| 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 |
| 256.a.512.1 |
256.a |
\( 2^{8} \) |
\( - 2^{9} \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/10\Z$ |
\(\mathrm{M}_2(\Q)\) |
\(\mathsf{CM}\) |
✓ |
$E_4$ |
|
✓ |
|
$C_4$ |
$D_4$ |
$6$ |
$2$ |
2.180.3, 3.540.6 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(1.000000\) |
\(26.841829\) |
\(0.134209\) |
$[26,-2,40,2]$ |
$[52,118,-36,-3949,512]$ |
$[742586,129623/4,-1521/8]$ |
$y^2 + y = 2x^5 - 3x^4 + x^3 + x^2 - x$ |
| 400.a.409600.1 |
400.a |
\( 2^{4} \cdot 5^{2} \) |
\( - 2^{14} \cdot 5^{2} \) |
$0$ |
$1$ |
$\Z/3\Z\oplus\Z/6\Z$ |
\(\mathrm{M}_2(\Q)\) |
\(\mathrm{M}_2(\Q)\) |
|
$E_1$ |
|
|
|
$D_4$ |
$D_4$ |
$4$ |
$0$ |
2.180.4, 3.17280.4 |
✓ |
✓ |
$1$ |
\( 3^{2} \) |
\(1.000000\) |
\(7.977095\) |
\(0.221586\) |
$[248,181,14873,50]$ |
$[992,39072,1945600,100853504,409600]$ |
$[58632501248/25,2327987904/25,4674304]$ |
$y^2 = x^6 + 4x^4 + 4x^2 + 1$ |
| 576.a.576.1 |
576.a |
\( 2^{6} \cdot 3^{2} \) |
\( - 2^{6} \cdot 3^{2} \) |
$0$ |
$1$ |
$\Z/10\Z$ |
\(\mathrm{M}_2(\Q)\) |
\(\mathsf{CM}\) |
✓ |
$E_2$ |
|
✓ |
|
$C_4$ |
$D_4$ |
$4$ |
$0$ |
2.180.4, 3.1080.16 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(22.396252\) |
\(0.223963\) |
$[68,124,2616,72]$ |
$[68,110,-36,-3637,576]$ |
$[22717712/9,540430/9,-289]$ |
$y^2 + (x^3 + x^2 + x + 1)y = -x^3 - x$ |
| 576.b.147456.1 |
576.b |
\( 2^{6} \cdot 3^{2} \) |
\( - 2^{14} \cdot 3^{2} \) |
$0$ |
$2$ |
$\Z/4\Z\oplus\Z/4\Z$ |
\(\mathrm{M}_2(\Q)\) |
\(\mathrm{M}_2(\Q)\) |
|
$E_1$ |
|
|
|
$D_4$ |
$D_4$ |
$4$ |
$0$ |
2.180.7, 3.2160.25 |
✓ |
✓ |
$1$ |
\( 2^{3} \) |
\(1.000000\) |
\(9.301119\) |
\(0.290660\) |
$[152,109,5469,18]$ |
$[608,14240,405504,10942208,147456]$ |
$[5071050752/9,195344320/9,1016576]$ |
$y^2 = x^6 + 2x^4 + 2x^2 + 1$ |
| 1152.a.147456.1 |
1152.a |
\( 2^{7} \cdot 3^{2} \) |
\( 2^{14} \cdot 3^{2} \) |
$0$ |
$1$ |
$\Z/8\Z$ |
\(\mathrm{M}_2(\Q)\) |
\(\Q \times \Q\) |
✓ |
$J(E_1)$ |
|
|
|
$C_2^2$ |
$D_4$ |
$4$ |
$2$ |
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 |
✓ |
✓ |
$1$ |
\( 2 \cdot 3 \) |
\(1.000000\) |
\(12.846191\) |
\(0.535258\) |
$[248,181,14873,50]$ |
$[992,39072,1945600,100853504,409600]$ |
$[58632501248/25,2327987904/25,4674304]$ |
$y^2 = x^6 - 4x^4 + 4x^2 - 1$ |
| 2304.b.147456.1 |
2304.b |
\( 2^{8} \cdot 3^{2} \) |
\( - 2^{14} \cdot 3^{2} \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/2\Z$ |
\(\mathrm{M}_2(\Q)\) |
\(\mathrm{M}_2(\Q)\) |
|
$E_1$ |
|
|
|
$D_4$ |
$D_4$ |
$0$ |
$0$ |
2.180.7, 3.2160.25 |
|
✓ |
$1$ |
\( 2 \) |
\(1.000000\) |
\(5.683509\) |
\(0.710439\) |
$[152,109,5469,18]$ |
$[608,14240,405504,10942208,147456]$ |
$[5071050752/9,195344320/9,1016576]$ |
$y^2 = -x^6 - 2x^4 - 2x^2 - 1$ |
| 4096.e.524288.1 |
4096.e |
\( 2^{12} \) |
\( - 2^{19} \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/2\Z$ |
\(\mathrm{M}_2(\Q)\) |
\(\mathsf{CM}\) |
✓ |
$E_4$ |
|
✓ |
|
$C_4$ |
$D_4$ |
$2$ |
$2$ |
2.180.3, 3.540.6 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(1.000000\) |
\(7.402544\) |
\(0.925318\) |
$[26,-2,40,2]$ |
$[208,1888,-2304,-1010944,524288]$ |
$[742586,129623/4,-1521/8]$ |
$y^2 = x^5 - 2x^4 - 2x^2 - x$ |
| 4608.a.4608.1 |
4608.a |
\( 2^{9} \cdot 3^{2} \) |
\( - 2^{9} \cdot 3^{2} \) |
$0$ |
$1$ |
$\Z/4\Z$ |
\(\mathrm{M}_2(\Q)\) |
\(\Q \times \Q\) |
✓ |
$J(E_1)$ |
|
|
|
$C_2^2$ |
$D_4$ |
$2$ |
$0$ |
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 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(10.282314\) |
\(0.642645\) |
$[152,109,5469,18]$ |
$[304,3560,50688,683888,4608]$ |
$[5071050752/9,195344320/9,1016576]$ |
$y^2 + x^3y = -x^4 + 2x^2 - 2$ |
| 4608.c.27648.1 |
4608.c |
\( 2^{9} \cdot 3^{2} \) |
\( - 2^{10} \cdot 3^{3} \) |
$0$ |
$3$ |
$\Z/2\Z\oplus\Z/2\Z\oplus\Z/2\Z$ |
\(\mathrm{M}_2(\Q)\) |
\(\Q\) |
|
$J(E_4)$ |
|
✓ |
|
$C_2$ |
$D_4$ |
$4$ |
$4$ |
2.360.2, 3.540.5 |
✓ |
✓ |
$1$ |
\( 2^{2} \) |
\(1.000000\) |
\(13.756159\) |
\(0.859760\) |
$[24,-72,-180,108]$ |
$[48,288,-1024,-33024,27648]$ |
$[9216,1152,-256/3]$ |
$y^2 = x^5 - x^4 + x^2 - x$ |
| 6400.b.12800.1 |
6400.b |
\( 2^{8} \cdot 5^{2} \) |
\( - 2^{9} \cdot 5^{2} \) |
$0$ |
$1$ |
$\Z/6\Z$ |
\(\mathrm{M}_2(\Q)\) |
\(\Q \times \Q\) |
✓ |
$J(E_1)$ |
|
|
|
$C_2^2$ |
$D_4$ |
$2$ |
$0$ |
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 |
✓ |
✓ |
$1$ |
\( 3 \) |
\(0.413437\) |
\(18.167258\) |
\(0.625918\) |
$[248,181,14873,50]$ |
$[496,9768,243200,6303344,12800]$ |
$[58632501248/25,2327987904/25,4674304]$ |
$y^2 + x^3y = -2x^4 + 4x^2 - 2$ |
| 6400.f.64000.1 |
6400.f |
\( 2^{8} \cdot 5^{2} \) |
\( - 2^{9} \cdot 5^{3} \) |
$2$ |
$4$ |
$\Z/2\Z\oplus\Z/2\Z$ |
\(\mathrm{M}_2(\Q)\) |
\(\mathsf{CM}\) |
✓ |
$E_4$ |
|
✓ |
|
$C_4$ |
$D_4$ |
$16$ |
$0$ |
2.90.6, 3.540.6 |
✓ |
✓ |
$1$ |
\( 2^{2} \) |
\(0.067032\) |
\(19.455210\) |
\(0.326031\) |
$[154,310,19480,250]$ |
$[308,3126,-164,-2455597,64000]$ |
$[5413568314/125,713561079/500,-243089/1000]$ |
$y^2 + x^3y = -2x^4 - 3x^3 + x^2 + 6x + 4$ |
| 6400.g.64000.1 |
6400.g |
\( 2^{8} \cdot 5^{2} \) |
\( - 2^{9} \cdot 5^{3} \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/2\Z$ |
\(\mathrm{M}_2(\Q)\) |
\(\mathsf{CM}\) |
✓ |
$E_4$ |
|
✓ |
|
$C_4$ |
$D_4$ |
$2$ |
$2$ |
2.180.3, 3.540.6 |
✓ |
✓ |
$1$ |
\( 2^{2} \) |
\(1.000000\) |
\(6.303153\) |
\(1.575788\) |
$[154,310,19480,250]$ |
$[308,3126,-164,-2455597,64000]$ |
$[5413568314/125,713561079/500,-243089/1000]$ |
$y^2 + (x^3 + x^2 + x + 1)y = -x^6 - x^3 - x - 1$ |
| 6400.i.409600.1 |
6400.i |
\( 2^{8} \cdot 5^{2} \) |
\( - 2^{14} \cdot 5^{2} \) |
$0$ |
$1$ |
$\Z/2\Z$ |
\(\mathrm{M}_2(\Q)\) |
\(\mathrm{M}_2(\Q)\) |
|
$E_1$ |
|
|
|
$D_4$ |
$D_4$ |
$0$ |
$0$ |
2.180.4, 3.8640.12 |
|
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(5.171827\) |
\(1.292957\) |
$[248,181,14873,50]$ |
$[992,39072,1945600,100853504,409600]$ |
$[58632501248/25,2327987904/25,4674304]$ |
$y^2 = -x^6 - 4x^4 - 4x^2 - 1$ |
| 8192.a.32768.1 |
8192.a |
\( 2^{13} \) |
\( 2^{15} \) |
$0$ |
$3$ |
$\Z/2\Z\oplus\Z/2\Z\oplus\Z/2\Z$ |
\(\mathrm{M}_2(\Q)\) |
\(\Q\) |
|
$J(E_4)$ |
|
✓ |
|
$C_2$ |
$D_4$ |
$4$ |
$4$ |
2.360.2, 3.270.1 |
✓ |
✓ |
$1$ |
\( 2^{2} \) |
\(1.000000\) |
\(16.855414\) |
\(1.053463\) |
$[67,82,1930,4]$ |
$[268,2118,-124,-1129789,32768]$ |
$[1350125107/32,318508017/256,-139159/512]$ |
$y^2 = x^5 - 3x^3 + 2x$ |
| 8192.b.131072.1 |
8192.b |
\( 2^{13} \) |
\( 2^{17} \) |
$0$ |
$3$ |
$\Z/2\Z\oplus\Z/2\Z\oplus\Z/2\Z$ |
\(\mathrm{M}_2(\Q)\) |
\(\Q\) |
|
$J(E_2)$ |
|
✓ |
|
$C_2$ |
$D_4$ |
$4$ |
$4$ |
2.360.2, 3.540.3 |
✓ |
✓ |
$1$ |
\( 2^{2} \) |
\(1.000000\) |
\(15.683046\) |
\(0.980190\) |
$[64,76,1552,16]$ |
$[256,1920,8192,-397312,131072]$ |
$[8388608,245760,4096]$ |
$y^2 = x^5 - 3x^4 + 6x^2 - 4x$ |
| 9216.a.36864.1 |
9216.a |
\( 2^{10} \cdot 3^{2} \) |
\( 2^{12} \cdot 3^{2} \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/2\Z$ |
\(\mathrm{M}_2(\Q)\) |
\(\Q \times \Q\) |
✓ |
$J(E_1)$ |
|
|
|
$C_2^2$ |
$D_4$ |
$2$ |
$2$ |
2.360.1, 3.1080.10 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(1.000000\) |
\(9.381457\) |
\(1.172682\) |
$[46,-44,-72,144]$ |
$[92,470,-684,-70957,36864]$ |
$[6436343/36,2859245/288,-10051/64]$ |
$y^2 = x^5 + x^3 + x$ |
| 12544.d.25088.1 |
12544.d |
\( 2^{8} \cdot 7^{2} \) |
\( - 2^{9} \cdot 7^{2} \) |
$2$ |
$3$ |
$\Z/2\Z$ |
\(\mathrm{M}_2(\Q)\) |
\(\mathsf{CM}\) |
✓ |
$E_4$ |
|
✓ |
|
$C_4$ |
$D_4$ |
$12$ |
$0$ |
2.45.1, 3.540.6 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(0.058077\) |
\(15.061274\) |
\(0.437354\) |
$[74,142,3272,98]$ |
$[148,534,-196,-78541,25088]$ |
$[138687914/49,13524351/196,-1369/8]$ |
$y^2 + (x^3 + x^2 + x + 1)y = x^4 - x^3 + x^2 - x$ |
| 12544.g.175616.1 |
12544.g |
\( 2^{8} \cdot 7^{2} \) |
\( - 2^{9} \cdot 7^{3} \) |
$1$ |
$2$ |
$\Z/2\Z$ |
\(\mathrm{M}_2(\Q)\) |
\(\Q\) |
|
$J(E_4)$ |
|
✓ |
|
$C_2$ |
$D_4$ |
$6$ |
$0$ |
2.90.1, 3.270.1 |
✓ |
✓ |
$1$ |
\( 2 \cdot 3 \) |
\(0.046418\) |
\(11.290429\) |
\(0.786126\) |
$[8,-203,455,686]$ |
$[16,552,-5632,-98704,175616]$ |
$[2048/343,4416/343,-2816/343]$ |
$y^2 + x^3y = x^5 + x^4 - 2x^2 - 4x - 2$ |
| 12800.c.128000.1 |
12800.c |
\( 2^{9} \cdot 5^{2} \) |
\( 2^{10} \cdot 5^{3} \) |
$0$ |
$3$ |
$\Z/2\Z\oplus\Z/2\Z\oplus\Z/2\Z$ |
\(\mathrm{M}_2(\Q)\) |
\(\Q\) |
|
$J(E_4)$ |
|
✓ |
|
$C_2$ |
$D_4$ |
$4$ |
$4$ |
2.360.2, 3.270.1 |
✓ |
✓ |
$1$ |
\( 2^{2} \) |
\(1.000000\) |
\(15.952863\) |
\(0.997054\) |
$[104,280,9140,500]$ |
$[208,1056,-1024,-332032,128000]$ |
$[380204032/125,9280128/125,-43264/125]$ |
$y^2 = x^5 - 3x^4 + 3x^2 - x$ |
| 16384.a.32768.1 |
16384.a |
\( 2^{14} \) |
\( 2^{15} \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/2\Z$ |
\(\mathrm{M}_2(\Q)\) |
\(\Q\) |
|
$J(E_4)$ |
|
✓ |
|
$C_2$ |
$D_4$ |
$2$ |
$2$ |
2.180.3, 3.270.1 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(1.000000\) |
\(8.427707\) |
\(1.053463\) |
$[67,82,1930,4]$ |
$[268,2118,-124,-1129789,32768]$ |
$[1350125107/32,318508017/256,-139159/512]$ |
$y^2 = x^5 + 3x^3 + 2x$ |
| 25600.a.102400.1 |
25600.a |
\( 2^{10} \cdot 5^{2} \) |
\( 2^{12} \cdot 5^{2} \) |
$1$ |
$3$ |
$\Z/2\Z\oplus\Z/2\Z$ |
\(\mathrm{M}_2(\Q)\) |
\(\Q \times \Q\) |
✓ |
$J(E_1)$ |
|
|
|
$C_2^2$ |
$D_4$ |
$4$ |
$2$ |
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.d.128000.1 |
25600.d |
\( 2^{10} \cdot 5^{2} \) |
\( - 2^{10} \cdot 5^{3} \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/2\Z$ |
\(\mathrm{M}_2(\Q)\) |
\(\mathsf{CM}\) |
✓ |
$E_4$ |
|
✓ |
|
$C_4$ |
$D_4$ |
$2$ |
$2$ |
2.180.3, 3.540.6 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(1.000000\) |
\(13.879043\) |
\(1.734880\) |
$[56,-80,-260,500]$ |
$[112,736,-1536,-178432,128000]$ |
$[17210368/125,1009792/125,-18816/125]$ |
$y^2 = x^5 + x^4 + x^2 - x$ |
| 25600.e.128000.1 |
25600.e |
\( 2^{10} \cdot 5^{2} \) |
\( - 2^{10} \cdot 5^{3} \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/2\Z$ |
\(\mathrm{M}_2(\Q)\) |
\(\mathsf{CM}\) |
✓ |
$E_4$ |
|
✓ |
|
$C_4$ |
$D_4$ |
$2$ |
$2$ |
2.180.3, 3.540.6 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(1.000000\) |
\(9.947770\) |
\(1.243471\) |
$[56,-80,-260,500]$ |
$[112,736,-1536,-178432,128000]$ |
$[17210368/125,1009792/125,-18816/125]$ |
$y^2 = x^5 - x^4 - x^2 - x$ |
| 36864.b.36864.1 |
36864.b |
\( 2^{12} \cdot 3^{2} \) |
\( 2^{12} \cdot 3^{2} \) |
$1$ |
$2$ |
$\Z/2\Z$ |
\(\mathrm{M}_2(\Q)\) |
\(\Q \times \Q\) |
✓ |
$J(E_1)$ |
|
|
|
$C_2^2$ |
$D_4$ |
$4$ |
$2$ |
2.180.5, 3.1080.10 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.675802\) |
\(9.381457\) |
\(1.585002\) |
$[46,-44,-72,144]$ |
$[92,470,-684,-70957,36864]$ |
$[6436343/36,2859245/288,-10051/64]$ |
$y^2 = x^5 - x^3 + x$ |
| 69696.c.627264.1 |
69696.c |
\( 2^{6} \cdot 3^{2} \cdot 11^{2} \) |
\( - 2^{6} \cdot 3^{4} \cdot 11^{2} \) |
$0$ |
$1$ |
$\Z/2\Z$ |
\(\mathrm{M}_2(\Q)\) |
\(\mathsf{CM}\) |
✓ |
$E_2$ |
|
✓ |
|
$C_4$ |
$D_4$ |
$0$ |
$0$ |
2.180.4, 3.1080.16 |
|
✓ |
$1$ |
\( 2 \) |
\(1.000000\) |
\(7.488051\) |
\(3.744026\) |
$[1220,3580,1448760,78408]$ |
$[1220,59630,3724380,247001675,627264]$ |
$[42229815050000/9801,1691859628750/9801,8837375]$ |
$y^2 + (x^3 + x^2 + x + 1)y = x^6 + 3x^4 - x^3 + 3x^2 - x + 1$ |
| 73728.c.884736.1 |
73728.c |
\( 2^{13} \cdot 3^{2} \) |
\( 2^{15} \cdot 3^{3} \) |
$1$ |
$3$ |
$\Z/2\Z\oplus\Z/2\Z$ |
\(\mathrm{M}_2(\Q)\) |
\(\Q\) |
|
$J(E_4)$ |
|
✓ |
|
$C_2$ |
$D_4$ |
$2$ |
$2$ |
2.180.3, 3.270.1 |
✓ |
✓ |
$1$ |
\( 2^{3} \) |
\(0.793842\) |
\(5.583154\) |
\(2.216071\) |
$[195,630,44910,108]$ |
$[780,18630,-380,-86843325,884736]$ |
$[10442615625/32,2558131875/256,-401375/1536]$ |
$y^2 = x^5 + 5x^3 + 6x$ |
| 73728.d.884736.1 |
73728.d |
\( 2^{13} \cdot 3^{2} \) |
\( 2^{15} \cdot 3^{3} \) |
$0$ |
$3$ |
$\Z/2\Z\oplus\Z/2\Z\oplus\Z/2\Z$ |
\(\mathrm{M}_2(\Q)\) |
\(\Q\) |
|
$J(E_4)$ |
|
✓ |
|
$C_2$ |
$D_4$ |
$4$ |
$4$ |
2.360.2, 3.270.1 |
✓ |
✓ |
$1$ |
\( 2^{3} \) |
\(1.000000\) |
\(11.166308\) |
\(1.395789\) |
$[195,630,44910,108]$ |
$[780,18630,-380,-86843325,884736]$ |
$[10442615625/32,2558131875/256,-401375/1536]$ |
$y^2 = 2x^5 - 5x^3 + 3x$ |
| 78400.a.78400.1 |
78400.a |
\( 2^{6} \cdot 5^{2} \cdot 7^{2} \) |
\( - 2^{6} \cdot 5^{2} \cdot 7^{2} \) |
$0$ |
$2$ |
$\Z/2\Z$ |
\(\mathrm{M}_2(\Q)\) |
\(\mathsf{CM}\) |
✓ |
$E_2$ |
|
✓ |
|
$C_4$ |
$D_4$ |
$0$ |
$0$ |
2.90.5, 3.1080.16 |
|
|
$2$ |
\( 1 \) |
\(1.000000\) |
\(6.009550\) |
\(3.004775\) |
$[452,1276,189752,9800]$ |
$[452,7662,151900,2488139,78400]$ |
$[294789628688/1225,11055476814/1225,395839]$ |
$y^2 + (x^3 + x^2 + x + 1)y = -x^6 - 3x^4 - x^3 - 3x^2 - x - 1$ |
| 102400.b.102400.1 |
102400.b |
\( 2^{12} \cdot 5^{2} \) |
\( - 2^{12} \cdot 5^{2} \) |
$1$ |
$2$ |
$\Z/2\Z$ |
\(\mathrm{M}_2(\Q)\) |
\(\Q\) |
|
$J(E_2)$ |
|
✓ |
|
$C_2$ |
$D_4$ |
$4$ |
$2$ |
2.90.3, 3.540.2 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.797280\) |
\(12.084061\) |
\(2.408596\) |
$[34,-116,-424,400]$ |
$[68,502,-2100,-98701,102400]$ |
$[1419857/100,1233163/800,-6069/64]$ |
$y^2 = x^5 - x^3 - x$ |
| 102400.e.102400.1 |
102400.e |
\( 2^{12} \cdot 5^{2} \) |
\( 2^{12} \cdot 5^{2} \) |
$0$ |
$1$ |
$\Z/2\Z$ |
\(\mathrm{M}_2(\Q)\) |
\(\Q \times \Q\) |
✓ |
$J(E_1)$ |
|
|
|
$C_2^2$ |
$D_4$ |
$2$ |
$2$ |
2.180.5, 3.1080.10 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(8.209049\) |
\(2.052262\) |
$[94,244,7096,400]$ |
$[188,822,-1100,-220621,102400]$ |
$[229345007/100,42671253/800,-24299/64]$ |
$y^2 = x^5 + 3x^3 + x$ |
| 135424.l.270848.1 |
135424.l |
\( 2^{8} \cdot 23^{2} \) |
\( - 2^{9} \cdot 23^{2} \) |
$0$ |
$2$ |
$\Z/2\Z$ |
\(\mathrm{M}_2(\Q)\) |
\(\mathsf{CM}\) |
✓ |
$E_4$ |
|
✓ |
|
$C_4$ |
$D_4$ |
$0$ |
$0$ |
2.45.1, 3.540.6 |
|
|
$2$ |
\( 2 \) |
\(1.000000\) |
\(5.075262\) |
\(5.075262\) |
$[170,430,23560,1058]$ |
$[340,3670,31740,-669325,270848]$ |
$[8874106250/529,1126919375/2116,108375/8]$ |
$y^2 + (x^3 + x^2 + x + 1)y = -x^6 - 2x^4 - x^3 - 2x^2 - x - 1$ |
| 147456.c.884736.1 |
147456.c |
\( 2^{14} \cdot 3^{2} \) |
\( 2^{15} \cdot 3^{3} \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/2\Z$ |
\(\mathrm{M}_2(\Q)\) |
\(\Q\) |
|
$J(E_4)$ |
|
✓ |
|
$C_2$ |
$D_4$ |
$2$ |
$2$ |
2.180.3, 3.270.1 |
✓ |
✓ |
$1$ |
\( 2^{2} \) |
\(1.000000\) |
\(5.583154\) |
\(1.395789\) |
$[195,630,44910,108]$ |
$[780,18630,-380,-86843325,884736]$ |
$[10442615625/32,2558131875/256,-401375/1536]$ |
$y^2 = 2x^5 + 5x^3 + 3x$ |
| 147456.e.884736.1 |
147456.e |
\( 2^{14} \cdot 3^{2} \) |
\( 2^{15} \cdot 3^{3} \) |
$1$ |
$3$ |
$\Z/2\Z\oplus\Z/2\Z$ |
\(\mathrm{M}_2(\Q)\) |
\(\Q\) |
|
$J(E_4)$ |
|
✓ |
|
$C_2$ |
$D_4$ |
$4$ |
$2$ |
2.180.3, 3.270.1 |
✓ |
✓ |
$1$ |
\( 2^{2} \) |
\(0.970167\) |
\(11.166308\) |
\(2.708295\) |
$[195,630,44910,108]$ |
$[780,18630,-380,-86843325,884736]$ |
$[10442615625/32,2558131875/256,-401375/1536]$ |
$y^2 = x^5 - 5x^3 + 6x$ |
| 193600.d.968000.1 |
193600.d |
\( 2^{6} \cdot 5^{2} \cdot 11^{2} \) |
\( - 2^{6} \cdot 5^{3} \cdot 11^{2} \) |
$0$ |
$2$ |
$\Z/2\Z$ |
\(\mathrm{M}_2(\Q)\) |
\(\mathsf{CM}\) |
✓ |
$E_4$ |
|
✓ |
|
$C_4$ |
$D_4$ |
$0$ |
$0$ |
2.45.1, 3.540.6 |
|
|
$2$ |
\( 2 \) |
\(1.000000\) |
\(3.888937\) |
\(3.888937\) |
$[292,2380,214520,121000]$ |
$[292,1966,-4356,-1284277,968000]$ |
$[33169145488/15125,764807422/15125,-47961/125]$ |
$y^2 + (x^3 + x^2 + x + 1)y = -x^6 - x^4 - x^3 - x^2 - x - 1$ |
| 193600.e.968000.1 |
193600.e |
\( 2^{6} \cdot 5^{2} \cdot 11^{2} \) |
\( - 2^{6} \cdot 5^{3} \cdot 11^{2} \) |
$2$ |
$3$ |
$\Z/2\Z$ |
\(\mathrm{M}_2(\Q)\) |
\(\mathsf{CM}\) |
✓ |
$E_4$ |
|
✓ |
|
$C_4$ |
$D_4$ |
$8$ |
$0$ |
2.45.1, 3.540.6 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(0.208207\) |
\(11.078708\) |
\(1.153332\) |
$[292,2380,214520,121000]$ |
$[292,1966,-4356,-1284277,968000]$ |
$[33169145488/15125,764807422/15125,-47961/125]$ |
$y^2 + (x^3 + x^2 + x + 1)y = 2x^4 - x^3 + 2x^2 - x$ |
| 262144.a.262144.1 |
262144.a |
\( 2^{18} \) |
\( - 2^{18} \) |
$1$ |
$2$ |
$\Z/2\Z$ |
\(\mathrm{M}_2(\Q)\) |
\(\Q\) |
|
$J(E_2)$ |
|
✓ |
|
$C_2$ |
$D_4$ |
$2$ |
$2$ |
2.90.3, 3.3240.5 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.123513\) |
\(10.883805\) |
\(3.057023\) |
$[4,-14,2,1]$ |
$[32,640,-6144,-151552,262144]$ |
$[128,80,-24]$ |
$y^2 = x^5 - 2x^3 - x$ |
| 262144.b.524288.1 |
262144.b |
\( 2^{18} \) |
\( 2^{19} \) |
$1$ |
$2$ |
$\Z/2\Z$ |
\(\mathrm{M}_2(\Q)\) |
\(\Q\) |
|
$J(E_4)$ |
|
✓ |
|
$C_2$ |
$D_4$ |
$2$ |
$2$ |
2.90.3, 3.270.1 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(0.970077\) |
\(7.048011\) |
\(3.418555\) |
$[26,-2,40,2]$ |
$[208,1888,-2304,-1010944,524288]$ |
$[742586,129623/4,-1521/8]$ |
$y^2 = x^5 + 2x^3 + 2x$ |
| 262144.c.524288.1 |
262144.c |
\( 2^{18} \) |
\( 2^{19} \) |
$1$ |
$2$ |
$\Z/2\Z$ |
\(\mathrm{M}_2(\Q)\) |
\(\Q\) |
|
$J(E_4)$ |
|
✓ |
|
$C_2$ |
$D_4$ |
$4$ |
$2$ |
2.90.3, 3.270.1 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(0.759196\) |
\(7.048011\) |
\(2.675411\) |
$[26,-2,40,2]$ |
$[208,1888,-2304,-1010944,524288]$ |
$[742586,129623/4,-1521/8]$ |
$y^2 = x^5 - 2x^3 + 2x$ |
| 278784.a.557568.1 |
278784.a |
\( 2^{8} \cdot 3^{2} \cdot 11^{2} \) |
\( 2^{9} \cdot 3^{2} \cdot 11^{2} \) |
$0$ |
$2$ |
$\Z/2\Z$ |
\(\mathrm{M}_2(\Q)\) |
\(\Q \times \Q\) |
✓ |
$J(E_1)$ |
|
|
|
$C_2^2$ |
$D_4$ |
$0$ |
$0$ |
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 |
|
✓ |
$1$ |
\( 1 \) |
\(2.415493\) |
\(4.989405\) |
\(3.012968\) |
$[1592,1189,630369,2178]$ |
$[3184,419240,73041408,14200416368,557568]$ |
$[639139022845952/1089,26430898598080/1089,1328059136]$ |
$y^2 + y = -6x^6 - 8x^4 - 4x^2 - 1$ |
| 331776.e.995328.1 |
331776.e |
\( 2^{12} \cdot 3^{4} \) |
\( 2^{12} \cdot 3^{5} \) |
$0$ |
$1$ |
$\Z/2\Z$ |
\(\mathrm{M}_2(\Q)\) |
\(\Q\) |
|
$J(E_4)$ |
|
✓ |
|
$C_2$ |
$D_4$ |
$2$ |
$2$ |
2.90.3, 3.540.7 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(1.000000\) |
\(6.346552\) |
\(3.173276\) |
$[58,28,856,16]$ |
$[348,4374,-1836,-4942701,995328]$ |
$[20511149/4,5926527/32,-14297/64]$ |
$y^2 = x^5 + 3x^3 + 3x$ |
| 331776.g.995328.1 |
331776.g |
\( 2^{12} \cdot 3^{4} \) |
\( 2^{12} \cdot 3^{5} \) |
$1$ |
$2$ |
$\Z/2\Z$ |
\(\mathrm{M}_2(\Q)\) |
\(\Q\) |
|
$J(E_4)$ |
|
✓ |
|
$C_2$ |
$D_4$ |
$4$ |
$2$ |
2.90.3, 3.540.7 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(0.770890\) |
\(6.346552\) |
\(2.446248\) |
$[58,28,856,16]$ |
$[348,4374,-1836,-4942701,995328]$ |
$[20511149/4,5926527/32,-14297/64]$ |
$y^2 = x^5 - 3x^3 + 3x$ |
| 589824.a.589824.1 |
589824.a |
\( 2^{16} \cdot 3^{2} \) |
\( 2^{16} \cdot 3^{2} \) |
$0$ |
$1$ |
$\Z/2\Z$ |
\(\mathrm{M}_2(\Q)\) |
\(\Q \times \Q\) |
✓ |
$J(E_1)$ |
|
|
|
$C_2^2$ |
$D_4$ |
$2$ |
$2$ |
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 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(2.544094\) |
\(6.879720\) |
\(4.375664\) |
$[68,124,2616,72]$ |
$[272,1760,-2304,-931072,589824]$ |
$[22717712/9,540430/9,-289]$ |
$y^2 = x^5 + 4x^3 + x$ |
| 692224.a.692224.1 |
692224.a |
\( 2^{12} \cdot 13^{2} \) |
\( - 2^{12} \cdot 13^{2} \) |
$0$ |
$1$ |
$\Z/2\Z$ |
\(\mathrm{M}_2(\Q)\) |
\(\Q\) |
|
$J(E_2)$ |
|
✓ |
|
$C_2$ |
$D_4$ |
$2$ |
$2$ |
2.90.3, 3.540.2 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(9.748988\) |
\(2.437247\) |
$[14,-404,-3928,-2704]$ |
$[28,1110,19604,-170797,-692224]$ |
$[-16807/676,-190365/5408,-1421/64]$ |
$y^2 = x^5 - 3x^3 - x$ |
| 778752.b.778752.1 |
778752.b |
\( 2^{9} \cdot 3^{2} \cdot 13^{2} \) |
\( 2^{9} \cdot 3^{2} \cdot 13^{2} \) |
$2$ |
$3$ |
$\Z/2\Z$ |
\(\mathrm{M}_2(\Q)\) |
\(\Q \times \Q\) |
✓ |
$J(E_1)$ |
|
|
|
$C_2^2$ |
$D_4$ |
$4$ |
$0$ |
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 |
|
|
$2$ |
\( 1 \) |
\(2.038974\) |
\(4.813693\) |
\(4.907496\) |
$[1880,1405,879765,3042]$ |
$[3760,585320,120706560,27814290800,778752]$ |
$[1467808044800000/1521,60769678360000/1521,2191328000]$ |
$y^2 + y = -6x^6 - 10x^4 - 5x^2 - 1$ |
