| 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 |
| 3319.a.3319.1 |
3319.a |
\( 3319 \) |
\( 3319 \) |
$2$ |
$2$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
|
✓ |
✓ |
$C_2$ |
$C_2$ |
$12$ |
$0$ |
|
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.007585\) |
\(25.359353\) |
\(0.192363\) |
$[68,3673,38093,424832]$ |
$[17,-141,205,-4099,3319]$ |
$[1419857/3319,-692733/3319,59245/3319]$ |
$y^2 + (x^3 + x + 1)y = x^5 + 2x^4 + x^3$ |
| 3391.b.3391.1 |
3391.b |
\( 3391 \) |
\( -3391 \) |
$2$ |
$2$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
|
✓ |
✓ |
$C_2$ |
$C_2$ |
$12$ |
$0$ |
|
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.008473\) |
\(22.961204\) |
\(0.194544\) |
$[252,105,105723,434048]$ |
$[63,161,-813,-19285,3391]$ |
$[992436543/3391,40257567/3391,-3226797/3391]$ |
$y^2 + (x^3 + x + 1)y = -x^5 - x^4$ |
| 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 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.007315\) |
\(28.081352\) |
\(0.205420\) |
$[196,6649,304573,-476288]$ |
$[49,-177,-187,-10123,-3721]$ |
$[-282475249/3721,20823873/3721,448987/3721]$ |
$y^2 + (x^3 + x + 1)y = -x^4 + x^3 + 3x^2 + x$ |
| 4021.a.4021.1 |
4021.a |
\( 4021 \) |
\( -4021 \) |
$2$ |
$2$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
|
✓ |
✓ |
$C_2$ |
$C_2$ |
$12$ |
$0$ |
|
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.008454\) |
\(25.264530\) |
\(0.213597\) |
$[228,2697,96981,-514688]$ |
$[57,23,861,12137,-4021]$ |
$[-601692057/4021,-4259439/4021,-2797389/4021]$ |
$y^2 + (x^3 + x + 1)y = x^5 + 2x^2 + x$ |
| 4356.b.470448.1 |
4356.b |
\( 2^{2} \cdot 3^{2} \cdot 11^{2} \) |
\( 2^{4} \cdot 3^{5} \cdot 11^{2} \) |
$1$ |
$1$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$12$ |
$0$ |
2.20.3 |
✓ |
✓ |
$1$ |
\( 3 \cdot 7 \) |
\(0.001197\) |
\(17.381062\) |
\(0.436802\) |
$[56,4741,-21505,58806]$ |
$[56,-3030,68688,-1333593,470448]$ |
$[34420736/29403,-11085760/9801,166208/363]$ |
$y^2 + x^3y = -x^4 - 6x^3 + 22x^2 - 24x + 9$ |
| 4673.a.4673.1 |
4673.a |
\( 4673 \) |
\( 4673 \) |
$2$ |
$2$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
|
✓ |
✓ |
$C_2$ |
$C_2$ |
$12$ |
$0$ |
|
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.010787\) |
\(25.100036\) |
\(0.270752\) |
$[216,2004,161568,-18692]$ |
$[108,152,-5016,-141208,-4673]$ |
$[-14693280768/4673,-191476224/4673,58506624/4673]$ |
$y^2 + x^3y = x^3 - x^2 - x + 1$ |
| 4925.b.4925.1 |
4925.b |
\( 5^{2} \cdot 197 \) |
\( 5^{2} \cdot 197 \) |
$2$ |
$2$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$3$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$12$ |
$0$ |
3.40.1 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.012038\) |
\(23.181407\) |
\(0.279065\) |
$[216,1140,86400,-19700]$ |
$[108,296,-984,-48472,-4925]$ |
$[-14693280768/4925,-372874752/4925,11477376/4925]$ |
$y^2 + x^3y = -x^4 - x^3 + x + 1$ |
| 5113.a.5113.1 |
5113.a |
\( 5113 \) |
\( -5113 \) |
$2$ |
$2$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$12$ |
$0$ |
2.10.1 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.011558\) |
\(24.766371\) |
\(0.286246\) |
$[300,10329,1082211,654464]$ |
$[75,-196,-5088,-105004,5113]$ |
$[2373046875/5113,-82687500/5113,-28620000/5113]$ |
$y^2 + (x^2 + x + 1)y = x^6 - 2x^4 - x$ |
| 5209.a.5209.1 |
5209.a |
\( 5209 \) |
\( -5209 \) |
$2$ |
$2$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
|
✓ |
✓ |
$C_2$ |
$C_2$ |
$12$ |
$0$ |
|
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.009447\) |
\(27.008148\) |
\(0.255151\) |
$[132,9657,203805,-666752]$ |
$[33,-357,941,-24099,-5209]$ |
$[-39135393/5209,12829509/5209,-1024749/5209]$ |
$y^2 + (x^3 + x + 1)y = x^4 + x^3 - x^2 - x$ |
| 5414.a.10828.1 |
5414.a |
\( 2 \cdot 2707 \) |
\( - 2^{2} \cdot 2707 \) |
$2$ |
$2$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
|
✓ |
✓ |
$C_2$ |
$C_2$ |
$12$ |
$0$ |
|
✓ |
✓ |
$1$ |
\( 2 \) |
\(0.007352\) |
\(20.103606\) |
\(0.295620\) |
$[108,3993,71523,1385984]$ |
$[27,-136,300,-2599,10828]$ |
$[14348907/10828,-669222/2707,54675/2707]$ |
$y^2 + (x^3 + 1)y = 2x^2 + x$ |
| 5449.b.5449.1 |
5449.b |
\( 5449 \) |
\( -5449 \) |
$2$ |
$2$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$12$ |
$0$ |
2.10.1 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.010593\) |
\(23.381067\) |
\(0.247684\) |
$[60,4857,73155,697472]$ |
$[15,-193,-165,-9931,5449]$ |
$[759375/5449,-651375/5449,-37125/5449]$ |
$y^2 + (x^3 + x + 1)y = x^4 + 2x^3 + x^2$ |
| 5476.b.21904.1 |
5476.b |
\( 2^{2} \cdot 37^{2} \) |
\( - 2^{4} \cdot 37^{2} \) |
$2$ |
$2$ |
$\mathsf{trivial}$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$12$ |
$0$ |
2.15.2, 3.90.1 |
✓ |
✓ |
$1$ |
\( 3 \) |
\(0.004919\) |
\(20.265680\) |
\(0.299062\) |
$[120,213,14793,2738]$ |
$[120,458,-4416,-184921,21904]$ |
$[1555200000/1369,49464000/1369,-3974400/1369]$ |
$y^2 + y = x^6 - x^2$ |
| 5501.a.5501.1 |
5501.a |
\( 5501 \) |
\( 5501 \) |
$2$ |
$2$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
|
✓ |
✓ |
$C_2$ |
$C_2$ |
$12$ |
$0$ |
|
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.010011\) |
\(26.164773\) |
\(0.261938\) |
$[732,22041,6292467,-704128]$ |
$[183,477,-26525,-1270401,-5501]$ |
$[-205236901143/5501,-2923288299/5501,888295725/5501]$ |
$y^2 + (x^3 + x^2 + 1)y = -2x^3 - 3x^2 + x + 2$ |
| 5599.a.5599.1 |
5599.a |
\( 11 \cdot 509 \) |
\( 11 \cdot 509 \) |
$2$ |
$2$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
|
✓ |
✓ |
$C_2$ |
$C_2$ |
$12$ |
$0$ |
|
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.012163\) |
\(21.606456\) |
\(0.262794\) |
$[28,937,106107,-716672]$ |
$[7,-37,-1397,-2787,-5599]$ |
$[-16807/5599,12691/5599,6223/509]$ |
$y^2 + (x^3 + x + 1)y = -x^4 + x^2 - 2x$ |
| 5618.a.11236.1 |
5618.a |
\( 2 \cdot 53^{2} \) |
\( - 2^{2} \cdot 53^{2} \) |
$2$ |
$2$ |
$\mathsf{trivial}$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$12$ |
$0$ |
2.60.2, 3.90.1 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(0.006408\) |
\(23.498592\) |
\(0.301139\) |
$[84,7305,129381,-1438208]$ |
$[21,-286,0,-20449,-11236]$ |
$[-4084101/11236,1324323/5618,0]$ |
$y^2 + (x^3 + 1)y = -x^5 + x^4 + x^2 - x$ |
| 5641.a.5641.1 |
5641.a |
\( 5641 \) |
\( 5641 \) |
$2$ |
$2$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
|
✓ |
✓ |
$C_2$ |
$C_2$ |
$12$ |
$0$ |
|
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.013760\) |
\(22.178341\) |
\(0.305182\) |
$[16,-380,-58424,22564]$ |
$[8,66,6352,11615,5641]$ |
$[32768/5641,33792/5641,406528/5641]$ |
$y^2 + y = x^6 - x^5 - x^4 + 2x^3 - x$ |
| 5705.a.5705.1 |
5705.a |
\( 5 \cdot 7 \cdot 163 \) |
\( - 5 \cdot 7 \cdot 163 \) |
$2$ |
$3$ |
$\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$12$ |
$0$ |
2.15.1 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.044428\) |
\(27.322834\) |
\(0.303472\) |
$[116,15673,-175603,-730240]$ |
$[29,-618,7756,-39250,-5705]$ |
$[-20511149/5705,15072402/5705,-931828/815]$ |
$y^2 + (x^3 + 1)y = x^5 + x^4 + x^3 + 4x^2 + 2x$ |
| 5911.b.5911.1 |
5911.b |
\( 23 \cdot 257 \) |
\( - 23 \cdot 257 \) |
$2$ |
$2$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$12$ |
$0$ |
2.20.2 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.013645\) |
\(19.752008\) |
\(0.269521\) |
$[156,-3015,-9981,756608]$ |
$[39,189,-1085,-19509,5911]$ |
$[90224199/5911,11211291/5911,-1650285/5911]$ |
$y^2 + (x^3 + x + 1)y = -2x^4 + x^3 - x^2$ |
| 6229.a.6229.1 |
6229.a |
\( 6229 \) |
\( 6229 \) |
$2$ |
$2$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
|
✓ |
✓ |
$C_2$ |
$C_2$ |
$12$ |
$0$ |
|
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.015603\) |
\(18.542125\) |
\(0.289308\) |
$[60,2793,63483,-797312]$ |
$[15,-107,-389,-4321,-6229]$ |
$[-759375/6229,361125/6229,87525/6229]$ |
$y^2 + (x^3 + x + 1)y = -2x^4 + 3x^3 - 3x^2$ |
| 6463.a.6463.1 |
6463.a |
\( 23 \cdot 281 \) |
\( - 23 \cdot 281 \) |
$2$ |
$2$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
|
✓ |
✓ |
$C_2$ |
$C_2$ |
$12$ |
$0$ |
|
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.014972\) |
\(22.488471\) |
\(0.336705\) |
$[396,7497,936315,827264]$ |
$[99,96,-2168,-55962,6463]$ |
$[9509900499/6463,93148704/6463,-21248568/6463]$ |
$y^2 + (x^2 + x + 1)y = x^6 - x^4$ |
| 6511.a.6511.1 |
6511.a |
\( 17 \cdot 383 \) |
\( 17 \cdot 383 \) |
$2$ |
$2$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
|
✓ |
✓ |
$C_2$ |
$C_2$ |
$12$ |
$0$ |
|
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.010491\) |
\(27.158650\) |
\(0.284927\) |
$[292,12169,711445,833408]$ |
$[73,-285,1301,3437,6511]$ |
$[2073071593/6511,-110869845/6511,6933029/6511]$ |
$y^2 + (x^3 + x + 1)y = x^5 + 2x^4 - 2x^2 - x$ |
| 6718.a.13436.1 |
6718.a |
\( 2 \cdot 3359 \) |
\( - 2^{2} \cdot 3359 \) |
$2$ |
$2$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
|
✓ |
✓ |
$C_2$ |
$C_2$ |
$12$ |
$0$ |
|
✓ |
✓ |
$1$ |
\( 2 \) |
\(0.008000\) |
\(21.445453\) |
\(0.343120\) |
$[620,9913,2068403,1719808]$ |
$[155,588,-2324,-176491,13436]$ |
$[89466096875/13436,547409625/3359,-13958525/3359]$ |
$y^2 + (x^2 + x + 1)y = x^6 + x^5 - x^2 - x$ |
| 6869.a.6869.1 |
6869.a |
\( 6869 \) |
\( 6869 \) |
$2$ |
$2$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
|
✓ |
✓ |
$C_2$ |
$C_2$ |
$12$ |
$0$ |
|
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.015090\) |
\(22.208533\) |
\(0.335132\) |
$[492,1689,502275,-879232]$ |
$[123,560,-264,-86518,-6869]$ |
$[-28153056843/6869,-1042085520/6869,3994056/6869]$ |
$y^2 + (x^2 + x + 1)y = x^6 - x^4 - x^2 - x$ |
| 7165.a.7165.1 |
7165.a |
\( 5 \cdot 1433 \) |
\( - 5 \cdot 1433 \) |
$2$ |
$3$ |
$\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$12$ |
$0$ |
2.15.1 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.058535\) |
\(23.252455\) |
\(0.340272\) |
$[244,3001,-262067,-917120]$ |
$[61,30,6284,95606,-7165]$ |
$[-844596301/7165,-1361886/1433,-23382764/7165]$ |
$y^2 + (x^3 + 1)y = x^4 + x^3 - 2x^2$ |
| 7225.a.36125.1 |
7225.a |
\( 5^{2} \cdot 17^{2} \) |
\( - 5^{3} \cdot 17^{2} \) |
$2$ |
$3$ |
$\Z/2\Z$ |
\(\mathsf{RM}\) |
\(\mathsf{RM}\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
✓ |
✓ |
$C_2$ |
$C_2$ |
$12$ |
$0$ |
2.45.1, 3.72.2 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(0.037430\) |
\(18.345600\) |
\(0.343342\) |
$[980,-2039,-2619067,-4624000]$ |
$[245,2586,64636,2287106,-36125]$ |
$[-7061881225/289,-304240314/289,-155191036/1445]$ |
$y^2 + (x^3 + 1)y = -x^5 + 2x^4 - 3x^2 - x$ |
| 7396.a.29584.1 |
7396.a |
\( 2^{2} \cdot 43^{2} \) |
\( - 2^{4} \cdot 43^{2} \) |
$2$ |
$2$ |
$\Z/3\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$12$ |
$0$ |
2.60.2, 3.720.4 |
✓ |
✓ |
$1$ |
\( 3 \) |
\(0.047749\) |
\(21.927407\) |
\(0.349006\) |
$[56,1285,33089,3698]$ |
$[56,-726,-15680,-351289,29584]$ |
$[34420736/1849,-7968576/1849,-3073280/1849]$ |
$y^2 + y = x^6 - 2x^4 + x^2$ |
| 7442.a.14884.1 |
7442.a |
\( 2 \cdot 61^{2} \) |
\( - 2^{2} \cdot 61^{2} \) |
$2$ |
$2$ |
$\mathsf{trivial}$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$12$ |
$0$ |
2.60.2, 3.90.1 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(0.009569\) |
\(18.191660\) |
\(0.348163\) |
$[140,3097,23747,1905152]$ |
$[35,-78,1024,7439,14884]$ |
$[52521875/14884,-1672125/7442,313600/3721]$ |
$y^2 + (x^3 + 1)y = x^4 + x^3 + x^2$ |
| 7945.c.198625.1 |
7945.c |
\( 5 \cdot 7 \cdot 227 \) |
\( - 5^{3} \cdot 7 \cdot 227 \) |
$2$ |
$2$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
|
✓ |
✓ |
$C_2$ |
$C_2$ |
$12$ |
$0$ |
|
✓ |
✓ |
$1$ |
\( 3 \) |
\(0.007898\) |
\(17.934446\) |
\(0.424929\) |
$[4644,123441,177145353,-25424000]$ |
$[1161,51020,2820924,168013091,-198625]$ |
$[-2109410476821801/198625,-15968609811324/39725,-3802382699004/198625]$ |
$y^2 + (x^3 + x + 1)y = -5x^4 + 3x^3 + 7x^2 + 2x$ |
| 8091.a.24273.1 |
8091.a |
\( 3^{2} \cdot 29 \cdot 31 \) |
\( 3^{3} \cdot 29 \cdot 31 \) |
$2$ |
$2$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$12$ |
$0$ |
2.20.2 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(0.007733\) |
\(21.522963\) |
\(0.332893\) |
$[1116,20889,8501427,-3106944]$ |
$[279,2373,-349,-1432125,-24273]$ |
$[-2019740427/29,-61572231/29,32457/29]$ |
$y^2 + (x^3 + x + 1)y = -x^4 - x^2 - 2x + 2$ |
| 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 |
✓ |
✓ |
$1$ |
\( 3 \) |
\(0.005669\) |
\(19.785401\) |
\(0.336475\) |
$[2596,375193,248614093,51938432]$ |
$[649,1917,-1907,-1228133,405769]$ |
$[115139273278249/405769,524030063733/405769,-803230307/405769]$ |
$y^2 + (x^3 + x + 1)y = -3x^5 + 9x^4 - 7x^3 - 2x^2 + x$ |
| 9093.b.63651.1 |
9093.b |
\( 3 \cdot 7 \cdot 433 \) |
\( 3 \cdot 7^{2} \cdot 433 \) |
$2$ |
$3$ |
$\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$12$ |
$0$ |
2.15.1 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(0.046117\) |
\(17.348802\) |
\(0.400038\) |
$[652,-3623,945923,-8147328]$ |
$[163,1258,-9948,-801022,-63651]$ |
$[-115063617043/63651,-5448079726/63651,88102804/21217]$ |
$y^2 + (x^3 + 1)y = 2x^5 + 3x^4 + x^3 - x$ |
| 9309.a.27927.1 |
9309.a |
\( 3 \cdot 29 \cdot 107 \) |
\( - 3^{2} \cdot 29 \cdot 107 \) |
$2$ |
$2$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
|
✓ |
✓ |
$C_2$ |
$C_2$ |
$12$ |
$0$ |
|
✓ |
✓ |
$1$ |
\( 2 \) |
\(0.010625\) |
\(19.437778\) |
\(0.413034\) |
$[176,5476,257752,111708]$ |
$[88,-590,-4752,-191569,27927]$ |
$[5277319168/27927,-402068480/27927,-4088832/3103]$ |
$y^2 + x^3y = x^4 - x^2 - x + 1$ |
| 9331.a.9331.1 |
9331.a |
\( 7 \cdot 31 \cdot 43 \) |
\( - 7 \cdot 31 \cdot 43 \) |
$2$ |
$2$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
|
✓ |
✓ |
$C_2$ |
$C_2$ |
$12$ |
$0$ |
|
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.014986\) |
\(26.237604\) |
\(0.393189\) |
$[144,5460,156888,-37324]$ |
$[72,-694,1632,-91033,-9331]$ |
$[-1934917632/9331,259034112/9331,-8460288/9331]$ |
$y^2 + x^3y = 4x^3 + 8x^2 + 5x + 1$ |
| 9496.a.18992.1 |
9496.a |
\( 2^{3} \cdot 1187 \) |
\( 2^{4} \cdot 1187 \) |
$2$ |
$2$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
|
✓ |
✓ |
$C_2$ |
$C_2$ |
$12$ |
$0$ |
|
✓ |
✓ |
$1$ |
\( 2 \) |
\(0.009368\) |
\(20.853052\) |
\(0.390682\) |
$[72,501,14049,-2374]$ |
$[72,-118,-4944,-92473,-18992]$ |
$[-120932352/1187,2752704/1187,1601856/1187]$ |
$y^2 + x^3y = -x^4 - 2x^3 + 2x + 1$ |
| 9532.a.38128.1 |
9532.a |
\( 2^{2} \cdot 2383 \) |
\( 2^{4} \cdot 2383 \) |
$2$ |
$2$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
|
✓ |
✓ |
$C_2$ |
$C_2$ |
$12$ |
$0$ |
|
✓ |
✓ |
$1$ |
\( 3 \) |
\(0.006911\) |
\(20.094314\) |
\(0.416617\) |
$[248,901,87281,-4766]$ |
$[248,1962,-896,-1017913,-38128]$ |
$[-58632501248/2383,-1870398144/2383,3444224/2383]$ |
$y^2 + y = x^6 - 2x^5 - x^4 + x^2 + x$ |
| 9565.a.9565.1 |
9565.a |
\( 5 \cdot 1913 \) |
\( - 5 \cdot 1913 \) |
$2$ |
$3$ |
$\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$12$ |
$0$ |
2.15.1 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.069903\) |
\(23.554899\) |
\(0.411640\) |
$[780,9081,2928915,1224320]$ |
$[195,1206,-3020,-510834,9565]$ |
$[56390124375/1913,1788467850/1913,-22967100/1913]$ |
$y^2 + (x^3 + x^2 + x)y = -x^4 - 2x + 1$ |
| 10345.c.51725.1 |
10345.c |
\( 5 \cdot 2069 \) |
\( 5^{2} \cdot 2069 \) |
$2$ |
$2$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
|
✓ |
✓ |
$C_2$ |
$C_2$ |
$12$ |
$0$ |
|
✓ |
✓ |
$1$ |
\( 2 \) |
\(0.011412\) |
\(18.163956\) |
\(0.414576\) |
$[144,5460,209592,-206900]$ |
$[72,-694,-4224,-196441,-51725]$ |
$[-1934917632/51725,259034112/51725,21897216/51725]$ |
$y^2 + x^3y = 2x^3 + 2x^2 + x + 1$ |
| 10839.a.32517.1 |
10839.a |
\( 3 \cdot 3613 \) |
\( - 3^{2} \cdot 3613 \) |
$2$ |
$2$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
|
✓ |
✓ |
$C_2$ |
$C_2$ |
$12$ |
$0$ |
|
✓ |
✓ |
$1$ |
\( 2 \) |
\(0.012492\) |
\(15.015401\) |
\(0.375157\) |
$[572,10489,1757251,4162176]$ |
$[143,415,-277,-52959,32517]$ |
$[59797108943/32517,1213545905/32517,-5664373/32517]$ |
$y^2 + (x^3 + x + 1)y = x^5 + 2x^4 + x^3 + 2x^2$ |
| 10952.a.21904.1 |
10952.a |
\( 2^{3} \cdot 37^{2} \) |
\( - 2^{4} \cdot 37^{2} \) |
$2$ |
$2$ |
$\mathsf{trivial}$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$12$ |
$0$ |
2.15.2, 3.90.1 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(0.008583\) |
\(24.568934\) |
\(0.421737\) |
$[72,4245,4383,-2738]$ |
$[72,-2614,53568,-744025,-21904]$ |
$[-120932352/1369,60979392/1369,-17356032/1369]$ |
$y^2 + y = x^6 - 3x^4 + 2x^2$ |
| 11011.b.77077.1 |
11011.b |
\( 7 \cdot 11^{2} \cdot 13 \) |
\( 7^{2} \cdot 11^{2} \cdot 13 \) |
$2$ |
$2$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$12$ |
$0$ |
2.15.2 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(0.013244\) |
\(17.651137\) |
\(0.467557\) |
$[432,1428,-631800,308308]$ |
$[216,1706,107808,5094023,77077]$ |
$[470184984576/77077,17192549376/77077,5029890048/77077]$ |
$y^2 + x^3y = x^5 + x^4 + 2x^3 + 6x^2 + 3x - 1$ |
| 11011.b.143143.1 |
11011.b |
\( 7 \cdot 11^{2} \cdot 13 \) |
\( - 7 \cdot 11^{2} \cdot 13^{2} \) |
$2$ |
$2$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$12$ |
$0$ |
2.15.2 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(0.013244\) |
\(17.651137\) |
\(0.467557\) |
$[48,14628,184440,572572]$ |
$[24,-2414,-4208,-1482097,143143]$ |
$[7962624/143143,-33371136/143143,-2423808/143143]$ |
$y^2 + x^3y = x^4 - 4x^3 + 3x^2 - x + 1$ |
| 11012.a.22024.1 |
11012.a |
\( 2^{2} \cdot 2753 \) |
\( 2^{3} \cdot 2753 \) |
$2$ |
$2$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$12$ |
$0$ |
2.10.1 |
✓ |
✓ |
$1$ |
\( 3 \) |
\(0.008550\) |
\(19.918548\) |
\(0.510898\) |
$[28,5377,190687,-2819072]$ |
$[7,-222,-2212,-16192,-22024]$ |
$[-16807/22024,38073/11012,27097/5506]$ |
$y^2 + (x^3 + x^2 + 1)y = x^4 - 2x^2 - x$ |
| 11113.a.11113.1 |
11113.a |
\( 11113 \) |
\( 11113 \) |
$2$ |
$2$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
|
✓ |
✓ |
$C_2$ |
$C_2$ |
$12$ |
$0$ |
|
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.020331\) |
\(22.917111\) |
\(0.465920\) |
$[12,10041,114099,-1422464]$ |
$[3,-418,-1236,-44608,-11113]$ |
$[-243/11113,11286/11113,11124/11113]$ |
$y^2 + (x^3 + 1)y = x^4 + x^3 - x$ |
| 11199.b.100791.1 |
11199.b |
\( 3 \cdot 3733 \) |
\( - 3^{3} \cdot 3733 \) |
$2$ |
$2$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
|
✓ |
✓ |
$C_2$ |
$C_2$ |
$12$ |
$0$ |
|
✓ |
✓ |
$1$ |
\( 3 \) |
\(0.010762\) |
\(14.256601\) |
\(0.460290\) |
$[216,3828,178560,403164]$ |
$[108,-152,2216,54056,100791]$ |
$[544195584/3733,-7091712/3733,957312/3733]$ |
$y^2 + x^3y = x^3 + x^2 - x + 1$ |
| 11236.a.44944.1 |
11236.a |
\( 2^{2} \cdot 53^{2} \) |
\( - 2^{4} \cdot 53^{2} \) |
$2$ |
$2$ |
$\mathsf{trivial}$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$12$ |
$0$ |
2.15.2, 3.90.1 |
✓ |
✓ |
$1$ |
\( 3 \) |
\(0.010182\) |
\(16.735874\) |
\(0.511197\) |
$[216,2400,149796,179776]$ |
$[108,86,-1728,-48505,44944]$ |
$[918330048/2809,6770952/2809,-1259712/2809]$ |
$y^2 + (x^3 + x)y = -x^2 + 1$ |
| 11271.b.912951.1 |
11271.b |
\( 3 \cdot 13 \cdot 17^{2} \) |
\( - 3^{5} \cdot 13 \cdot 17^{2} \) |
$2$ |
$2$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
|
✓ |
✓ |
$C_2$ |
$C_2$ |
$12$ |
$0$ |
|
✓ |
✓ |
$1$ |
\( 5 \) |
\(0.007288\) |
\(12.663441\) |
\(0.461473\) |
$[504,9588,1468800,3651804]$ |
$[252,1048,-14296,-1175224,912951]$ |
$[4182119424/3757,69017088/3757,-11208064/11271]$ |
$y^2 + x^3y = 3x^3 + 7x^2 + 7x + 3$ |
| 11383.a.11383.1 |
11383.a |
\( 11383 \) |
\( -11383 \) |
$2$ |
$2$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
|
✓ |
✓ |
$C_2$ |
$C_2$ |
$12$ |
$0$ |
|
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.018180\) |
\(22.993630\) |
\(0.418013\) |
$[180,4857,-36819,-1457024]$ |
$[45,-118,3252,33104,-11383]$ |
$[-184528125/11383,10752750/11383,-6585300/11383]$ |
$y^2 + (x^3 + 1)y = -x^4 + 2x^3 - x$ |
| 11565.a.34695.1 |
11565.a |
\( 3^{2} \cdot 5 \cdot 257 \) |
\( - 3^{3} \cdot 5 \cdot 257 \) |
$2$ |
$2$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
|
✓ |
✓ |
$C_2$ |
$C_2$ |
$12$ |
$0$ |
|
✓ |
✓ |
$1$ |
\( 3 \) |
\(0.007031\) |
\(23.285228\) |
\(0.491128\) |
$[680,14356,2629040,-138780]$ |
$[340,2424,24840,642456,-34695]$ |
$[-908708480000/6939,-6351526400/2313,-21270400/257]$ |
$y^2 + x^3y = -2x^4 - x^3 + 7x^2 - 5x + 1$ |
| 11705.a.11705.1 |
11705.a |
\( 5 \cdot 2341 \) |
\( - 5 \cdot 2341 \) |
$2$ |
$3$ |
$\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$12$ |
$0$ |
2.15.1 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.079630\) |
\(24.103001\) |
\(0.479833\) |
$[244,14137,55181,-1498240]$ |
$[61,-434,9740,101446,-11705]$ |
$[-844596301/11705,98509754/11705,-7248508/2341]$ |
$y^2 + (x^3 + 1)y = -x^4 + x^3 + 2x^2 - 2x$ |
| 11708.a.23416.1 |
11708.a |
\( 2^{2} \cdot 2927 \) |
\( - 2^{3} \cdot 2927 \) |
$2$ |
$2$ |
$\Z/3\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,3$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$12$ |
$0$ |
2.10.1, 3.80.1 |
✓ |
✓ |
$1$ |
\( 3 \) |
\(0.081920\) |
\(19.241825\) |
\(0.525430\) |
$[4,145,-301991,-2997248]$ |
$[1,-6,4196,1040,-23416]$ |
$[-1/23416,3/11708,-1049/5854]$ |
$y^2 + (x^3 + x + 1)y = -x^4 + x^3 - 2x$ |
