |
|
✓ |
$1$ |
\( 1 \) |
\(2.415493\) |
\(4.989405\) |
\(3.012968\) |
$[1592,1189,630369,2178]$ |
$[3184,419240,73041408,14200416368,557568]$ |
$[639139022845952/1089,26430898598080/1089,1328059136]$ |
$y^2 + y = -6x^6 - 8x^4 - 4x^2 - 1$ |
| 589824.a.589824.1 |
589824.a |
\( 2^{16} \cdot 3^{2} \) |
\( 2^{16} \cdot 3^{2} \) |
$0$ |
$1$ |
$\Z/2\Z$ |
\(\mathrm{M}_2(\Q)\) |
\(\Q \times \Q\) |
✓ |
$J(E_1)$ |
|
|
|
$C_2^2$ |
$D_4$ |
$2$ |
$2$ |
2.180.5, 3.1080.10 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(13.759439\) |
\(3.439860\) |
$[68,124,2616,72]$ |
$[272,1760,-2304,-931072,589824]$ |
$[22717712/9,540430/9,-289]$ |
$y^2 = x^5 - 4x^3 + x$ |
| 589824.b.589824.1 |
589824.b |
\( 2^{16} \cdot 3^{2} \) |
\( 2^{16} \cdot 3^{2} \) |
$2$ |
$3$ |
$\Z/2\Z$ |
\(\mathrm{M}_2(\Q)\) |
\(\Q \times \Q\) |
✓ |
$J(E_1)$ |
|
|
|
$C_2^2$ |
$D_4$ |
$2$ |
$2$ |
2.180.5, 3.1080.10 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(2.544094\) |
\(6.879720\) |
\(4.375664\) |
$[68,124,2616,72]$ |
$[272,1760,-2304,-931072,589824]$ |
$[22717712/9,540430/9,-289]$ |
$y^2 = x^5 + 4x^3 + x$ |
| 778752.b.778752.1 |
778752.b |
\( 2^{9} \cdot 3^{2} \cdot 13^{2} \) |
\( 2^{9} \cdot 3^{2} \cdot 13^{2} \) |
$2$ |
$3$ |
$\Z/2\Z$ |
\(\mathrm{M}_2(\Q)\) |
\(\Q \times \Q\) |
✓ |
$J(E_1)$ |
|
|
|
$C_2^2$ |
$D_4$ |
$4$ |
$0$ |
2.90.5, 3.1080.10 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.538669\) |
\(10.957992\) |
\(4.215180\) |
$[1880,1405,879765,3042]$ |
$[3760,585320,120706560,27814290800,778752]$ |
$[1467808044800000/1521,60769678360000/1521,2191328000]$ |
$y^2 + y = 6x^6 - 10x^4 + 5x^2 - 1$ |
| 778752.c.778752.1 |
778752.c |
\( 2^{9} \cdot 3^{2} \cdot 13^{2} \) |
\( - 2^{9} \cdot 3^{2} \cdot 13^{2} \) |
$2$ |
$4$ |
$\Z/2\Z$ |
\(\mathrm{M}_2(\Q)\) |
\(\Q \times \Q\) |
✓ |
$J(E_1)$ |
|
|
|
$C_2^2$ |
$D_4$ |
$0$ |
$0$ |
2.90.5, 3.1080.10 |
|
|
$2$ |
\( 1 \) |
\(2.038974\) |
\(4.813693\) |
\(4.907496\) |
$[1880,1405,879765,3042]$ |
$[3760,585320,120706560,27814290800,778752]$ |
$[1467808044800000/1521,60769678360000/1521,2191328000]$ |
$y^2 + y = -6x^6 - 10x^4 - 5x^2 - 1$ |
