| 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 |
|
|
$2$ |
\( 2 \) |
\(1.000000\) |
\(1.113349\) |
\(0.278337\) |
$[16916,151117825,232872423961,-21504]$ |
$[16916,-88822256,277597802496,-798387183476800,-172032]$ |
$[-1352659309173012149/168,419870026410625699/168,-461744933079368]$ |
$y^2 + (x^3 + x)y = -x^6 - 16x^4 - 75x^2 + 56$ |
| 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 |
|
|
$2$ |
\( 1 \) |
\(1.000000\) |
\(0.626117\) |
\(0.313058\) |
$[2740,15382525,36170522453,3136]$ |
$[2740,-9942200,-24298750736,-41356479464160,25088]$ |
$[301635777856250/49,-399451653071875/49,-712598832131225/98]$ |
$y^2 + (x^2 + 1)y = -x^6 - 3x^5 + 7x^4 + 2x^3 - 49x^2 + 41x - 9$ |
| 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 |
|
|
$2$ |
\( 1 \) |
\(1.000000\) |
\(5.616097\) |
\(0.449288\) |
$[11260,503521,1770579599,123008]$ |
$[2815,309196,43449708,6677190401,961]$ |
$[176763257309509375/961,6897140364776500/961,344305262376300/961]$ |
$y^2 + (x^3 + x + 1)y = -x^6 + 2x^5 - 8x^4 + 12x^3 - 18x^2 + 12x - 7$ |
| 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 |
|
|
$2$ |
\( 1 \) |
\(1.000000\) |
\(0.712625\) |
\(0.356313\) |
$[14220,9418737,54280328031,17664]$ |
$[14220,2146192,-16790479872,-60841690970176,141312]$ |
$[189267815942240625/46,2008843709918625/46,-24026098775400]$ |
$y^2 + (x^3 + x)y = -x^6 - 3x^4 + 29x^2 - 46$ |
| 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 |
|
|
$2$ |
\( 2 \) |
\(1.000000\) |
\(6.691213\) |
\(0.418201\) |
$[48576,2301,37257288,504]$ |
$[48576,98316290,265314615552,805457471422463,4032]$ |
$[469554780013829554176/7,19564477241823191040/7,155268783788507136]$ |
$y^2 + xy = -x^6 - 12x^4 - 48x^2 - 63$ |
| 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 |
|
|
$2$ |
\( 2 \) |
\(1.000000\) |
\(8.519256\) |
\(0.532453\) |
$[2556,6897,5825079,376320]$ |
$[639,16726,574080,21769511,2940]$ |
$[35512646315733/980,727349955399/490,3906815328/49]$ |
$y^2 + (x^2 + x)y = -x^6 + 2x^5 - 5x^4 + 4x^3 - 5x^2 + 2x - 1$ |
| 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 |
|
|
$2$ |
\( 2 \) |
\(1.000000\) |
\(5.099516\) |
\(0.566613\) |
$[52684,91537,1605316279,28720000]$ |
$[13171,7224321,5280645071,4340140579775,224375]$ |
$[396363585850146434851/224375,16506434926310410731/224375,916061176327187111/224375]$ |
$y^2 + (x^3 + x^2 + x)y = -x^6 - 8x^4 + 3x^3 - 23x^2 + 6x - 23$ |
| 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 |
|
|
$2$ |
\( 1 \) |
\(1.000000\) |
\(5.602674\) |
\(0.311260\) |
$[51708,997905,16868749287,508928]$ |
$[12927,6921226,4915471148,3909731546780,3976]$ |
$[360984657535082593407/3976,7475603889680115579/1988,413184735572859/2]$ |
$y^2 + (x^2 + x)y = 6x^6 + 16x^5 + 31x^4 + 35x^3 + 31x^2 + 16x + 6$ |
| 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 |
|
|
$2$ |
\( 2^{2} \) |
\(1.000000\) |
\(6.719123\) |
\(0.839890\) |
$[16716,21945,119839251,2107392]$ |
$[4179,726754,168337344,43827596015,16464]$ |
$[1238643936365031/16,25772655805407/8,178562334636]$ |
$y^2 + (x^3 + 1)y = -3x^6 + 5x^5 - 11x^4 + 10x^3 - 11x^2 + 5x - 3$ |
| 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 |
|
|
$2$ |
\( 2 \) |
\(1.000000\) |
\(2.228239\) |
\(0.557060\) |
$[14220,9418737,54280328031,17664]$ |
$[14220,2146192,-16790479872,-60841690970176,141312]$ |
$[189267815942240625/46,2008843709918625/46,-24026098775400]$ |
$y^2 + (x^3 + x)y = -x^6 + 2x^4 + 29x^2 + 46$ |
| 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 |
|
|
$2$ |
\( 3 \) |
\(1.000000\) |
\(5.060189\) |
\(0.843365\) |
$[27960,133920,1232036820,39744]$ |
$[13980,8121030,6274451520,5441425997175,9936]$ |
$[1236095741507400000/23,51362822628555000/23,123418006728000]$ |
$y^2 + (x^3 + x)y = -x^6 - 8x^4 - 24x^2 - 23$ |
| 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 |
|
|
$2$ |
\( 2^{2} \) |
\(1.000000\) |
\(4.951816\) |
\(0.618977\) |
$[4248,2904,4071996,672]$ |
$[8496,2999840,1408899072,742741622528,172032]$ |
$[1801197437083776/7,74856652932240/7,591152665536]$ |
$y^2 + y = -12x^6 - 36x^5 - 61x^4 - 62x^3 - 42x^2 - 17x - 4$ |
| 2872.a.367616.1 |
2872.a |
\( 2^{3} \cdot 359 \) |
\( - 2^{10} \cdot 359 \) |
$1$ |
$3$ |
$\Z/4\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$0$ |
$0$ |
2.15.1 |
|
|
$2$ |
\( 2 \) |
\(0.379949\) |
\(4.123656\) |
\(0.391695\) |
$[52152,30585,530058255,45952]$ |
$[52152,113305906,328168275184,1069100888228783,367616]$ |
$[376751407549293075168/359,15695150888732498127/359,871642853702611839/359]$ |
$y^2 + xy = -8x^6 - 28x^5 - 65x^4 - 88x^3 - 88x^2 - 51x - 20$ |
| 2890.b.49130.1 |
2890.b |
\( 2 \cdot 5 \cdot 17^{2} \) |
\( - 2 \cdot 5 \cdot 17^{3} \) |
$0$ |
$2$ |
$\Z/2\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$0$ |
$0$ |
2.45.1, 3.720.5 |
|
|
$2$ |
\( 1 \) |
\(1.000000\) |
\(2.094518\) |
\(1.047259\) |
$[2476,2018425,2623405459,6288640]$ |
$[619,-68136,-21426460,-4476373309,49130]$ |
$[90876845839099/49130,-475302024636/1445,-2840755654/17]$ |
$y^2 + (x^3 + 1)y = -x^6 + 5x^5 - 9x^4 + 4x^3 - 9x^2 + 5x - 1$ |
| 2955.a.2955.1 |
2955.a |
\( 3 \cdot 5 \cdot 197 \) |
\( - 3 \cdot 5 \cdot 197 \) |
$0$ |
$2$ |
$\Z/4\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$0$ |
$0$ |
2.15.1 |
|
|
$2$ |
\( 1 \) |
\(1.000000\) |
\(6.381009\) |
\(0.797626\) |
$[784,17572,3807505,11820]$ |
$[392,3474,35279,440173,2955]$ |
$[9256148959232/2955,69753621504/985,5421112256/2955]$ |
$y^2 + (x^3 + x)y = -x^6 - x^4 - x^3 - 3x^2 - 2x - 1$ |
| 3072.b.196608.2 |
3072.b |
\( 2^{10} \cdot 3 \) |
\( - 2^{16} \cdot 3 \) |
$0$ |
$3$ |
$\Z/2\Z\oplus\Z/2\Z$ |
\(\mathsf{CM} \times \Q\) |
\(\Q \times \Q\) |
✓ |
$N(\mathrm{U}(1)\times\mathrm{SU}(2))$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$0$ |
$0$ |
2.90.6, 3.270.2 |
|
|
$2$ |
\( 1 \) |
\(1.000000\) |
\(6.143062\) |
\(0.767883\) |
$[2376,321,254043,24]$ |
$[9504,3760160,1981759488,1173959737088,196608]$ |
$[394394593494528,16418157695280,910463659776]$ |
$y^2 = 2x^6 + 9x^4 + 13x^2 + 6$ |
| 3120.b.199680.1 |
3120.b |
\( 2^{4} \cdot 3 \cdot 5 \cdot 13 \) |
\( - 2^{10} \cdot 3 \cdot 5 \cdot 13 \) |
$0$ |
$3$ |
$\Z/2\Z\oplus\Z/2\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$0$ |
$0$ |
2.90.6, 3.90.1 |
|
|
$2$ |
\( 2 \) |
\(1.000000\) |
\(3.338010\) |
\(0.834502\) |
$[2397240,72897,58245771285,24960]$ |
$[2397240,239448268802,31889707498721280,4777952242989938687999,199680]$ |
$[5154260479603163815124340000/13,214760809729321817508682425/13,917780865738818887929600]$ |
$y^2 + xy = -80x^6 - 189x^4 - 149x^2 - 39$ |
| 3168.a.684288.1 |
3168.a |
\( 2^{5} \cdot 3^{2} \cdot 11 \) |
\( - 2^{8} \cdot 3^{5} \cdot 11 \) |
$0$ |
$3$ |
$\Z/2\Z\oplus\Z/4\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$0$ |
$0$ |
2.180.7, 3.90.1 |
|
|
$2$ |
\( 2^{3} \) |
\(1.000000\) |
\(3.716043\) |
\(0.929011\) |
$[7444,76621,183223627,85536]$ |
$[7444,2257800,897608448,396034111728,684288]$ |
$[89287745446261204/2673,1212671977685150/891,1962567037712/27]$ |
$y^2 + (x^3 + x)y = -x^6 - 7x^4 - 17x^2 - 11$ |
| 3200.e.819200.1 |
3200.e |
\( 2^{7} \cdot 5^{2} \) |
\( - 2^{15} \cdot 5^{2} \) |
$0$ |
$2$ |
$\Z/6\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$0$ |
$0$ |
2.90.5, 3.720.4 |
|
|
$2$ |
\( 3 \) |
\(1.000000\) |
\(4.252877\) |
\(0.708813\) |
$[520,1141,186367,100]$ |
$[2080,168096,17260544,1911416576,819200]$ |
$[47525504000,1846534560,91157248]$ |
$y^2 = -x^6 - 5x^4 - 7x^2 - 2$ |
| 3280.a.3280.1 |
3280.a |
\( 2^{4} \cdot 5 \cdot 41 \) |
\( - 2^{4} \cdot 5 \cdot 41 \) |
$0$ |
$2$ |
$\Z/4\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$0$ |
$0$ |
2.45.1 |
|
|
$2$ |
\( 1 \) |
\(1.000000\) |
\(7.166426\) |
\(0.895803\) |
$[1048,9112,2898332,13120]$ |
$[524,9922,232064,5788863,3280]$ |
$[2469087337664/205,2176152088/5,3982450304/205]$ |
$y^2 + (x + 1)y = -x^6 + 2x^5 - 4x^4 + 3x^3 - 3x^2 - 1$ |
| 3360.b.241920.1 |
3360.b |
\( 2^{5} \cdot 3 \cdot 5 \cdot 7 \) |
\( - 2^{8} \cdot 3^{3} \cdot 5 \cdot 7 \) |
$0$ |
$3$ |
$\Z/2\Z\oplus\Z/6\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$0$ |
$0$ |
2.90.6, 3.720.4 |
|
|
$2$ |
\( 2^{2} \cdot 3 \) |
\(1.000000\) |
\(3.848391\) |
\(0.641398\) |
$[182340,50613,3073006935,30240]$ |
$[182340,1385294408,14032351630080,159904599848179184,241920]$ |
$[5832248478791381977500/7,243004434356588125950/7,1928513067842084400]$ |
$y^2 + (x^2 + 1)y = -135x^6 - 96x^4 - 23x^2 - 2$ |
| 3568.a.3568.1 |
3568.a |
\( 2^{4} \cdot 223 \) |
\( - 2^{4} \cdot 223 \) |
$0$ |
$2$ |
$\Z/4\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$0$ |
$0$ |
2.15.1 |
|
|
$2$ |
\( 1 \) |
\(1.000000\) |
\(7.927399\) |
\(0.990925\) |
$[536,2104,345084,14272]$ |
$[268,2642,32320,420399,3568]$ |
$[86408006848/223,3178463384/223,145084480/223]$ |
$y^2 + xy = -x^6 - 4x^5 - 9x^4 - 11x^3 - 9x^2 - 4x - 1$ |
| 3570.a.3570.1 |
3570.a |
\( 2 \cdot 3 \cdot 5 \cdot 7 \cdot 17 \) |
\( - 2 \cdot 3 \cdot 5 \cdot 7 \cdot 17 \) |
$1$ |
$4$ |
$\Z/2\Z\oplus\Z/2\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$0$ |
$0$ |
2.90.6, 3.90.1 |
|
|
$2$ |
\( 1 \) |
\(0.532647\) |
\(5.545665\) |
\(0.369235\) |
$[173580,307977,17764634235,456960]$ |
$[43395,78450752,189070577220,512549302274099,3570]$ |
$[10259051370111445708125/238,213695282234728087200/119,99732135721219650]$ |
$y^2 + (x^3 + 1)y = -10x^6 + 23x^5 - 47x^4 + 50x^3 - 47x^2 + 23x - 10$ |
| 3584.c.458752.1 |
3584.c |
\( 2^{9} \cdot 7 \) |
\( 2^{16} \cdot 7 \) |
$0$ |
$2$ |
$\Z/4\Z$ |
\(\mathsf{CM} \times \Q\) |
\(\Q \times \Q\) |
✓ |
$N(\mathrm{U}(1)\times\mathrm{SU}(2))$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$0$ |
$0$ |
2.45.1, 3.2160.9 |
|
|
$2$ |
\( 2 \) |
\(1.000000\) |
\(3.475514\) |
\(0.868879\) |
$[828,16635,5308452,56]$ |
$[3312,279616,-54648832,-64795509760,458752]$ |
$[6080953884912/7,155007628668/7,-1306723104]$ |
$y^2 + x^3y = x^6 - 4x^5 - 13x^4 - 22x^3 - 21x^2 - 12x - 4$ |
| 3732.b.477696.1 |
3732.b |
\( 2^{2} \cdot 3 \cdot 311 \) |
\( 2^{9} \cdot 3 \cdot 311 \) |
$0$ |
$1$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$3$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$0$ |
$0$ |
3.80.2 |
|
|
$2$ |
\( 1 \) |
\(1.000000\) |
\(0.383045\) |
\(0.766090\) |
$[37220,101230897,771030827689,61145088]$ |
$[9305,-610328,2058420288,4695275128064,477696]$ |
$[69756051129891565625/477696,-61464229238358875/59712,928251329460475/2488]$ |
$y^2 + (x^3 + x + 1)y = -x^6 + 6x^4 + 10x^3 - 33x^2 - 14x + 3$ |
| 4046.a.4046.1 |
4046.a |
\( 2 \cdot 7 \cdot 17^{2} \) |
\( - 2 \cdot 7 \cdot 17^{2} \) |
$0$ |
$2$ |
$\Z/4\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$0$ |
$0$ |
2.45.1, 3.90.1 |
|
|
$2$ |
\( 1 \) |
\(1.000000\) |
\(7.171882\) |
\(0.896485\) |
$[1308,24465,9528807,517888]$ |
$[327,3436,41188,415595,4046]$ |
$[3738856210407/4046,60071215194/2023,314585118/289]$ |
$y^2 + (x^2 + x)y = -x^6 + 2x^5 - 3x^4 + 2x^3 - 3x^2 + 2x - 1$ |
| 4158.a.16632.1 |
4158.a |
\( 2 \cdot 3^{3} \cdot 7 \cdot 11 \) |
\( - 2^{3} \cdot 3^{3} \cdot 7 \cdot 11 \) |
$0$ |
$4$ |
$\Z/6\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$0$ |
$0$ |
2.45.1, 3.720.4 |
|
|
$8$ |
\( 3 \) |
\(1.000000\) |
\(1.221349\) |
\(0.814233\) |
$[260796,1850978385,134364376171431,2128896]$ |
$[65199,99997134,172172445984,306511124374215,16632]$ |
$[43635595725427687775037/616,513235392243926913579/308,44004900412520412]$ |
$y^2 + (x^2 + x)y = -15x^6 + 32x^5 - 53x^4 + 64x^3 - 53x^2 + 32x - 15$ |
| 4264.a.699296.1 |
4264.a |
\( 2^{3} \cdot 13 \cdot 41 \) |
\( - 2^{5} \cdot 13 \cdot 41^{2} \) |
$0$ |
$2$ |
$\Z/10\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,5$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$0$ |
$0$ |
2.45.1 |
|
|
$2$ |
\( 2 \cdot 5 \) |
\(1.000000\) |
\(4.514986\) |
\(0.902997\) |
$[9296,52144,158718244,2797184]$ |
$[4648,891472,226027260,63963094424,699296]$ |
$[67792339032986624/21853,2797409767346432/21853,90776904120/13]$ |
$y^2 + (x + 1)y = -3x^6 + 8x^5 - 16x^4 + 18x^3 - 17x^2 + 8x - 4$ |
| 4336.a.138752.1 |
4336.a |
\( 2^{4} \cdot 271 \) |
\( 2^{9} \cdot 271 \) |
$0$ |
$1$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$3$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$0$ |
$0$ |
3.80.2 |
|
|
$2$ |
\( 1 \) |
\(1.000000\) |
\(0.376283\) |
\(0.752566\) |
$[12440,748636,21969201218,-17344]$ |
$[12440,5948976,-13347212816,-50357410719904,-138752]$ |
$[-581878004510200000/271,-22368321536682000/271,4034236783676050/271]$ |
$y^2 + (x + 1)y = -11x^6 + 6x^5 + 22x^4 - 16x^3 - 6x^2 + 11x - 5$ |
| 4340.a.555520.1 |
4340.a |
\( 2^{2} \cdot 5 \cdot 7 \cdot 31 \) |
\( 2^{9} \cdot 5 \cdot 7 \cdot 31 \) |
$0$ |
$2$ |
$\Z/2\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$0$ |
$0$ |
2.45.1, 3.720.5 |
|
|
$2$ |
\( 3 \) |
\(1.000000\) |
\(0.551819\) |
\(0.827728\) |
$[744212,6706463065,1480606015487837,71106560]$ |
$[186053,1162885656,8785903013440,70585141107250496,555520]$ |
$[31848233290693980783646499/79360,133739291487211871618577/9920,4379757318496324709/8]$ |
$y^2 + (x^3 + 1)y = -x^6 - 11x^5 - 24x^4 + 127x^3 - 24x^2 - 11x - 1$ |
| 4482.a.4482.1 |
4482.a |
\( 2 \cdot 3^{3} \cdot 83 \) |
\( - 2 \cdot 3^{3} \cdot 83 \) |
$0$ |
$1$ |
$\Z/5\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$3,5$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$0$ |
$0$ |
3.80.2 |
|
|
$2$ |
\( 1 \) |
\(1.000000\) |
\(7.242158\) |
\(0.579373\) |
$[8664,7884,22484025,17928]$ |
$[4332,780612,187266479,50470823121,4482]$ |
$[28251953315947008/83,1175186536293504/83,195238038478072/249]$ |
$y^2 + xy = -3x^6 - 3x^5 - 9x^4 - 5x^3 - 8x^2 - 2x - 2$ |
