| 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 |
| 336.a.172032.1 |
336.a |
\( 2^{4} \cdot 3 \cdot 7 \) |
\( - 2^{13} \cdot 3 \cdot 7 \) |
$0$ |
$2$ |
$\Z/2\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$0$ |
$0$ |
2.45.1, 3.720.5 |
|
|
$2$ |
\( 1 \) |
\(1.000000\) |
\(0.356066\) |
\(0.178033\) |
$[16916,151117825,232872423961,-21504]$ |
$[16916,-88822256,277597802496,-798387183476800,-172032]$ |
$[-1352659309173012149/168,419870026410625699/168,-461744933079368]$ |
$y^2 + (x^3 + x)y = -x^6 + 15x^4 - 75x^2 - 56$ |
| 644.a.2576.1 |
644.a |
\( 2^{2} \cdot 7 \cdot 23 \) |
\( - 2^{4} \cdot 7 \cdot 23 \) |
$0$ |
$2$ |
$\Z/6\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$0$ |
$0$ |
2.45.1, 3.720.4 |
|
|
$2$ |
\( 1 \) |
\(1.000000\) |
\(3.928431\) |
\(0.218246\) |
$[39036,4124865,50880984159,329728]$ |
$[9759,3796384,1910683600,1058457444236,2576]$ |
$[88516980336138032799/2576,220529201888022246/161,70640465629725]$ |
$y^2 + (x^2 + x)y = -5x^6 + 11x^5 - 20x^4 + 20x^3 - 20x^2 + 11x - 5$ |
| 672.a.172032.1 |
672.a |
\( 2^{5} \cdot 3 \cdot 7 \) |
\( 2^{13} \cdot 3 \cdot 7 \) |
$0$ |
$2$ |
$\Z/4\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$0$ |
$0$ |
2.45.1, 3.720.5 |
|
|
$2$ |
\( 2 \) |
\(1.000000\) |
\(1.113349\) |
\(0.278337\) |
$[16916,151117825,232872423961,-21504]$ |
$[16916,-88822256,277597802496,-798387183476800,-172032]$ |
$[-1352659309173012149/168,419870026410625699/168,-461744933079368]$ |
$y^2 + (x^3 + x)y = -x^6 - 16x^4 - 75x^2 + 56$ |
| 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 |
|
✓ |
$1$ |
\( 3 \) |
\(1.000000\) |
\(7.177121\) |
\(0.265819\) |
$[1244,1249,129167,2249728]$ |
$[311,3978,72332,1667692,17576]$ |
$[2909390022551/17576,4602275343/676,10349147/26]$ |
$y^2 + (x^2 + x)y = -x^6 + 3x^5 - 6x^4 + 6x^3 - 6x^2 + 3x - 1$ |
| 708.a.181248.1 |
708.a |
\( 2^{2} \cdot 3 \cdot 59 \) |
\( - 2^{10} \cdot 3 \cdot 59 \) |
$0$ |
$3$ |
$\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,5$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$0$ |
$0$ |
2.15.1 |
✓ |
✓ |
$4$ |
\( 1 \) |
\(1.000000\) |
\(0.325344\) |
\(0.325344\) |
$[234100,3468879025,202585466081177,-23199744]$ |
$[58525,-1820975,60952909,62829762150,-181248]$ |
$[-686605237334059580078125/181248,365029741228054296875/181248,-208774418179643125/181248]$ |
$y^2 + (x^3 + 1)y = -x^6 - 4x^5 + 9x^4 + 48x^3 - 41x^2 - 98x - 36$ |
| 784.b.25088.1 |
784.b |
\( 2^{4} \cdot 7^{2} \) |
\( - 2^{9} \cdot 7^{2} \) |
$0$ |
$2$ |
$\Z/2\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2$ |
$C_2$ |
$0$ |
$0$ |
2.45.1, 3.720.5 |
|
|
$2$ |
\( 1 \) |
\(1.000000\) |
\(0.626117\) |
\(0.313058\) |
$[2740,15382525,36170522453,3136]$ |
$[2740,-9942200,-24298750736,-41356479464160,25088]$ |
$[301635777856250/49,-399451653071875/49,-712598832131225/98]$ |
$y^2 + (x^2 + 1)y = -x^6 - 3x^5 + 7x^4 + 2x^3 - 49x^2 + 41x - 9$ |
| 784.b.76832.1 |
784.b |
\( 2^{4} \cdot 7^{2} \) |
\( - 2^{5} \cdot 7^{4} \) |
$0$ |
$1$ |
$\Z/6\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2$ |
$C_2$ |
$0$ |
$0$ |
2.45.1, 3.2160.20 |
|
✓ |
$1$ |
\( 3 \) |
\(1.000000\) |
\(3.756700\) |
\(0.313058\) |
$[1520,132280,50979316,307328]$ |
$[760,2020,6076,134340,76832]$ |
$[7923516800000/2401,27710360000/2401,2238200/49]$ |
$y^2 + (x + 1)y = -x^6 + 4x^5 - 4x^4 - 2x^3 + 10x - 9$ |
| 800.a.8000.1 |
800.a |
\( 2^{5} \cdot 5^{2} \) |
\( 2^{6} \cdot 5^{3} \) |
$0$ |
$1$ |
$\Z/4\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$0$ |
$0$ |
2.90.4, 3.720.5 |
|
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(5.590050\) |
\(0.349378\) |
$[192,11604,322392,-1000]$ |
$[192,-6200,142400,-2774800,-8000]$ |
$[-4076863488/125,27426816/5,-3280896/5]$ |
$y^2 + (x^3 + x^2 + x + 1)y = -x^6 + 2x^4 + 4x^3 + 2x^2 - 1$ |
| 816.b.52224.1 |
816.b |
\( 2^{4} \cdot 3 \cdot 17 \) |
\( - 2^{10} \cdot 3 \cdot 17 \) |
$0$ |
$2$ |
$\Z/6\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$0$ |
$0$ |
2.45.1, 3.720.4 |
|
|
$2$ |
\( 3 \) |
\(1.000000\) |
\(2.423742\) |
\(0.403957\) |
$[15964,2380825,11444690699,6528]$ |
$[15964,9031504,6282991104,4683401370560,52224]$ |
$[1012531723491160951/51,35882713644370099/51,30660536527816]$ |
$y^2 + (x^3 + x)y = -x^6 - 12x^4 - 27x^2 - 17$ |
| 847.d.847.1 |
847.d |
\( 7 \cdot 11^{2} \) |
\( - 7 \cdot 11^{2} \) |
$0$ |
$1$ |
$\Z/3\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$0$ |
$0$ |
2.15.2, 3.720.4 |
|
|
$2$ |
\( 1 \) |
\(1.000000\) |
\(1.179535\) |
\(0.262119\) |
$[80408,402403732,8094753026048,3388]$ |
$[40204,281112,1967560,19956424,847]$ |
$[105037970421355597057024/847,18267839107785466368/847,454326923025280/121]$ |
$y^2 + (x^3 + x^2 + x + 1)y = -12x^6 - 15x^5 + 9x^4 + 31x^3 + 9x^2 - 15x - 12$ |
| 847.d.456533.1 |
847.d |
\( 7 \cdot 11^{2} \) |
\( 7^{3} \cdot 11^{3} \) |
$0$ |
$1$ |
$\Z/15\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$0$ |
$0$ |
2.15.2, 3.2160.20 |
|
|
$2$ |
\( 3 \) |
\(1.000000\) |
\(9.829455\) |
\(0.262119\) |
$[90952,10132,303847072,1826132]$ |
$[45476,86167752,217689875480,618695823148744,456533]$ |
$[194496275421254111077376/456533,736713878289412204032/41503,10847340081772160/11]$ |
$y^2 + y = -x^6 - 9x^5 - 22x^4 + 3x^3 + 37x^2 - 24x + 4$ |
| 936.a.1872.1 |
936.a |
\( 2^{3} \cdot 3^{2} \cdot 13 \) |
\( - 2^{4} \cdot 3^{2} \cdot 13 \) |
$0$ |
$3$ |
$\Z/2\Z\oplus\Z/4\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$0$ |
$0$ |
2.90.6, 3.90.1 |
|
|
$2$ |
\( 2 \) |
\(1.000000\) |
\(7.131061\) |
\(0.445691\) |
$[45352,11224,169415364,7488]$ |
$[22676,21423170,26983749312,38232821637503,1872]$ |
$[374724646811252438336/117,15612163699641478120/117,7411896491650496]$ |
$y^2 + (x^3 + x)y = -x^6 - 9x^4 - 32x^2 - 39$ |
| 961.a.961.1 |
961.a |
\( 31^{2} \) |
\( - 31^{2} \) |
$0$ |
$1$ |
$\mathsf{trivial}$ |
\(\mathsf{RM}\) |
\(\mathsf{RM}\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
✓ |
✓ |
$C_2$ |
$C_2$ |
$0$ |
$0$ |
2.15.2, 3.72.2 |
|
|
$2$ |
\( 1 \) |
\(1.000000\) |
\(0.224644\) |
\(0.449288\) |
$[66980,1011437281,14016353908561,-123008]$ |
$[16745,-30460094,12221475912,-180792178085599,-961]$ |
$[-1316514841399349215625/961,143016680917998700750/961,-3426841043882137800/961]$ |
$y^2 + (x^3 + x + 1)y = -x^6 - x^5 - 7x^4 + 74x^3 - 145x^2 + 99x - 33$ |
| 961.a.961.2 |
961.a |
\( 31^{2} \) |
\( - 31^{2} \) |
$0$ |
$1$ |
$\Z/5\Z$ |
\(\mathsf{RM}\) |
\(\mathsf{RM}\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
✓ |
✓ |
$C_2$ |
$C_2$ |
$0$ |
$0$ |
2.15.2, 3.72.2 |
|
|
$2$ |
\( 1 \) |
\(1.000000\) |
\(5.616097\) |
\(0.449288\) |
$[11260,503521,1770579599,123008]$ |
$[2815,309196,43449708,6677190401,961]$ |
$[176763257309509375/961,6897140364776500/961,344305262376300/961]$ |
$y^2 + (x^3 + x + 1)y = -x^6 + 2x^5 - 8x^4 + 12x^3 - 18x^2 + 12x - 7$ |
| 980.a.878080.1 |
980.a |
\( 2^{2} \cdot 5 \cdot 7^{2} \) |
\( - 2^{9} \cdot 5 \cdot 7^{3} \) |
$0$ |
$1$ |
$\Z/12\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$0$ |
$0$ |
2.45.1, 3.2160.20 |
|
✓ |
$1$ |
\( 2^{2} \cdot 3 \) |
\(1.000000\) |
\(4.677173\) |
\(0.389764\) |
$[2508,50745,41700723,112394240]$ |
$[627,14266,359660,5497016,878080]$ |
$[96903107471907/878080,251175228777/62720,144278343/896]$ |
$y^2 + (x^3 + 1)y = -x^6 + x^5 - 4x^4 + 2x^3 - 4x^2 + x - 1$ |
| 1050.a.131250.1 |
1050.a |
\( 2 \cdot 3 \cdot 5^{2} \cdot 7 \) |
\( - 2 \cdot 3 \cdot 5^{5} \cdot 7 \) |
$0$ |
$3$ |
$\Z/2\Z\oplus\Z/4\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$0$ |
$0$ |
2.90.6, 3.90.1 |
|
|
$2$ |
\( 2 \) |
\(1.000000\) |
\(6.612551\) |
\(0.413284\) |
$[11868,198609,759217863,16800000]$ |
$[2967,358520,56735700,9949557875,131250]$ |
$[76641937806559869/43750,312136655012892/4375,475666111026/125]$ |
$y^2 + (x^2 + x)y = 3x^6 + 8x^5 + 15x^4 + 17x^3 + 15x^2 + 8x + 3$ |
| 1083.b.87723.1 |
1083.b |
\( 3 \cdot 19^{2} \) |
\( - 3^{5} \cdot 19^{2} \) |
$0$ |
$1$ |
$\Z/15\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$0$ |
$0$ |
2.15.2, 3.720.4 |
|
|
$2$ |
\( 5 \) |
\(1.000000\) |
\(5.981341\) |
\(0.265837\) |
$[5464,8692,15768656,350892]$ |
$[2732,309544,46549080,7838649656,87723]$ |
$[152196082896530432/87723,6311963449851392/87723,1429770125440/361]$ |
$y^2 + y = -x^6 - 3x^5 - 8x^4 - 11x^3 - 14x^2 - 9x - 6$ |
| 1083.b.390963.1 |
1083.b |
\( 3 \cdot 19^{2} \) |
\( - 3 \cdot 19^{4} \) |
$0$ |
$1$ |
$\mathsf{trivial}$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$0$ |
$0$ |
2.15.2, 3.720.5 |
|
|
$2$ |
\( 1 \) |
\(1.000000\) |
\(0.132919\) |
\(0.265837\) |
$[150440,1945515892,68956865081488,-1563852]$ |
$[75220,-88500632,98386538568,-107931608328616,-390963]$ |
$[-2408056349828975363200000/390963,1982406707133537344000/20577,-27053302090985600/19]$ |
$y^2 + y = -x^6 + 3x^5 - 50x^4 + 95x^3 - 14x^2 - 33x - 6$ |
| 1104.b.141312.1 |
1104.b |
\( 2^{4} \cdot 3 \cdot 23 \) |
\( - 2^{11} \cdot 3 \cdot 23 \) |
$0$ |
$2$ |
$\Z/2\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$0$ |
$0$ |
2.45.1, 3.90.1 |
|
|
$2$ |
\( 1 \) |
\(1.000000\) |
\(0.712625\) |
\(0.356313\) |
$[14220,9418737,54280328031,17664]$ |
$[14220,2146192,-16790479872,-60841690970176,141312]$ |
$[189267815942240625/46,2008843709918625/46,-24026098775400]$ |
$y^2 + (x^3 + x)y = -x^6 - 3x^4 + 29x^2 - 46$ |
| 1170.a.10530.1 |
1170.a |
\( 2 \cdot 3^{2} \cdot 5 \cdot 13 \) |
\( - 2 \cdot 3^{4} \cdot 5 \cdot 13 \) |
$0$ |
$4$ |
$\Z/2\Z\oplus\Z/6\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$0$ |
$0$ |
2.90.6, 3.720.4 |
✓ |
✓ |
$4$ |
\( 3 \) |
\(1.000000\) |
\(5.542030\) |
\(0.461836\) |
$[507196,192673,32552199279,1347840]$ |
$[126799,669908072,4718980180980,37396285759331459,10530]$ |
$[32777750301275239538233999/10530,682861614668954802420364/5265,7205289570406928666]$ |
$y^2 + (x^2 + x)y = 15x^6 + 28x^5 + 62x^4 + 59x^3 + 62x^2 + 28x + 15$ |
| 1253.a.1253.1 |
1253.a |
\( 7 \cdot 179 \) |
\( - 7 \cdot 179 \) |
$0$ |
$1$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$3$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$0$ |
$0$ |
3.720.5 |
|
|
$2$ |
\( 1 \) |
\(1.000000\) |
\(0.207464\) |
\(0.414928\) |
$[413532,9381037161,999361725629499,160384]$ |
$[103383,54458647,-97243994481,-3254780028624958,1253]$ |
$[1687126365978608485162449/179,8596391751971448839127/179,-829487756384515053]$ |
$y^2 + (x^3 + x^2 + 1)y = -x^6 + 2x^5 - 33x^3 + 43x^2 + 15x - 330$ |
| 1269.b.102789.1 |
1269.b |
\( 3^{3} \cdot 47 \) |
\( - 3^{7} \cdot 47 \) |
$0$ |
$2$ |
$\Z/10\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,5$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$0$ |
$0$ |
2.15.1 |
|
|
$2$ |
\( 5 \) |
\(1.000000\) |
\(4.110305\) |
\(0.411030\) |
$[91192,19900,603982075,1692]$ |
$[136788,779593356,5923938871071,50639487394179303,102789]$ |
$[197075993647247827966976/423,2737061778548953841408/141,152047414479420367856/141]$ |
$y^2 + (x^3 + x)y = -2x^6 - x^5 - 21x^4 - 8x^3 - 80x^2 - 16x - 103$ |
| 1344.a.4032.1 |
1344.a |
\( 2^{6} \cdot 3 \cdot 7 \) |
\( - 2^{6} \cdot 3^{2} \cdot 7 \) |
$0$ |
$3$ |
$\Z/2\Z\oplus\Z/4\Z$ |
\(\mathsf{CM} \times \Q\) |
\(\Q \times \Q\) |
✓ |
$N(\mathrm{U}(1)\times\mathrm{SU}(2))$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$0$ |
$0$ |
2.90.6, 3.270.2 |
|
|
$2$ |
\( 2 \) |
\(1.000000\) |
\(6.691213\) |
\(0.418201\) |
$[48576,2301,37257288,504]$ |
$[48576,98316290,265314615552,805457471422463,4032]$ |
$[469554780013829554176/7,19564477241823191040/7,155268783788507136]$ |
$y^2 + xy = -x^6 - 12x^4 - 48x^2 - 63$ |
| 1460.a.5840.1 |
1460.a |
\( 2^{2} \cdot 5 \cdot 73 \) |
\( - 2^{4} \cdot 5 \cdot 73 \) |
$0$ |
$1$ |
$\Z/6\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$0$ |
$0$ |
2.90.1, 3.720.4 |
✓ |
✓ |
$1$ |
\( 3 \) |
\(1.000000\) |
\(6.680554\) |
\(0.556713\) |
$[139800,8112,377842260,23360]$ |
$[69900,203582398,790567831360,3453724659158399,5840]$ |
$[20859115637937375000000/73,869124046354917525000/73,661425056456040000]$ |
$y^2 + (x^3 + x)y = x^6 + 14x^4 + 56x^2 + 73$ |
| 1470.a.2940.1 |
1470.a |
\( 2 \cdot 3 \cdot 5 \cdot 7^{2} \) |
\( - 2^{2} \cdot 3 \cdot 5 \cdot 7^{2} \) |
$0$ |
$3$ |
$\Z/2\Z\oplus\Z/4\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$0$ |
$0$ |
2.180.7, 3.90.1 |
|
|
$2$ |
\( 2 \) |
\(1.000000\) |
\(8.519256\) |
\(0.532453\) |
$[2556,6897,5825079,376320]$ |
$[639,16726,574080,21769511,2940]$ |
$[35512646315733/980,727349955399/490,3906815328/49]$ |
$y^2 + (x^2 + x)y = -x^6 + 2x^5 - 5x^4 + 4x^3 - 5x^2 + 2x - 1$ |
| 1560.a.199680.1 |
1560.a |
\( 2^{3} \cdot 3 \cdot 5 \cdot 13 \) |
\( 2^{10} \cdot 3 \cdot 5 \cdot 13 \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/2\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$0$ |
$0$ |
2.90.6, 3.90.1 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(1.000000\) |
\(4.908583\) |
\(0.613573\) |
$[2397240,72897,58245771285,24960]$ |
$[2397240,239448268802,31889707498721280,4777952242989938687999,199680]$ |
$[5154260479603163815124340000/13,214760809729321817508682425/13,917780865738818887929600]$ |
$y^2 + x^2y = 39x^6 - 149x^4 + 189x^2 - 80$ |
| 1564.a.50048.1 |
1564.a |
\( 2^{2} \cdot 17 \cdot 23 \) |
\( 2^{7} \cdot 17 \cdot 23 \) |
$0$ |
$2$ |
$\Z/6\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$0$ |
$0$ |
2.45.1, 3.720.4 |
|
|
$2$ |
\( 3 \) |
\(1.000000\) |
\(2.971202\) |
\(0.495200\) |
$[21108,16867065,141771021933,6406144]$ |
$[5277,457486,-598707020,-842167596184,50048]$ |
$[4091998547529050157/50048,33613140838101219/25024,-10659867094845/32]$ |
$y^2 + (x^3 + 1)y = -x^6 + 7x^5 + 8x^4 + 17x^3 + 8x^2 + 7x - 1$ |
| 1680.a.16800.1 |
1680.a |
\( 2^{4} \cdot 3 \cdot 5 \cdot 7 \) |
\( - 2^{5} \cdot 3 \cdot 5^{2} \cdot 7 \) |
$0$ |
$3$ |
$\Z/2\Z\oplus\Z/4\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$0$ |
$0$ |
2.90.6, 3.90.1 |
|
|
$2$ |
\( 2^{2} \) |
\(1.000000\) |
\(5.090690\) |
\(0.636336\) |
$[404040,44088,5935895700,67200]$ |
$[202020,1700496002,19085068732800,240969733145567999,16800]$ |
$[20029151526577171524000,834544374130868293620,46363176164438078400]$ |
$y^2 + (x^3 + x)y = -x^6 - 18x^4 - 136x^2 - 350$ |
| 1795.a.224375.1 |
1795.a |
\( 5 \cdot 359 \) |
\( - 5^{4} \cdot 359 \) |
$0$ |
$2$ |
$\Z/6\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,3$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$0$ |
$0$ |
2.15.1, 3.80.1 |
|
|
$2$ |
\( 2 \) |
\(1.000000\) |
\(5.099516\) |
\(0.566613\) |
$[52684,91537,1605316279,28720000]$ |
$[13171,7224321,5280645071,4340140579775,224375]$ |
$[396363585850146434851/224375,16506434926310410731/224375,916061176327187111/224375]$ |
$y^2 + (x^3 + x^2 + x)y = -x^6 - 8x^4 + 3x^3 - 23x^2 + 6x - 23$ |
| 1870.a.226270.1 |
1870.a |
\( 2 \cdot 5 \cdot 11 \cdot 17 \) |
\( 2 \cdot 5 \cdot 11^{3} \cdot 17 \) |
$0$ |
$0$ |
$\Z/3\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,3$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$0$ |
$0$ |
2.20.2, 3.720.4 |
✓ |
✓ |
$1$ |
\( 3 \) |
\(1.000000\) |
\(1.924846\) |
\(0.641615\) |
$[14568,14455716,51876443577,-905080]$ |
$[7284,-198592,5333559,-147284677,-226270]$ |
$[-10252261852576307712/113135,38374397094057984/113135,-1169342169912/935]$ |
$y^2 + (x + 1)y = -2x^6 + x^5 - x^4 + 9x^3 - 2x^2 + 2x - 9$ |
| 1920.a.368640.1 |
1920.a |
\( 2^{7} \cdot 3 \cdot 5 \) |
\( - 2^{13} \cdot 3^{2} \cdot 5 \) |
$0$ |
$3$ |
$\Z/2\Z\oplus\Z/4\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$0$ |
$0$ |
2.90.6, 3.90.1 |
|
|
$2$ |
\( 2^{2} \) |
\(1.000000\) |
\(5.004698\) |
\(0.625587\) |
$[8952,6072,17987052,1440]$ |
$[17904,13340192,13237770240,14762078945024,368640]$ |
$[24952719973569408/5,1038436236963696/5,11510985848256]$ |
$y^2 + (x^3 + x^2 + x + 1)y = 5x^6 + 6x^5 + 17x^4 + 12x^3 + 17x^2 + 6x + 5$ |
| 1923.a.1923.1 |
1923.a |
\( 3 \cdot 641 \) |
\( - 3 \cdot 641 \) |
$0$ |
$1$ |
$\Z/5\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$5$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$0$ |
$0$ |
|
|
|
$2$ |
\( 1 \) |
\(1.000000\) |
\(8.754490\) |
\(0.700359\) |
$[1180,5521,2133607,246144]$ |
$[295,3396,48644,704291,1923]$ |
$[2234138434375/1923,29061128500/641,4233244100/1923]$ |
$y^2 + (x^3 + x + 1)y = -x^6 + x^5 - 3x^4 + 2x^3 - 3x^2 + x - 1$ |
| 1988.a.3976.1 |
1988.a |
\( 2^{2} \cdot 7 \cdot 71 \) |
\( - 2^{3} \cdot 7 \cdot 71 \) |
$0$ |
$2$ |
$\Z/6\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$0$ |
$0$ |
2.45.1, 3.720.4 |
|
|
$2$ |
\( 1 \) |
\(1.000000\) |
\(5.602674\) |
\(0.311260\) |
$[51708,997905,16868749287,508928]$ |
$[12927,6921226,4915471148,3909731546780,3976]$ |
$[360984657535082593407/3976,7475603889680115579/1988,413184735572859/2]$ |
$y^2 + (x^2 + x)y = 6x^6 + 16x^5 + 31x^4 + 35x^3 + 31x^2 + 16x + 6$ |
| 2016.a.4032.1 |
2016.a |
\( 2^{5} \cdot 3^{2} \cdot 7 \) |
\( - 2^{6} \cdot 3^{2} \cdot 7 \) |
$0$ |
$1$ |
$\Z/4\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$0$ |
$0$ |
2.45.1, 3.90.1 |
|
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(8.388518\) |
\(0.524282\) |
$[320,52,2616,504]$ |
$[320,4232,76608,1651184,4032]$ |
$[52428800000/63,2166784000/63,1945600]$ |
$y^2 + y = -2x^6 - 6x^5 - 10x^4 - 10x^3 - 7x^2 - 3x - 1$ |
| 2058.a.2058.1 |
2058.a |
\( 2 \cdot 3 \cdot 7^{3} \) |
\( 2 \cdot 3 \cdot 7^{3} \) |
$0$ |
$3$ |
$\Z/4\Z$ |
\(\mathsf{CM} \times \Q\) |
\(\Q \times \Q\) |
✓ |
$N(\mathrm{U}(1)\times\mathrm{SU}(2))$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$0$ |
$0$ |
2.45.1, 3.270.2 |
|
✓ |
$4$ |
\( 1 \) |
\(1.000000\) |
\(3.359562\) |
\(0.839890\) |
$[40908,115154025,1158334769067,-263424]$ |
$[10227,-440104,18634308,-779615725,-2058]$ |
$[-108724120940360583/2,228746634549804,-947031470154]$ |
$y^2 + (x^3 + 1)y = 5x^6 - 4x^5 - 5x^4 + 14x^3 - 5x^2 - 4x + 5$ |
| 2058.a.16464.1 |
2058.a |
\( 2 \cdot 3 \cdot 7^{3} \) |
\( - 2^{4} \cdot 3 \cdot 7^{3} \) |
$0$ |
$2$ |
$\Z/8\Z$ |
\(\mathsf{CM} \times \Q\) |
\(\Q \times \Q\) |
✓ |
$N(\mathrm{U}(1)\times\mathrm{SU}(2))$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$0$ |
$0$ |
2.45.1, 3.270.2 |
|
|
$2$ |
\( 2^{2} \) |
\(1.000000\) |
\(6.719123\) |
\(0.839890\) |
$[16716,21945,119839251,2107392]$ |
$[4179,726754,168337344,43827596015,16464]$ |
$[1238643936365031/16,25772655805407/8,178562334636]$ |
$y^2 + (x^3 + 1)y = -3x^6 + 5x^5 - 11x^4 + 10x^3 - 11x^2 + 5x - 3$ |
| 2178.a.13068.1 |
2178.a |
\( 2 \cdot 3^{2} \cdot 11^{2} \) |
\( - 2^{2} \cdot 3^{3} \cdot 11^{2} \) |
$0$ |
$1$ |
$\Z/4\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$0$ |
$0$ |
2.180.4, 3.90.1 |
|
✓ |
$1$ |
\( 2 \) |
\(1.000000\) |
\(6.589693\) |
\(0.823712\) |
$[1196,22441,8056043,1672704]$ |
$[299,2790,27648,120663,13068]$ |
$[2389769101499/13068,4143289345/726,22886656/121]$ |
$y^2 + (x^3 + 1)y = -x^6 - x^4 - x^2 - 1$ |
| 2178.b.287496.1 |
2178.b |
\( 2 \cdot 3^{2} \cdot 11^{2} \) |
\( - 2^{3} \cdot 3^{3} \cdot 11^{3} \) |
$0$ |
$1$ |
$\Z/2\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$0$ |
$0$ |
2.90.1, 3.720.5 |
|
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(2.382791\) |
\(0.595698\) |
$[8284,1201825,3762835279,36799488]$ |
$[2071,128634,-2892384,-5634208305,287496]$ |
$[38097852361039351/287496,17312195022539/4356,-1423961612/33]$ |
$y^2 + (x^2 + x)y = -x^6 - 2x^5 + 3x^4 - 8x^2 + 9x - 3$ |
| 2208.a.141312.1 |
2208.a |
\( 2^{5} \cdot 3 \cdot 23 \) |
\( 2^{11} \cdot 3 \cdot 23 \) |
$0$ |
$2$ |
$\Z/4\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$0$ |
$0$ |
2.45.1, 3.90.1 |
|
|
$2$ |
\( 2 \) |
\(1.000000\) |
\(2.228239\) |
\(0.557060\) |
$[14220,9418737,54280328031,17664]$ |
$[14220,2146192,-16790479872,-60841690970176,141312]$ |
$[189267815942240625/46,2008843709918625/46,-24026098775400]$ |
$y^2 + (x^3 + x)y = -x^6 + 2x^4 + 29x^2 + 46$ |
| 2280.a.4560.1 |
2280.a |
\( 2^{3} \cdot 3 \cdot 5 \cdot 19 \) |
\( - 2^{4} \cdot 3 \cdot 5 \cdot 19 \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/2\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$0$ |
$0$ |
2.90.6, 3.90.1 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(1.000000\) |
\(6.444145\) |
\(0.805518\) |
$[110088,26232,961521588,18240]$ |
$[55044,126239042,386012372160,1327842322024319,4560]$ |
$[10527098668705143569088/95,438613920807785896536/95,256481682672194496]$ |
$y^2 + (x^3 + x)y = x^6 + 13x^4 + 48x^2 + 57$ |
| 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 |
|
✓ |
$1$ |
\( 2 \) |
\(1.000000\) |
\(5.683509\) |
\(0.710439\) |
$[152,109,5469,18]$ |
$[608,14240,405504,10942208,147456]$ |
$[5071050752/9,195344320/9,1016576]$ |
$y^2 = -x^6 - 2x^4 - 2x^2 - 1$ |
| 2312.c.591872.1 |
2312.c |
\( 2^{3} \cdot 17^{2} \) |
\( - 2^{11} \cdot 17^{2} \) |
$0$ |
$2$ |
$\Z/4\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$0$ |
$0$ |
2.45.1, 3.90.1 |
|
|
$2$ |
\( 1 \) |
\(1.000000\) |
\(4.435882\) |
\(0.554485\) |
$[25032,12945,107835483,73984]$ |
$[25032,26099746,36272201728,56692253097695,591872]$ |
$[4798967385220266384/289,399781759107157497/578,11097753293700864/289]$ |
$y^2 + xy = -32x^6 - 31x^4 - 10x^2 - 1$ |
| 2380.a.33320.1 |
2380.a |
\( 2^{2} \cdot 5 \cdot 7 \cdot 17 \) |
\( - 2^{3} \cdot 5 \cdot 7^{2} \cdot 17 \) |
$0$ |
$2$ |
$\Z/6\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$0$ |
$0$ |
2.45.1, 3.720.4 |
|
|
$2$ |
\( 2 \cdot 3 \) |
\(1.000000\) |
\(2.653125\) |
\(0.884375\) |
$[420444,26532705,3672958564431,4264960]$ |
$[105111,459241234,2669460305260,17421782785085276,33320]$ |
$[754730529630134311594503/1960,15685792362611161588431/980,1770291589173321231/2]$ |
$y^2 + (x^2 + x)y = -14x^6 + 26x^5 - 56x^4 + 53x^3 - 56x^2 + 26x - 14$ |
| 2484.a.9936.1 |
2484.a |
\( 2^{2} \cdot 3^{3} \cdot 23 \) |
\( - 2^{4} \cdot 3^{3} \cdot 23 \) |
$0$ |
$2$ |
$\Z/6\Z$ |
\(\mathsf{CM} \times \Q\) |
\(\Q \times \Q\) |
✓ |
$N(\mathrm{U}(1)\times\mathrm{SU}(2))$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$0$ |
$0$ |
2.45.1, 3.720.4 |
|
|
$2$ |
\( 3 \) |
\(1.000000\) |
\(5.060189\) |
\(0.843365\) |
$[27960,133920,1232036820,39744]$ |
$[13980,8121030,6274451520,5441425997175,9936]$ |
$[1236095741507400000/23,51362822628555000/23,123418006728000]$ |
$y^2 + (x^3 + x)y = -x^6 - 8x^4 - 24x^2 - 23$ |
| 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 |
|
✓ |
$1$ |
\( 5 \) |
\(1.000000\) |
\(3.411821\) |
\(0.682364\) |
$[860,36865,8199455,16384]$ |
$[1075,9750,107500,5125000,400000]$ |
$[459401384375/128,1937983125/64,9938375/32]$ |
$y^2 + (x^3 + 1)y = -2x^6 - 2x^5 + 2x^3 - 2x - 2$ |
| 2520.c.680400.1 |
2520.c |
\( 2^{3} \cdot 3^{2} \cdot 5 \cdot 7 \) |
\( - 2^{4} \cdot 3^{5} \cdot 5^{2} \cdot 7 \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/4\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$0$ |
$0$ |
2.90.6, 3.90.1 |
|
✓ |
$1$ |
\( 2^{3} \) |
\(1.000000\) |
\(4.065285\) |
\(0.508161\) |
$[202664,70648,4771785956,2721600]$ |
$[101332,427828818,2408353617600,15251447816841519,680400]$ |
$[95392679863974687468736/6075,1324861868713610149384/2025,981325180099899712/27]$ |
$y^2 + (x^2 + 1)y = -75x^6 - 65x^4 - 19x^2 - 2$ |
| 2610.a.2610.1 |
2610.a |
\( 2 \cdot 3^{2} \cdot 5 \cdot 29 \) |
\( - 2 \cdot 3^{2} \cdot 5 \cdot 29 \) |
$0$ |
$4$ |
$\Z/2\Z\oplus\Z/4\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$0$ |
$0$ |
2.90.6, 3.90.1 |
✓ |
✓ |
$4$ |
\( 1 \) |
\(1.000000\) |
\(6.376791\) |
\(0.398549\) |
$[127180,225577,9528751755,334080]$ |
$[31795,42112352,74354061060,147659295107699,2610]$ |
$[6498664883066809874375/522,135358641081021227600/261,28799294242815650]$ |
$y^2 + (x^3 + 1)y = 8x^6 + 19x^5 + 39x^4 + 41x^3 + 39x^2 + 19x + 8$ |
| 2640.a.2640.1 |
2640.a |
\( 2^{4} \cdot 3 \cdot 5 \cdot 11 \) |
\( - 2^{4} \cdot 3 \cdot 5 \cdot 11 \) |
$0$ |
$3$ |
$\Z/2\Z\oplus\Z/2\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$0$ |
$0$ |
2.90.6, 3.90.1 |
|
|
$2$ |
\( 1 \) |
\(1.000000\) |
\(6.936322\) |
\(0.867040\) |
$[63768,10392,220729308,10560]$ |
$[31884,42356162,75020763840,149479393726079,2640]$ |
$[686471900571962215488/55,28601826290311163976/55,28888377841215936]$ |
$y^2 + (x^3 + x)y = -x^6 - 10x^4 - 40x^2 - 55$ |
| 2688.a.172032.1 |
2688.a |
\( 2^{7} \cdot 3 \cdot 7 \) |
\( - 2^{13} \cdot 3 \cdot 7 \) |
$0$ |
$3$ |
$\Z/2\Z\oplus\Z/4\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$0$ |
$0$ |
2.90.6, 3.90.1 |
|
|
$2$ |
\( 2^{2} \) |
\(1.000000\) |
\(4.951816\) |
\(0.618977\) |
$[4248,2904,4071996,672]$ |
$[8496,2999840,1408899072,742741622528,172032]$ |
$[1801197437083776/7,74856652932240/7,591152665536]$ |
$y^2 + y = -12x^6 - 36x^5 - 61x^4 - 62x^3 - 42x^2 - 17x - 4$ |
| 2730.a.13650.1 |
2730.a |
\( 2 \cdot 3 \cdot 5 \cdot 7 \cdot 13 \) |
\( 2 \cdot 3 \cdot 5^{2} \cdot 7 \cdot 13 \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/2\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$0$ |
$0$ |
2.90.6, 3.90.1 |
|
✓ |
$1$ |
\( 2 \) |
\(1.000000\) |
\(7.805946\) |
\(0.975743\) |
$[656916,183993,40270870029,1747200]$ |
$[164229,1123790852,10253140797900,105239295264858299,13650]$ |
$[3063265468298882029687491/350,63817595233091546052726/175,20259278131640062086]$ |
$y^2 + (x^3 + 1)y = -x^6 - 5x^5 + 3x^4 + 56x^3 - 7x^2 - 195x + 131$ |
