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 |
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 |
|
✓ |
$1$ |
\( 3 \) |
\(1.000000\) |
\(7.177121\) |
\(0.265819\) |
$[1244,1249,129167,2249728]$ |
$[311,3978,72332,1667692,17576]$ |
$[2909390022551/17576,4602275343/676,10349147/26]$ |
$y^2 + (x^2 + x)y = -x^6 + 3x^5 - 6x^4 + 6x^3 - 6x^2 + 3x - 1$ |
713.b.713.1 |
713.b |
\( 23 \cdot 31 \) |
\( 23 \cdot 31 \) |
$0$ |
$0$ |
$\Z/9\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,3$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$4$ |
$0$ |
2.20.2, 3.80.1 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(23.149881\) |
\(0.285801\) |
$[92,73,6379,-91264]$ |
$[23,19,-41,-326,-713]$ |
$[-279841/31,-10051/31,943/31]$ |
$y^2 + (x^3 + x + 1)y = -x^4$ |
745.a.745.1 |
745.a |
\( 5 \cdot 149 \) |
\( - 5 \cdot 149 \) |
$0$ |
$0$ |
$\Z/9\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,3$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$4$ |
$0$ |
2.10.1, 3.80.1 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(24.572840\) |
\(0.303368\) |
$[124,1417,38763,95360]$ |
$[31,-19,39,212,745]$ |
$[28629151/745,-566029/745,37479/745]$ |
$y^2 + (x^3 + x + 1)y = -x$ |
862.b.862.1 |
862.b |
\( 2 \cdot 431 \) |
\( 2 \cdot 431 \) |
$0$ |
$0$ |
$\Z/9\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,3$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$3$ |
$1$ |
2.6.1, 3.80.1 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(27.488991\) |
\(0.339370\) |
$[552,696,112755,3448]$ |
$[276,3058,45033,769436,862]$ |
$[800784050688/431,32146576704/431,1715216904/431]$ |
$y^2 + (x^3 + x)y = -2x^4 + 3x^2 - x - 1$ |
1042.a.1042.1 |
1042.a |
\( 2 \cdot 521 \) |
\( 2 \cdot 521 \) |
$0$ |
$0$ |
$\Z/9\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,3$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$3$ |
$1$ |
2.6.1, 3.80.1 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(30.423017\) |
\(0.375593\) |
$[480,3912,728889,-4168]$ |
$[240,1748,-5521,-1095136,-1042]$ |
$[-398131200000/521,-12082176000/521,159004800/521]$ |
$y^2 + (x^3 + x)y = -x^4 - x^3 - x^2 + 2x + 2$ |
1696.b.434176.1 |
1696.b |
\( 2^{5} \cdot 53 \) |
\( - 2^{13} \cdot 53 \) |
$0$ |
$0$ |
$\Z/9\Z$ |
\(\Q \times \Q\) |
\(\Q\) |
|
$N(\mathrm{SU}(2)\times\mathrm{SU}(2))$ |
|
✓ |
|
$C_2$ |
$C_2$ |
$2$ |
$0$ |
2.10.1, 3.2880.1 |
✓ |
✓ |
$1$ |
\( 3^{2} \) |
\(1.000000\) |
\(5.985343\) |
\(0.665038\) |
$[11236,7908289,22291799553,54272]$ |
$[11236,-11872,-76224768,-214150609408,434176]$ |
$[3299763591802133/8,-155150527903/4,-44328573381/2]$ |
$y^2 + xy = x^6 - 2x^5 + 2x^4 + 9x^3 - 12x^2 + 3x + 26$ |
2230.a.8920.1 |
2230.a |
\( 2 \cdot 5 \cdot 223 \) |
\( 2^{3} \cdot 5 \cdot 223 \) |
$0$ |
$0$ |
$\Z/9\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,3$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$3$ |
$1$ |
2.6.1, 3.80.1 |
✓ |
✓ |
$1$ |
\( 3 \) |
\(1.000000\) |
\(21.369475\) |
\(0.791462\) |
$[600,1488,910149,-35680]$ |
$[300,3502,-17961,-4413076,-8920]$ |
$[-60750000000/223,-2363850000/223,40412250/223]$ |
$y^2 + xy = x^5 + x^4 - x^3 + 2x^2 - 3x + 1$ |
2404.a.4808.1 |
2404.a |
\( 2^{2} \cdot 601 \) |
\( 2^{3} \cdot 601 \) |
$0$ |
$0$ |
$\Z/9\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,3$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$4$ |
$0$ |
2.10.1, 3.80.1 |
✓ |
✓ |
$1$ |
\( 3 \) |
\(1.000000\) |
\(17.574040\) |
\(0.650890\) |
$[20,-3623,-42723,615424]$ |
$[5,152,384,-5296,4808]$ |
$[3125/4808,2375/601,1200/601]$ |
$y^2 + (x^3 + 1)y = -x^4 + x^2 + x$ |
2673.a.8019.1 |
2673.a |
\( 3^{5} \cdot 11 \) |
\( 3^{6} \cdot 11 \) |
$0$ |
$0$ |
$\Z/9\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,3$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$4$ |
$0$ |
2.10.1, 3.2160.20 |
✓ |
✓ |
$1$ |
\( 3 \) |
\(1.000000\) |
\(14.314402\) |
\(0.530163\) |
$[108,-639,-15921,4224]$ |
$[81,513,1809,-29160,8019]$ |
$[4782969/11,373977/11,16281/11]$ |
$y^2 + (x^3 + x + 1)y = -2x^4 + 2x^2 + x$ |
2768.a.354304.1 |
2768.a |
\( 2^{4} \cdot 173 \) |
\( 2^{11} \cdot 173 \) |
$1$ |
$1$ |
$\Z/9\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$3$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$8$ |
$0$ |
3.80.1 |
✓ |
✓ |
$1$ |
\( 3^{2} \) |
\(0.305902\) |
\(13.034562\) |
\(0.443033\) |
$[76,889,21843,-44288]$ |
$[76,-352,-5888,-142848,-354304]$ |
$[-2476099/346,75449/173,16606/173]$ |
$y^2 + y = x^6 - 4x^4 - 5x^3 - 2x^2$ |
2810.a.89920.1 |
2810.a |
\( 2 \cdot 5 \cdot 281 \) |
\( 2^{6} \cdot 5 \cdot 281 \) |
$0$ |
$0$ |
$\Z/9\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,3$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$3$ |
$1$ |
2.6.1, 3.80.1 |
✓ |
✓ |
$1$ |
\( 2 \cdot 3 \) |
\(1.000000\) |
\(11.919749\) |
\(0.882944\) |
$[3000,168,-70221,359680]$ |
$[1500,93722,7831969,741035054,89920]$ |
$[23730468750000/281,988474218750/281,220274128125/1124]$ |
$y^2 + xy = -x^6 - 3x^5 + 5x^3 - 3x + 1$ |
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.b.11664.1 |
2916.b |
\( 2^{2} \cdot 3^{6} \) |
\( - 2^{4} \cdot 3^{6} \) |
$0$ |
$0$ |
$\Z/3\Z\oplus\Z/3\Z$ |
\(\mathrm{M}_2(\mathsf{CM})\) |
\(\Q \times \Q\) |
✓ |
$D_{3,2}$ |
|
|
|
$C_2^2$ |
$C_3:D_4$ |
$4$ |
$0$ |
2.60.2, 3.17280.1 |
✓ |
✓ |
$1$ |
\( 3 \) |
\(1.000000\) |
\(17.695032\) |
\(0.655372\) |
$[40,45,555,6]$ |
$[120,330,-320,-36825,11664]$ |
$[6400000/3,440000/9,-32000/81]$ |
$y^2 + y = x^6$ |
3274.a.13096.1 |
3274.a |
\( 2 \cdot 1637 \) |
\( 2^{3} \cdot 1637 \) |
$0$ |
$0$ |
$\Z/9\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,3$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$3$ |
$1$ |
2.6.1, 3.80.1 |
✓ |
✓ |
$1$ |
\( 3 \) |
\(1.000000\) |
\(25.579411\) |
\(0.947386\) |
$[864,17376,4198167,52384]$ |
$[432,4880,67681,1355948,13096]$ |
$[1880739938304/1637,49179156480/1637,1578862368/1637]$ |
$y^2 + xy = x^5 - 4x^3 + 3x + 1$ |
3428.a.6856.1 |
3428.a |
\( 2^{2} \cdot 857 \) |
\( - 2^{3} \cdot 857 \) |
$0$ |
$0$ |
$\Z/9\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,3$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$4$ |
$0$ |
2.10.1, 3.80.1 |
✓ |
✓ |
$1$ |
\( 3 \) |
\(1.000000\) |
\(19.712294\) |
\(0.730085\) |
$[236,7129,366307,877568]$ |
$[59,-152,256,-2000,6856]$ |
$[714924299/6856,-3902201/857,111392/857]$ |
$y^2 + (x^3 + 1)y = x^4 + x^2 - x$ |
3568.d.913408.1 |
3568.d |
\( 2^{4} \cdot 223 \) |
\( 2^{12} \cdot 223 \) |
$1$ |
$1$ |
$\Z/9\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$3$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$8$ |
$0$ |
3.80.1 |
✓ |
✓ |
$1$ |
\( 3^{2} \) |
\(0.306137\) |
\(15.038004\) |
\(0.511522\) |
$[20,4297,2661,114176]$ |
$[20,-2848,13568,-1959936,913408]$ |
$[3125/892,-11125/446,1325/223]$ |
$y^2 + x^3y = x^4 - 5x^3 + 5x^2 - 2x + 1$ |
4132.a.66112.1 |
4132.a |
\( 2^{2} \cdot 1033 \) |
\( 2^{6} \cdot 1033 \) |
$0$ |
$0$ |
$\Z/9\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,3$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$3$ |
$1$ |
2.6.1, 3.80.1 |
✓ |
✓ |
$1$ |
\( 3^{2} \) |
\(1.000000\) |
\(8.083726\) |
\(0.898192\) |
$[948,10569,4333701,8462336]$ |
$[237,1900,-384,-925252,66112]$ |
$[747724704957/66112,6323225175/16528,-337014/1033]$ |
$y^2 + (x^3 + 1)y = x^3 - 2x^2 + 2x - 2$ |
4752.d.608256.1 |
4752.d |
\( 2^{4} \cdot 3^{3} \cdot 11 \) |
\( - 2^{11} \cdot 3^{3} \cdot 11 \) |
$0$ |
$0$ |
$\Z/9\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,3$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$2$ |
$0$ |
2.10.1, 3.80.1 |
✓ |
✓ |
$1$ |
\( 3^{2} \) |
\(1.000000\) |
\(6.188368\) |
\(0.687596\) |
$[4428,5769,8489115,76032]$ |
$[4428,813120,198158336,54070244352,608256]$ |
$[61570735315641/22,116062274790,70264159344/11]$ |
$y^2 + x^3y = x^5 + 5x^4 + 11x^3 + 26x^2 + 28x + 33$ |
4900.a.98000.1 |
4900.a |
\( 2^{2} \cdot 5^{2} \cdot 7^{2} \) |
\( - 2^{4} \cdot 5^{3} \cdot 7^{2} \) |
$0$ |
$0$ |
$\Z/3\Z\oplus\Z/3\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$2$ |
$0$ |
2.60.2, 3.5760.3 |
✓ |
✓ |
$1$ |
\( 3^{2} \) |
\(1.000000\) |
\(8.504322\) |
\(0.944925\) |
$[1112,1549,528677,12250]$ |
$[1112,50490,3032000,205585975,98000]$ |
$[106268353943552/6125,867820181184/1225,1874600704/49]$ |
$y^2 + y = x^6 + 4x^4 + 4x^2 + 1$ |
7012.a.112192.1 |
7012.a |
\( 2^{2} \cdot 1753 \) |
\( - 2^{6} \cdot 1753 \) |
$0$ |
$0$ |
$\Z/9\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,3$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$4$ |
$0$ |
2.10.1, 3.80.1 |
✓ |
✓ |
$1$ |
\( 2 \cdot 3 \) |
\(1.000000\) |
\(13.839677\) |
\(1.025161\) |
$[1132,109273,29658339,14360576]$ |
$[283,-1216,-1536,-478336,112192]$ |
$[1815232161643/112192,-430638553/1753,-1922136/1753]$ |
$y^2 + (x^3 + 1)y = 2x^4 + 4x^2 - 2x$ |
7562.a.241984.1 |
7562.a |
\( 2 \cdot 19 \cdot 199 \) |
\( 2^{6} \cdot 19 \cdot 199 \) |
$0$ |
$0$ |
$\Z/9\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,3$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$3$ |
$1$ |
2.6.1, 3.80.1 |
✓ |
✓ |
$1$ |
\( 2 \cdot 3 \) |
\(1.000000\) |
\(17.898697\) |
\(1.325829\) |
$[2544,102576,97720377,-967936]$ |
$[1272,50320,-53169,-649933342,-241984]$ |
$[-52030210457088/3781,-1618161978240/3781,1344165489/3781]$ |
$y^2 + (x^2 + 1)y = x^6 - 3x^5 + 2x^4 - x^3 - x^2 + 3x + 1$ |
10260.b.164160.1 |
10260.b |
\( 2^{2} \cdot 3^{3} \cdot 5 \cdot 19 \) |
\( 2^{6} \cdot 3^{3} \cdot 5 \cdot 19 \) |
$1$ |
$1$ |
$\Z/9\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,3$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$7$ |
$1$ |
2.6.1, 3.80.1 |
✓ |
✓ |
$1$ |
\( 3^{2} \) |
\(0.505447\) |
\(15.932181\) |
\(0.894764\) |
$[3348,18297,16345485,21012480]$ |
$[837,28428,1307584,71574156,164160]$ |
$[15214704636591/6080,154347260373/1520,530123157/95]$ |
$y^2 + (x^3 + 1)y = -2x^4 + 6x^2 - 4$ |
10449.a.31347.1 |
10449.a |
\( 3^{5} \cdot 43 \) |
\( - 3^{6} \cdot 43 \) |
$0$ |
$0$ |
$\Z/9\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,3$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$4$ |
$0$ |
2.10.1, 3.80.1 |
✓ |
✓ |
$1$ |
\( 3 \) |
\(1.000000\) |
\(16.450609\) |
\(0.609282\) |
$[180,3393,141489,16512]$ |
$[135,-513,351,-53946,31347]$ |
$[61509375/43,-1731375/43,8775/43]$ |
$y^2 + (x^3 + x + 1)y = x^4 + 2x^2 - 2x$ |
11536.a.369152.1 |
11536.a |
\( 2^{4} \cdot 7 \cdot 103 \) |
\( 2^{9} \cdot 7 \cdot 103 \) |
$0$ |
$0$ |
$\Z/9\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,3$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$4$ |
$0$ |
2.10.1, 3.80.1 |
✓ |
✓ |
$1$ |
\( 3^{2} \) |
\(1.000000\) |
\(12.484653\) |
\(1.387184\) |
$[100,397,12333,-46144]$ |
$[100,152,-1296,-38176,-369152]$ |
$[-19531250/721,-296875/721,50625/1442]$ |
$y^2 + (x + 1)y = x^6 - x^4 + x^3$ |
11728.d.187648.1 |
11728.d |
\( 2^{4} \cdot 733 \) |
\( - 2^{8} \cdot 733 \) |
$0$ |
$0$ |
$\Z/9\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,3$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$4$ |
$0$ |
2.10.1, 3.80.1 |
✓ |
✓ |
$1$ |
\( 3^{2} \) |
\(1.000000\) |
\(13.862884\) |
\(1.540320\) |
$[224,3592,191172,750592]$ |
$[112,-76,636,16364,187648]$ |
$[68841472/733,-417088/733,31164/733]$ |
$y^2 + (x^3 + x)y = x^3 - x + 1$ |
11792.b.377344.1 |
11792.b |
\( 2^{4} \cdot 11 \cdot 67 \) |
\( - 2^{9} \cdot 11 \cdot 67 \) |
$0$ |
$0$ |
$\Z/9\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,3$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$4$ |
$0$ |
2.10.1, 3.80.1 |
✓ |
✓ |
$1$ |
\( 3^{2} \) |
\(1.000000\) |
\(13.072948\) |
\(1.452550\) |
$[116,1069,28477,47168]$ |
$[116,-152,1264,30880,377344]$ |
$[41022298/737,-463391/737,66439/1474]$ |
$y^2 + (x + 1)y = x^6 + x^4 - x^3$ |
17689.d.866761.1 |
17689.d |
\( 7^{2} \cdot 19^{2} \) |
\( 7^{4} \cdot 19^{2} \) |
$2$ |
$2$ |
$\Z/9\Z$ |
\(\mathsf{RM}\) |
\(\mathsf{RM}\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
✓ |
✓ |
$C_2$ |
$C_2$ |
$10$ |
$0$ |
2.12.2, 3.720.4 |
✓ |
✓ |
$1$ |
\( 3 \) |
\(1.596240\) |
\(11.235399\) |
\(0.664237\) |
$[3196,1064809,806830683,-110945408]$ |
$[799,-17767,-178217,-114515418,-866761]$ |
$[-325637113603999/866761,9062633983033/866761,113773911017/866761]$ |
$y^2 + (x^3 + x^2 + 1)y = 2x^4 - 2x^2 - 7x + 5$ |
23012.a.368192.1 |
23012.a |
\( 2^{2} \cdot 11 \cdot 523 \) |
\( - 2^{6} \cdot 11 \cdot 523 \) |
$0$ |
$0$ |
$\Z/9\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,3$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$3$ |
$1$ |
2.6.1, 3.80.1 |
✓ |
✓ |
$1$ |
\( 3^{2} \) |
\(1.000000\) |
\(15.758966\) |
\(1.750996\) |
$[84,368889,-132834675,-47128576]$ |
$[21,-15352,1934608,-48764284,-368192]$ |
$[-4084101/368192,17771859/46024,-53322633/23012]$ |
$y^2 + (x^2 + x + 1)y = 4x^5 + 8x^4 + x^2 + x$ |
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 |
✓ |
✓ |
$1$ |
\( 3^{2} \) |
\(1.000000\) |
\(14.148765\) |
\(1.572085\) |
$[60,945,2295,82944]$ |
$[45,-270,3780,24300,157464]$ |
$[9375/8,-625/4,875/18]$ |
$y^2 + (x^3 + 1)y = 2x^3$ |
26244.d.314928.1 |
26244.d |
\( 2^{2} \cdot 3^{8} \) |
\( 2^{4} \cdot 3^{9} \) |
$1$ |
$1$ |
$\Z/3\Z\oplus\Z/3\Z$ |
\(\mathrm{M}_2(\Q)\) |
\(\Q\) |
|
$J(E_3)$ |
|
✓ |
|
$C_2$ |
$D_6$ |
$6$ |
$0$ |
2.20.3, 3.5760.3 |
✓ |
✓ |
$1$ |
\( 3^{2} \) |
\(0.985565\) |
\(12.739642\) |
\(1.395083\) |
$[24,189,1107,-162]$ |
$[72,-918,-3024,-265113,-314928]$ |
$[-6144,1088,448/9]$ |
$y^2 + y = x^6 - 2x^3$ |
26244.e.472392.1 |
26244.e |
\( 2^{2} \cdot 3^{8} \) |
\( - 2^{3} \cdot 3^{10} \) |
$0$ |
$0$ |
$\Z/3\Z\oplus\Z/3\Z$ |
\(\mathrm{M}_2(\Q)\) |
\(\Q\) |
|
$J(E_3)$ |
|
✓ |
|
$C_2$ |
$D_6$ |
$4$ |
$0$ |
2.20.3, 3.5760.3 |
✓ |
✓ |
$1$ |
\( 3^{2} \) |
\(1.000000\) |
\(12.048083\) |
\(1.338676\) |
$[356,3969,419553,248832]$ |
$[267,1482,-2884,-741588,472392]$ |
$[5584059449/1944,174127343/2916,-5711041/13122]$ |
$y^2 + (x^3 + 1)y = 2$ |
31775.a.158875.1 |
31775.a |
\( 5^{2} \cdot 31 \cdot 41 \) |
\( - 5^{3} \cdot 31 \cdot 41 \) |
$0$ |
$0$ |
$\Z/9\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,3$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$4$ |
$0$ |
2.10.1, 3.80.1 |
✓ |
✓ |
$1$ |
\( 3 \) |
\(1.000000\) |
\(20.895853\) |
\(0.773920\) |
$[1892,166729,81871317,-20336000]$ |
$[473,2375,20625,1028750,-158875]$ |
$[-23675856753593/158875,-2010652523/1271,-36915285/1271]$ |
$y^2 + (x^3 + x + 1)y = -3x^4 + 6x^2 + 2x$ |
50220.a.803520.1 |
50220.a |
\( 2^{2} \cdot 3^{4} \cdot 5 \cdot 31 \) |
\( 2^{6} \cdot 3^{4} \cdot 5 \cdot 31 \) |
$0$ |
$0$ |
$\Z/9\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,3$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$3$ |
$1$ |
2.6.1, 3.80.1 |
✓ |
✓ |
$1$ |
\( 3^{2} \) |
\(1.000000\) |
\(14.071295\) |
\(1.563477\) |
$[9036,1201257,4222582731,-102850560]$ |
$[2259,162576,-554256,-6920755020,-803520]$ |
$[-726266706536979/9920,-1446105990699/620,2182417641/620]$ |
$y^2 + (x^3 + 1)y = -x^5 - x^4 + x^3 + 7x^2 + 16x + 10$ |
52488.a.629856.1 |
52488.a |
\( 2^{3} \cdot 3^{8} \) |
\( - 2^{5} \cdot 3^{9} \) |
$1$ |
$1$ |
$\Z/3\Z\oplus\Z/3\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$6$ |
$0$ |
2.15.2, 3.5760.3 |
✓ |
✓ |
$1$ |
\( 3^{2} \) |
\(0.611870\) |
\(16.925754\) |
\(1.150706\) |
$[264,15984,2059452,10368]$ |
$[396,-17442,-3397248,-412383393,629856]$ |
$[15460896,-1719652,-7612352/9]$ |
$y^2 + (x^3 + x)y = x^4 - 7x^2 + 6$ |
68225.a.341125.1 |
68225.a |
\( 5^{2} \cdot 2729 \) |
\( - 5^{3} \cdot 2729 \) |
$0$ |
$0$ |
$\Z/9\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,3$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$4$ |
$0$ |
2.10.1, 3.80.1 |
✓ |
✓ |
$1$ |
\( 3 \) |
\(1.000000\) |
\(11.741537\) |
\(0.434872\) |
$[2108,334729,172160683,43664000]$ |
$[527,-2375,-10625,-2810000,341125]$ |
$[40649300451407/341125,-2780900477/2729,-23606965/2729]$ |
$y^2 + (x^3 + x + 1)y = 2x^4 + 6x^2 - 3x$ |
98172.a.589032.1 |
98172.a |
\( 2^{2} \cdot 3^{5} \cdot 101 \) |
\( - 2^{3} \cdot 3^{6} \cdot 101 \) |
$0$ |
$0$ |
$\Z/9\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,3$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$4$ |
$0$ |
2.10.1, 3.80.1 |
✓ |
✓ |
$1$ |
\( 3^{2} \) |
\(1.000000\) |
\(18.381989\) |
\(2.042443\) |
$[1116,66897,19025703,-310272]$ |
$[837,4104,55296,7359984,-589032]$ |
$[-563507579133/808,-412635141/101,-6642432/101]$ |
$y^2 + (x^3 + 1)y = -3x^4 + 9x^2 + 3x$ |
150660.a.903960.1 |
150660.a |
\( 2^{2} \cdot 3^{5} \cdot 5 \cdot 31 \) |
\( - 2^{3} \cdot 3^{6} \cdot 5 \cdot 31 \) |
$0$ |
$0$ |
$\Z/9\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,3$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$4$ |
$0$ |
2.10.1, 3.80.1 |
✓ |
✓ |
$1$ |
\( 3^{2} \) |
\(1.000000\) |
\(10.076856\) |
\(1.119651\) |
$[1188,99153,29008089,476160]$ |
$[891,-4104,-38016,-12678768,903960]$ |
$[770301940419/1240,-497763387/155,-5174928/155]$ |
$y^2 + (x^3 + 1)y = 3x^4 + 9x^2 - 3x$ |
163782.b.491346.1 |
163782.b |
\( 2 \cdot 3^{5} \cdot 337 \) |
\( 2 \cdot 3^{6} \cdot 337 \) |
$0$ |
$2$ |
$\Z/9\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$3$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$0$ |
$0$ |
3.80.1 |
✓ |
✓ |
$4$ |
\( 3 \) |
\(1.000000\) |
\(10.078942\) |
\(1.493177\) |
$[30672,-3816,-40481955,8088]$ |
$[46008,88203060,225480683961,648533878578522,491346]$ |
$[141386924928583581696/337,5891504205359139840/337,327354660820051488/337]$ |
$y^2 + (x^2 + 1)y = -2x^6 + 17x^4 - 9x^3 - 26x^2 - 6x + 32$ |