| 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 |
| 169.a.169.1 |
169.a |
\( 13^{2} \) |
\( - 13^{2} \) |
$0$ |
$0$ |
$\Z/19\Z$ |
\(\mathrm{M}_2(\Q)\) |
\(\mathsf{CM}\) |
✓ |
$E_6$ |
|
✓ |
|
$C_6$ |
$D_6$ |
$6$ |
$0$ |
2.40.3, 3.480.12 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(32.667031\) |
\(0.090490\) |
$[4,793,3757,-21632]$ |
$[1,-33,-43,-283,-169]$ |
$[-1/169,33/169,43/169]$ |
$y^2 + (x^3 + x + 1)y = x^5 + x^4$ |
| 196.a.21952.1 |
196.a |
\( 2^{2} \cdot 7^{2} \) |
\( - 2^{6} \cdot 7^{3} \) |
$0$ |
$2$ |
$\Z/6\Z\oplus\Z/6\Z$ |
\(\mathrm{M}_2(\Q)\) |
\(\mathrm{M}_2(\Q)\) |
|
$E_1$ |
|
|
|
$D_6$ |
$D_6$ |
$6$ |
$0$ |
2.360.3, 3.17280.1 |
✓ |
✓ |
$1$ |
\( 2^{2} \cdot 3 \) |
\(1.000000\) |
\(11.777148\) |
\(0.109048\) |
$[1340,1345,149855,2809856]$ |
$[335,4620,90160,2214800,21952]$ |
$[4219140959375/21952,6203236875/784,12905875/28]$ |
$y^2 + (x^2 + x)y = x^6 + 3x^5 + 6x^4 + 7x^3 + 6x^2 + 3x + 1$ |
| 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 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(1.000000\) |
\(26.841829\) |
\(0.134209\) |
$[26,-2,40,2]$ |
$[52,118,-36,-3949,512]$ |
$[742586,129623/4,-1521/8]$ |
$y^2 + y = 2x^5 - 3x^4 + x^3 + x^2 - x$ |
| 324.a.648.1 |
324.a |
\( 2^{2} \cdot 3^{4} \) |
\( - 2^{3} \cdot 3^{4} \) |
$0$ |
$0$ |
$\Z/21\Z$ |
\(\mathrm{M}_2(\Q)\) |
\(\mathsf{CM}\) |
✓ |
$E_3$ |
|
✓ |
|
$C_6$ |
$D_6$ |
$6$ |
$0$ |
2.40.3, 3.1920.3 |
✓ |
✓ |
$1$ |
\( 3 \) |
\(1.000000\) |
\(25.521769\) |
\(0.173617\) |
$[60,945,2295,82944]$ |
$[15,-30,140,300,648]$ |
$[9375/8,-625/4,875/18]$ |
$y^2 + (x^3 + x + 1)y = x^5 + 2x^4 + 2x^3 + x^2$ |
| 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 |
✓ |
✓ |
$1$ |
\( 2^{3} \) |
\(1.000000\) |
\(9.301119\) |
\(0.290660\) |
$[152,109,5469,18]$ |
$[608,14240,405504,10942208,147456]$ |
$[5071050752/9,195344320/9,1016576]$ |
$y^2 = x^6 + 2x^4 + 2x^2 + 1$ |
| 676.b.17576.1 |
676.b |
\( 2^{2} \cdot 13^{2} \) |
\( - 2^{3} \cdot 13^{3} \) |
$0$ |
$0$ |
$\Z/3\Z\oplus\Z/3\Z$ |
\(\mathrm{M}_2(\Q)\) |
\(\mathrm{M}_2(\Q)\) |
|
$E_1$ |
|
|
|
$D_6$ |
$D_6$ |
$0$ |
$0$ |
2.120.4, 3.17280.1 |
|
✓ |
$1$ |
\( 3 \) |
\(1.000000\) |
\(7.177121\) |
\(0.265819\) |
$[1244,1249,129167,2249728]$ |
$[311,3978,72332,1667692,17576]$ |
$[2909390022551/17576,4602275343/676,10349147/26]$ |
$y^2 + (x^2 + x)y = -x^6 + 3x^5 - 6x^4 + 6x^3 - 6x^2 + 3x - 1$ |
| 784.c.614656.1 |
784.c |
\( 2^{4} \cdot 7^{2} \) |
\( 2^{8} \cdot 7^{4} \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/2\Z$ |
\(\mathrm{M}_2(\Q)\) |
\(\mathsf{CM}\) |
✓ |
$E_3$ |
|
✓ |
|
$C_6$ |
$D_6$ |
$3$ |
$3$ |
2.240.1, 3.5760.7 |
✓ |
✓ |
$1$ |
\( 3^{2} \) |
\(1.000000\) |
\(5.731485\) |
\(0.358218\) |
$[398,9016,912086,2401]$ |
$[796,2358,-2348,-1857293,614656]$ |
$[1248318403996/2401,9291226221/4802,-23245787/9604]$ |
$y^2 = x^5 - 4x^4 - 13x^3 - 9x^2 - x$ |
| 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 |
✓ |
✓ |
$1$ |
\( 2^{2} \) |
\(1.000000\) |
\(7.270694\) |
\(0.454418\) |
$[152,109,5469,18]$ |
$[608,14240,405504,10942208,147456]$ |
$[5071050752/9,195344320/9,1016576]$ |
$y^2 = x^6 - 2x^4 + 2x^2 - 1$ |
| 1296.a.20736.1 |
1296.a |
\( 2^{4} \cdot 3^{4} \) |
\( 2^{8} \cdot 3^{4} \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/6\Z$ |
\(\mathrm{M}_2(\Q)\) |
\(\mathsf{CM}\) |
✓ |
$E_3$ |
|
✓ |
|
$C_6$ |
$D_6$ |
$3$ |
$3$ |
2.240.1, 3.1920.3 |
✓ |
✓ |
$1$ |
\( 3 \) |
\(1.000000\) |
\(23.235042\) |
\(0.484063\) |
$[78,216,4806,81]$ |
$[156,438,-428,-64653,20736]$ |
$[4455516,160381/2,-18083/36]$ |
$y^2 = x^5 - x^4 - 3x^3 + 4x^2 - x$ |
| 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 |
✓ |
✓ |
$1$ |
\( 2 \cdot 3 \) |
\(1.000000\) |
\(12.846191\) |
\(0.535258\) |
$[248,181,14873,50]$ |
$[992,39072,1945600,100853504,409600]$ |
$[58632501248/25,2327987904/25,4674304]$ |
$y^2 = x^6 - 4x^4 + 4x^2 - 1$ |
| 2187.a.6561.1 |
2187.a |
\( 3^{7} \) |
\( 3^{8} \) |
$0$ |
$1$ |
$\Z/6\Z$ |
\(\mathrm{M}_2(\Q)\) |
\(\Q\) |
|
$J(E_3)$ |
|
✓ |
|
$C_2$ |
$D_6$ |
$3$ |
$1$ |
2.120.1, 3.5760.5 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(1.000000\) |
\(10.925677\) |
\(0.606982\) |
$[124,297,13275,3456]$ |
$[93,249,-239,-21057,6561]$ |
$[28629151/27,2472653/81,-229679/729]$ |
$y^2 + (x^3 + 1)y = -1$ |
| 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 |
|
✓ |
$1$ |
\( 2 \) |
\(1.000000\) |
\(5.683509\) |
\(0.710439\) |
$[152,109,5469,18]$ |
$[608,14240,405504,10942208,147456]$ |
$[5071050752/9,195344320/9,1016576]$ |
$y^2 = -x^6 - 2x^4 - 2x^2 - 1$ |
| 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 |
|
✓ |
$1$ |
\( 5 \) |
\(1.000000\) |
\(3.411821\) |
\(0.682364\) |
$[860,36865,8199455,16384]$ |
$[1075,9750,107500,5125000,400000]$ |
$[459401384375/128,1937983125/64,9938375/32]$ |
$y^2 + (x^3 + 1)y = -2x^6 - 2x^5 + 2x^3 - 2x - 2$ |
| 2704.a.43264.1 |
2704.a |
\( 2^{4} \cdot 13^{2} \) |
\( 2^{8} \cdot 13^{2} \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/2\Z$ |
\(\mathrm{M}_2(\Q)\) |
\(\mathsf{CM}\) |
✓ |
$E_6$ |
|
✓ |
|
$C_6$ |
$D_6$ |
$3$ |
$3$ |
2.240.1, 3.1440.1 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(11.781851\) |
\(0.736366\) |
$[110,520,15470,169]$ |
$[220,630,-620,-133325,43264]$ |
$[2013137500/169,52408125/338,-468875/676]$ |
$y^2 = x^5 - 5x^3 - 5x^2 - x$ |
| 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 |
✓ |
✓ |
$1$ |
\( 3^{3} \) |
\(1.000000\) |
\(19.520681\) |
\(0.722988\) |
$[324,12609,1778337,73728]$ |
$[243,-2268,-314496,-20391588,139968]$ |
$[387420489/64,-3720087/16,-132678]$ |
$y^2 + (x^2 + x + 1)y = x^6 - 3x^5 + 5x^4 - 6x^3 + x$ |
| 3721.a.3721.1 |
3721.a |
\( 61^{2} \) |
\( - 61^{2} \) |
$2$ |
$2$ |
$\mathsf{trivial}$ |
\(\mathrm{M}_2(\Q)\) |
\(\mathsf{CM}\) |
✓ |
$E_6$ |
|
✓ |
|
$C_6$ |
$D_6$ |
$12$ |
$0$ |
2.40.3, 3.480.12 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.007315\) |
\(28.081352\) |
\(0.205420\) |
$[196,6649,304573,-476288]$ |
$[49,-177,-187,-10123,-3721]$ |
$[-282475249/3721,20823873/3721,448987/3721]$ |
$y^2 + (x^3 + x + 1)y = -x^4 + x^3 + 3x^2 + x$ |
| 3969.b.35721.1 |
3969.b |
\( 3^{4} \cdot 7^{2} \) |
\( 3^{6} \cdot 7^{2} \) |
$2$ |
$2$ |
$\mathsf{trivial}$ |
\(\mathrm{M}_2(\Q)\) |
\(\mathsf{CM}\) |
✓ |
$E_6$ |
|
✓ |
|
$C_6$ |
$D_6$ |
$18$ |
$0$ |
2.80.1, 3.480.12 |
✓ |
✓ |
$1$ |
\( 3 \) |
\(0.003155\) |
\(23.234167\) |
\(0.219945\) |
$[268,2961,216951,18816]$ |
$[201,573,-563,-110373,35721]$ |
$[1350125107/147,57445733/441,-2527307/3969]$ |
$y^2 + (x^3 + x + 1)y = -2x^5 + 3x^4 - 3x^2$ |
| 3969.c.35721.1 |
3969.c |
\( 3^{4} \cdot 7^{2} \) |
\( 3^{6} \cdot 7^{2} \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/2\Z$ |
\(\mathrm{M}_2(\Q)\) |
\(\mathsf{CM}\) |
✓ |
$E_6$ |
|
✓ |
|
$C_6$ |
$D_6$ |
$3$ |
$3$ |
2.240.1, 3.480.12 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(12.485061\) |
\(0.780316\) |
$[268,2961,216951,18816]$ |
$[201,573,-563,-110373,35721]$ |
$[1350125107/147,57445733/441,-2527307/3969]$ |
$y^2 + (x^2 + x)y = x^5 - 5x^4 + 4x^3 - x$ |
| 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 |
✓ |
✓ |
$1$ |
\( 2^{3} \) |
\(1.000000\) |
\(13.559050\) |
\(0.753281\) |
$[452,-15543,-660459,131712]$ |
$[339,10617,-211009,-46063185,250047]$ |
$[18424351793/1029,5106412483/3087,-2694373921/27783]$ |
$y^2 + (x^2 + x + 1)y = -3x^5 + 5x^4 - 4x^3 + x$ |
| 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 |
✓ |
✓ |
$1$ |
\( 2^{2} \) |
\(1.000000\) |
\(13.756159\) |
\(0.859760\) |
$[24,-72,-180,108]$ |
$[48,288,-1024,-33024,27648]$ |
$[9216,1152,-256/3]$ |
$y^2 = x^5 - x^4 + x^2 - x$ |
| 4608.c.884736.1 |
4608.c |
\( 2^{9} \cdot 3^{2} \) |
\( 2^{15} \cdot 3^{3} \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/2\Z$ |
\(\mathrm{M}_2(\Q)\) |
\(\Q\) |
|
$J(E_4)$ |
|
✓ |
|
$C_2$ |
$C_2$ |
$2$ |
$2$ |
2.180.3, 3.540.5 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(1.000000\) |
\(6.878080\) |
\(0.859760\) |
$[1140,1197,445455,108]$ |
$[4560,853632,210319360,57592172544,884736]$ |
$[2228489100000,91485342000,14829158000/3]$ |
$y^2 = 2x^5 + 7x^4 - 2x^3 - 13x^2 + 10x - 2$ |
| 4608.c.884736.2 |
4608.c |
\( 2^{9} \cdot 3^{2} \) |
\( 2^{15} \cdot 3^{3} \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/4\Z$ |
\(\mathrm{M}_2(\Q)\) |
\(\Q\) |
|
$J(E_4)$ |
|
✓ |
|
$C_2$ |
$C_2$ |
$2$ |
$2$ |
2.180.3, 3.540.5 |
✓ |
✓ |
$1$ |
\( 2^{2} \) |
\(1.000000\) |
\(13.756159\) |
\(0.859760\) |
$[1140,1197,445455,108]$ |
$[4560,853632,210319360,57592172544,884736]$ |
$[2228489100000,91485342000,14829158000/3]$ |
$y^2 = 2x^5 - 7x^4 - 2x^3 + 13x^2 + 10x + 2$ |
| 6075.a.18225.1 |
6075.a |
\( 3^{5} \cdot 5^{2} \) |
\( 3^{6} \cdot 5^{2} \) |
$0$ |
$1$ |
$\Z/6\Z$ |
\(\mathrm{M}_2(\Q)\) |
\(\Q\) |
|
$J(E_6)$ |
|
✓ |
|
$C_2$ |
$D_6$ |
$3$ |
$1$ |
2.120.1, 3.2880.4 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(1.000000\) |
\(15.574664\) |
\(0.865259\) |
$[164,2745,106365,-9600]$ |
$[123,-399,-409,-52377,-18225]$ |
$[-115856201/75,9166493/225,687529/2025]$ |
$y^2 + (x^3 + 1)y = x^3 + 1$ |
| 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.a.131072.1 |
8192.a |
\( 2^{13} \) |
\( 2^{17} \) |
$0$ |
$1$ |
$\Z/8\Z$ |
\(\mathrm{M}_2(\Q)\) |
\(\Q\) |
|
$J(E_4)$ |
|
✓ |
|
$C_2$ |
$C_2$ |
$4$ |
$2$ |
2.180.2, 3.270.1 |
✓ |
✓ |
$1$ |
\( 2^{2} \) |
\(1.000000\) |
\(16.855414\) |
\(1.053463\) |
$[472,7942,1038800,16]$ |
$[1888,63808,910336,-588186624,131072]$ |
$[183020620544,3276205808,24756872]$ |
$y^2 + y = 4x^5 + 15x^4 + 8x^3 - 3x^2 - x$ |
| 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 |
✓ |
✓ |
$1$ |
\( 2^{2} \) |
\(1.000000\) |
\(15.683046\) |
\(0.980190\) |
$[64,76,1552,16]$ |
$[256,1920,8192,-397312,131072]$ |
$[8388608,245760,4096]$ |
$y^2 = x^5 - 3x^4 + 6x^2 - 4x$ |
| 8281.b.405769.1 |
8281.b |
\( 7^{2} \cdot 13^{2} \) |
\( 7^{4} \cdot 13^{2} \) |
$2$ |
$2$ |
$\mathsf{trivial}$ |
\(\mathrm{M}_2(\Q)\) |
\(\mathsf{CM}\) |
✓ |
$E_6$ |
|
✓ |
|
$C_6$ |
$D_6$ |
$12$ |
$0$ |
2.80.1, 3.480.12 |
✓ |
✓ |
$1$ |
\( 3 \) |
\(0.005669\) |
\(19.785401\) |
\(0.336475\) |
$[2596,375193,248614093,51938432]$ |
$[649,1917,-1907,-1228133,405769]$ |
$[115139273278249/405769,524030063733/405769,-803230307/405769]$ |
$y^2 + (x^3 + x + 1)y = -3x^5 + 9x^4 - 7x^3 - 2x^2 + x$ |
| 8281.c.405769.1 |
8281.c |
\( 7^{2} \cdot 13^{2} \) |
\( 7^{4} \cdot 13^{2} \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/2\Z$ |
\(\mathrm{M}_2(\Q)\) |
\(\mathsf{CM}\) |
✓ |
$E_6$ |
|
✓ |
|
$C_6$ |
$D_6$ |
$3$ |
$3$ |
2.240.1, 3.480.12 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(19.785401\) |
\(1.236588\) |
$[2596,375193,248614093,51938432]$ |
$[649,1917,-1907,-1228133,405769]$ |
$[115139273278249/405769,524030063733/405769,-803230307/405769]$ |
$y^2 + (x^2 + x)y = x^5 + 8x^4 + 11x^3 + 3x^2 - x$ |
| 8649.b.700569.1 |
8649.b |
\( 3^{2} \cdot 31^{2} \) |
\( 3^{6} \cdot 31^{2} \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/2\Z$ |
\(\mathrm{M}_2(\Q)\) |
\(\mathsf{CM}\) |
✓ |
$E_6$ |
|
✓ |
|
$C_6$ |
$D_6$ |
$3$ |
$3$ |
2.240.1, 3.480.12 |
✓ |
✓ |
$1$ |
\( 2^{2} \) |
\(1.000000\) |
\(5.541100\) |
\(1.385275\) |
$[1132,73377,21088959,369024]$ |
$[849,2517,-2507,-2115933,700569]$ |
$[1815232161643/2883,19016091893/8649,-200783123/77841]$ |
$y^2 + (x^2 + x)y = 9x^5 + 2x^4 - 21x^3 - 22x^2 - 8x - 1$ |
| 8649.c.700569.1 |
8649.c |
\( 3^{2} \cdot 31^{2} \) |
\( 3^{6} \cdot 31^{2} \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/2\Z$ |
\(\mathrm{M}_2(\Q)\) |
\(\mathsf{CM}\) |
✓ |
$E_6$ |
|
✓ |
|
$C_6$ |
$D_6$ |
$3$ |
$3$ |
2.240.1, 3.480.12 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(18.772889\) |
\(1.173306\) |
$[1132,73377,21088959,369024]$ |
$[849,2517,-2507,-2115933,700569]$ |
$[1815232161643/2883,19016091893/8649,-200783123/77841]$ |
$y^2 + (x^2 + x)y = x^5 + 9x^4 + 13x^3 + 4x^2 - x$ |
| 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 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(1.000000\) |
\(9.381457\) |
\(1.172682\) |
$[46,-44,-72,144]$ |
$[92,470,-684,-70957,36864]$ |
$[6436343/36,2859245/288,-10051/64]$ |
$y^2 = x^5 + x^3 + x$ |
| 11881.a.11881.1 |
11881.a |
\( 109^{2} \) |
\( 109^{2} \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/2\Z$ |
\(\mathrm{M}_2(\Q)\) |
\(\mathsf{CM}\) |
✓ |
$E_6$ |
|
✓ |
|
$C_6$ |
$D_6$ |
$3$ |
$3$ |
2.240.1, 3.480.12 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(19.585813\) |
\(1.224113\) |
$[484,6649,988957,1520768]$ |
$[121,333,-323,-37493,11881]$ |
$[25937424601/11881,589929813/11881,-4729043/11881]$ |
$y^2 + (x^2 + x)y = x^5 - 3x^4 + 2x^2 - x$ |
| 12321.a.36963.1 |
12321.a |
\( 3^{2} \cdot 37^{2} \) |
\( - 3^{3} \cdot 37^{2} \) |
$2$ |
$2$ |
$\mathsf{trivial}$ |
\(\mathrm{M}_2(\Q)\) |
\(\mathsf{CM}\) |
✓ |
$E_6$ |
|
✓ |
|
$C_6$ |
$D_6$ |
$12$ |
$0$ |
2.40.3, 3.480.12 |
✓ |
✓ |
$1$ |
\( 3 \) |
\(0.007338\) |
\(18.952746\) |
\(0.417205\) |
$[4,6697,85285,-4731264]$ |
$[1,-279,-1107,-19737,-36963]$ |
$[-1/36963,31/4107,41/1369]$ |
$y^2 + (x^3 + x + 1)y = x^5 + 3x^4 + 4x^3 + 2x^2$ |
| 12544.a.12544.1 |
12544.a |
\( 2^{8} \cdot 7^{2} \) |
\( 2^{8} \cdot 7^{2} \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/2\Z$ |
\(\mathrm{M}_2(\Q)\) |
\(\mathsf{CM}\) |
✓ |
$E_6$ |
|
✓ |
|
$C_6$ |
$D_6$ |
$3$ |
$3$ |
2.240.1, 3.480.12 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(18.675725\) |
\(1.167233\) |
$[62,112,2114,49]$ |
$[124,342,-332,-39533,12544]$ |
$[114516604/49,5094261/98,-79763/196]$ |
$y^2 = x^5 + 2x^4 - x^3 - 3x^2 - x$ |
| 12544.c.12544.1 |
12544.c |
\( 2^{8} \cdot 7^{2} \) |
\( 2^{8} \cdot 7^{2} \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/2\Z$ |
\(\mathrm{M}_2(\Q)\) |
\(\mathsf{CM}\) |
✓ |
$E_6$ |
|
✓ |
|
$C_6$ |
$D_6$ |
$3$ |
$3$ |
2.240.1, 3.480.12 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(21.839889\) |
\(1.364993\) |
$[62,112,2114,49]$ |
$[124,342,-332,-39533,12544]$ |
$[114516604/49,5094261/98,-79763/196]$ |
$y^2 = x^5 - 2x^4 - x^3 + 3x^2 - x$ |
| 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 |
✓ |
✓ |
$1$ |
\( 2 \cdot 3 \) |
\(0.046418\) |
\(11.290429\) |
\(0.786126\) |
$[8,-203,455,686]$ |
$[16,552,-5632,-98704,175616]$ |
$[2048/343,4416/343,-2816/343]$ |
$y^2 + x^3y = x^5 + x^4 - 2x^2 - 4x - 2$ |
| 12544.i.614656.1 |
12544.i |
\( 2^{8} \cdot 7^{2} \) |
\( 2^{8} \cdot 7^{4} \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/2\Z$ |
\(\mathrm{M}_2(\Q)\) |
\(\mathsf{CM}\) |
✓ |
$E_3$ |
|
✓ |
|
$C_6$ |
$D_6$ |
$3$ |
$3$ |
2.240.1, 3.2880.16 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(19.017610\) |
\(1.188601\) |
$[398,9016,912086,2401]$ |
$[796,2358,-2348,-1857293,614656]$ |
$[1248318403996/2401,9291226221/4802,-23245787/9604]$ |
$y^2 = x^5 + 4x^4 - 13x^3 + 9x^2 - x$ |
