| 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 |
| 448.a.448.1 |
448.a |
\( 2^{6} \cdot 7 \) |
\( 2^{6} \cdot 7 \) |
$0$ |
$1$ |
$\Z/6\Z$ |
\(\mathsf{CM} \times \Q\) |
\(\Q \times \Q\) |
✓ |
$N(\mathrm{U}(1)\times\mathrm{SU}(2))$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$2$ |
$0$ |
2.45.1, 3.2160.5 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(7.792789\) |
\(0.216466\) |
$[828,16635,5308452,56]$ |
$[828,17476,-853888,-253107460,448]$ |
$[6080953884912/7,155007628668/7,-1306723104]$ |
$y^2 + (x^3 + x)y = x^4 - 7$ |
| 504.a.27216.1 |
504.a |
\( 2^{3} \cdot 3^{2} \cdot 7 \) |
\( - 2^{4} \cdot 3^{5} \cdot 7 \) |
$0$ |
$2$ |
$\Z/4\Z\oplus\Z/4\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$2$ |
$0$ |
2.90.6, 3.90.1 |
✓ |
✓ |
$1$ |
\( 2^{3} \) |
\(1.000000\) |
\(7.782699\) |
\(0.243209\) |
$[8456,9496,26675348,108864]$ |
$[4228,743250,173847744,45651924783,27216]$ |
$[12063042849801664/243,167186257609000/81,3083035208512/27]$ |
$y^2 + (x^3 + x)y = 3x^4 + 15x^2 + 21$ |
| 523.a.523.2 |
523.a |
\( 523 \) |
\( -523 \) |
$0$ |
$1$ |
$\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,5$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$2$ |
$2$ |
2.30.3 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(0.992796\) |
\(0.248199\) |
$[332400,10084860,1107044456391,-2092]$ |
$[166200,1149254190,10581558955401,109467476288772525,-523]$ |
$[-126810465636208320000000000/523,-5276053055713522320000000/523,-292288477352026798440000/523]$ |
$y^2 + xy = x^5 - 31x^4 - 110x^3 + 21x^2 - x$ |
| 640.a.81920.1 |
640.a |
\( 2^{7} \cdot 5 \) |
\( - 2^{14} \cdot 5 \) |
$0$ |
$1$ |
$\Z/12\Z$ |
\(\mathsf{CM} \times \Q\) |
\(\Q \times \Q\) |
✓ |
$N(\mathrm{U}(1)\times\mathrm{SU}(2))$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$2$ |
$0$ |
2.90.1, 3.2160.5 |
✓ |
✓ |
$1$ |
\( 2 \cdot 3 \) |
\(1.000000\) |
\(7.405674\) |
\(0.308570\) |
$[912,147,44562,10]$ |
$[3648,552928,111431680,25193348864,81920]$ |
$[39432490647552/5,1638374321664/5,18102076416]$ |
$y^2 + x^3y = 3x^4 + 13x^2 + 20$ |
| 644.a.659456.1 |
644.a |
\( 2^{2} \cdot 7 \cdot 23 \) |
\( 2^{12} \cdot 7 \cdot 23 \) |
$0$ |
$1$ |
$\Z/2\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$2$ |
$2$ |
2.90.3, 3.720.5 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(0.872985\) |
\(0.218246\) |
$[161796,1070662305,46065265919409,84410368]$ |
$[40449,23560804,14638854160,9253881697856,659456]$ |
$[108277681088425330677249/659456,389810454818831018649/164864,9297727292338785/256]$ |
$y^2 + (x^2 + x)y = -3x^6 - 13x^5 + 4x^4 + 51x^3 + 4x^2 - 13x - 3$ |
| 686.a.686.1 |
686.a |
\( 2 \cdot 7^{3} \) |
\( 2 \cdot 7^{3} \) |
$0$ |
$1$ |
$\Z/6\Z$ |
\(\mathsf{CM} \times \Q\) |
\(\Q \times \Q\) |
✓ |
$N(\mathrm{U}(1)\times\mathrm{SU}(2))$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$2$ |
$2$ |
2.90.3, 3.2160.5 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(11.491655\) |
\(0.319213\) |
$[420,4305,640185,87808]$ |
$[105,280,-980,-45325,686]$ |
$[37209375/2,472500,-15750]$ |
$y^2 + (x^2 + x)y = x^5 + x^4 + 2x^3 + x^2 + x$ |
| 720.a.6480.1 |
720.a |
\( 2^{4} \cdot 3^{2} \cdot 5 \) |
\( - 2^{4} \cdot 3^{4} \cdot 5 \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/4\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$2$ |
$0$ |
2.180.7, 3.90.1 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(1.000000\) |
\(9.444268\) |
\(0.295133\) |
$[2360,11992,9047820,25920]$ |
$[1180,56018,3453120,234166319,6480]$ |
$[28596971960000/81,1150492082200/81,6677950400/9]$ |
$y^2 + (x^3 + x)y = 2x^4 + 7x^2 + 5$ |
| 784.a.43904.1 |
784.a |
\( 2^{4} \cdot 7^{2} \) |
\( - 2^{7} \cdot 7^{3} \) |
$0$ |
$1$ |
$\Z/12\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$2$ |
$0$ |
2.90.1, 3.2160.20 |
✓ |
✓ |
$1$ |
\( 2 \cdot 3 \) |
\(1.000000\) |
\(6.931117\) |
\(0.288797\) |
$[21288,3000,20891172,175616]$ |
$[10644,4720114,2790613504,1855953490895,43904]$ |
$[1067368445729034408/343,6352710665144931/49,50408453477952/7]$ |
$y^2 + (x^3 + x)y = 4x^4 + 27x^2 + 56$ |
| 841.a.841.1 |
841.a |
\( 29^{2} \) |
\( - 29^{2} \) |
$0$ |
$0$ |
$\Z/7\Z$ |
\(\mathsf{RM}\) |
\(\mathsf{RM}\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
✓ |
✓ |
$C_2$ |
$C_2$ |
$2$ |
$0$ |
2.60.2, 3.72.2 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(14.284557\) |
\(0.291522\) |
$[1420,4201,1973899,107648]$ |
$[355,5076,93408,1848516,841]$ |
$[5638216721875/841,227094529500/841,11771743200/841]$ |
$y^2 + (x^3 + x^2 + x)y = x^4 + x^3 + 3x^2 + x + 2$ |
| 862.a.862.1 |
862.a |
\( 2 \cdot 431 \) |
\( - 2 \cdot 431 \) |
$0$ |
$1$ |
$\Z/8\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$2$ |
$0$ |
2.15.1 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(23.926605\) |
\(0.373853\) |
$[1940,2609665,270472593,-110336]$ |
$[485,-98935,11156681,-1094285985,-862]$ |
$[-26835438303125/862,11286912906875/862,-2624330288225/862]$ |
$y^2 + (x^3 + 1)y = x^5 - 2x^4 - 7x^3 + 7x^2 + 2x + 5$ |
| 882.a.302526.1 |
882.a |
\( 2 \cdot 3^{2} \cdot 7^{2} \) |
\( - 2 \cdot 3^{2} \cdot 7^{5} \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/4\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2$ |
$C_2$ |
$2$ |
$0$ |
2.90.6, 3.90.1 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(1.000000\) |
\(12.542623\) |
\(0.391957\) |
$[2572,-283391,165464399,38723328]$ |
$[643,29035,-3791761,-820283387,302526]$ |
$[109914468611443/302526,7718888172745/302526,-1567699793689/302526]$ |
$y^2 + (x^3 + 1)y = x^5 - 2x^4 - 5x^3 + 11x^2 - 12x + 5$ |
| 930.a.930.1 |
930.a |
\( 2 \cdot 3 \cdot 5 \cdot 31 \) |
\( 2 \cdot 3 \cdot 5 \cdot 31 \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/4\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$2$ |
$2$ |
2.180.3, 3.90.1 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(24.846489\) |
\(0.388226\) |
$[46596,239073,3674852529,119040]$ |
$[11649,5644172,3640360380,2637470125259,930]$ |
$[71502622649365111083/310,1487013548016809538/155,531176338621566]$ |
$y^2 + (x^2 + x)y = -x^5 - 7x^4 + 37x^2 - 45x + 15$ |
| 960.a.245760.1 |
960.a |
\( 2^{6} \cdot 3 \cdot 5 \) |
\( 2^{14} \cdot 3 \cdot 5 \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/4\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$2$ |
$2$ |
2.180.3, 3.90.1 |
✓ |
✓ |
$1$ |
\( 2^{2} \) |
\(1.000000\) |
\(6.402317\) |
\(0.400145\) |
$[120,213,10095,30]$ |
$[480,7328,-15360,-15268096,245760]$ |
$[103680000,3297600,-14400]$ |
$y^2 = 2x^5 + x^4 + 4x^3 + x^2 + 2x$ |
| 960.a.368640.1 |
960.a |
\( 2^{6} \cdot 3 \cdot 5 \) |
\( 2^{13} \cdot 3^{2} \cdot 5 \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/4\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$2$ |
$2$ |
2.180.3, 3.90.1 |
✓ |
✓ |
$1$ |
\( 2^{2} \) |
\(1.000000\) |
\(6.402317\) |
\(0.400145\) |
$[8952,6072,17987052,1440]$ |
$[17904,13340192,13237770240,14762078945024,368640]$ |
$[24952719973569408/5,1038436236963696/5,11510985848256]$ |
$y^2 = x^5 + 13x^4 + 44x^3 + 13x^2 + x$ |
| 960.a.983040.1 |
960.a |
\( 2^{6} \cdot 3 \cdot 5 \) |
\( - 2^{16} \cdot 3 \cdot 5 \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/4\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$2$ |
$2$ |
2.180.3, 3.90.1 |
✓ |
✓ |
$1$ |
\( 2^{2} \) |
\(1.000000\) |
\(6.402317\) |
\(0.400145\) |
$[9,33,666,120]$ |
$[36,-298,-34260,-330541,983040]$ |
$[19683/320,-36207/2560,-46251/1024]$ |
$y^2 = x^5 - 2x^4 - x^3 - 2x^2 + x$ |
| 961.a.961.3 |
961.a |
\( 31^{2} \) |
\( 31^{2} \) |
$0$ |
$0$ |
$\Z/5\Z$ |
\(\mathsf{RM}\) |
\(\mathsf{RM}\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
✓ |
✓ |
$C_2$ |
$C_2$ |
$2$ |
$0$ |
2.120.2, 3.72.2 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(11.232193\) |
\(0.449288\) |
$[260,1681,185209,123008]$ |
$[65,106,-672,-13729,961]$ |
$[1160290625/961,29110250/961,-2839200/961]$ |
$y^2 + (x^3 + x + 1)y = x^5 + x^4 + x^3 - x - 1$ |
| 961.a.923521.1 |
961.a |
\( 31^{2} \) |
\( 31^{4} \) |
$0$ |
$0$ |
$\Z/5\Z$ |
\(\mathsf{RM}\) |
\(\mathsf{RM}\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
✓ |
✓ |
$C_2$ |
$C_2$ |
$2$ |
$0$ |
2.120.2, 3.72.2 |
✓ |
✓ |
$1$ |
\( 5 \) |
\(1.000000\) |
\(2.246439\) |
\(0.449288\) |
$[4100,78961,94151689,118210688]$ |
$[1025,40486,2121888,133954751,923521]$ |
$[1131408212890625/923521,1406419156250/29791,2319780000/961]$ |
$y^2 + (x^3 + x^2 + 1)y = -5x^4 + 4x^3 + 3x^2 - 2x - 3$ |
| 990.a.8910.1 |
990.a |
\( 2 \cdot 3^{2} \cdot 5 \cdot 11 \) |
\( 2 \cdot 3^{4} \cdot 5 \cdot 11 \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/4\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$2$ |
$2$ |
2.180.3, 3.90.1 |
✓ |
✓ |
$1$ |
\( 2^{2} \) |
\(1.000000\) |
\(6.174937\) |
\(0.385934\) |
$[3268,252577,318023313,1140480]$ |
$[817,17288,-766260,-231227341,8910]$ |
$[364007458703857/8910,4713906106372/4455,-57404054]$ |
$y^2 + (x^2 + x)y = 3x^5 + 4x^4 + 7x^3 + 4x^2 + 3x$ |
| 990.a.240570.1 |
990.a |
\( 2 \cdot 3^{2} \cdot 5 \cdot 11 \) |
\( 2 \cdot 3^{7} \cdot 5 \cdot 11 \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/2\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$2$ |
$2$ |
2.180.3, 3.90.1 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(1.000000\) |
\(3.087468\) |
\(0.385934\) |
$[153028,6848257,343366646113,30792960]$ |
$[38257,60697908,127876480380,301983618580299,240570]$ |
$[81951056110393451083057/240570,188813894774599018858/13365,7001861848004294/9]$ |
$y^2 + (x^2 + x)y = 3x^5 + 28x^4 + 72x^3 + 28x^2 + 3x$ |
| 1038.a.1038.2 |
1038.a |
\( 2 \cdot 3 \cdot 173 \) |
\( - 2 \cdot 3 \cdot 173 \) |
$0$ |
$1$ |
$\Z/6\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,3$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$2$ |
$0$ |
2.15.1, 3.80.1 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(15.397347\) |
\(0.427704\) |
$[844,4129,1133983,132864]$ |
$[211,1683,16079,140045,1038]$ |
$[418227202051/1038,5269995291/346,715853159/1038]$ |
$y^2 + (x^3 + 1)y = x^4 + 2x^2 + x + 1$ |
| 1088.a.1088.1 |
1088.a |
\( 2^{6} \cdot 17 \) |
\( - 2^{6} \cdot 17 \) |
$0$ |
$1$ |
$\Z/6\Z$ |
\(\Q \times \Q\) |
\(\Q\) |
|
$N(\mathrm{SU}(2)\times\mathrm{SU}(2))$ |
|
✓ |
|
$C_2$ |
$C_2^2$ |
$2$ |
$0$ |
2.90.1, 3.2880.5 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(15.720126\) |
\(0.436670\) |
$[196,28,632,136]$ |
$[196,1582,17884,250635,1088]$ |
$[4519603984/17,186120718/17,631463]$ |
$y^2 + (x^3 + x^2 + x + 1)y = x^4 + x^3 + 2x^2 + x + 1$ |
| 1088.b.2176.1 |
1088.b |
\( 2^{6} \cdot 17 \) |
\( - 2^{7} \cdot 17 \) |
$0$ |
$1$ |
$\Z/6\Z$ |
\(\mathsf{CM} \times \Q\) |
\(\Q \times \Q\) |
✓ |
$N(\mathrm{U}(1)\times\mathrm{SU}(2))$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$2$ |
$0$ |
2.45.1, 3.2160.5 |
✓ |
✓ |
$1$ |
\( 3 \) |
\(1.000000\) |
\(5.893944\) |
\(0.491162\) |
$[7572,68115,166006308,272]$ |
$[7572,2343556,952909568,430794130940,2176]$ |
$[194465720403941544/17,7948719687495546/17,25108109106912]$ |
$y^2 + (x^3 + x)y = 4x^4 + 24x^2 + 34$ |
| 1088.b.2176.2 |
1088.b |
\( 2^{6} \cdot 17 \) |
\( 2^{7} \cdot 17 \) |
$0$ |
$1$ |
$\Z/12\Z$ |
\(\mathsf{CM} \times \Q\) |
\(\Q \times \Q\) |
✓ |
$N(\mathrm{U}(1)\times\mathrm{SU}(2))$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$2$ |
$0$ |
2.90.1, 3.2160.5 |
✓ |
✓ |
$1$ |
\( 3 \) |
\(1.000000\) |
\(23.575776\) |
\(0.491162\) |
$[7572,68115,166006308,272]$ |
$[7572,2343556,952909568,430794130940,2176]$ |
$[194465720403941544/17,7948719687495546/17,25108109106912]$ |
$y^2 + (x^3 + x)y = -5x^4 + 24x^2 - 34$ |
| 1122.a.1122.1 |
1122.a |
\( 2 \cdot 3 \cdot 11 \cdot 17 \) |
\( 2 \cdot 3 \cdot 11 \cdot 17 \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/2\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$2$ |
$2$ |
2.180.3, 3.90.1 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(6.820719\) |
\(0.426295\) |
$[56004,288321,5331417537,143616]$ |
$[14001,8155820,6325887612,5512838145803,1122]$ |
$[179338702480653356667/374,3730727674118765970/187,1105214886926046]$ |
$y^2 + (x^2 + x)y = x^5 + 7x^4 - 43x^2 + 51x - 17$ |
| 1146.a.2292.1 |
1146.a |
\( 2 \cdot 3 \cdot 191 \) |
\( 2^{2} \cdot 3 \cdot 191 \) |
$0$ |
$1$ |
$\Z/6\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,3$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$2$ |
$2$ |
2.30.3, 3.80.1 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(1.000000\) |
\(9.256014\) |
\(0.514223\) |
$[104,1096,61011,9168]$ |
$[52,-70,-3815,-50820,2292]$ |
$[95051008/573,-2460640/573,-2578940/573]$ |
$y^2 + xy = x^5 + 3x^4 + 5x^3 + 4x^2 + 2x$ |
| 1176.a.2352.1 |
1176.a |
\( 2^{3} \cdot 3 \cdot 7^{2} \) |
\( - 2^{4} \cdot 3 \cdot 7^{2} \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/4\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$2$ |
$0$ |
2.180.7, 3.90.1 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(1.000000\) |
\(12.624711\) |
\(0.394522\) |
$[1032,984,324564,9408]$ |
$[516,10930,305472,9539663,2352]$ |
$[762091768512/49,31284414360/49,1694453184/49]$ |
$y^2 + (x^3 + x)y = x^4 + 3x^2 + 3$ |
| 1184.a.606208.2 |
1184.a |
\( 2^{5} \cdot 37 \) |
\( - 2^{14} \cdot 37 \) |
$0$ |
$1$ |
$\Z/8\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$2$ |
$0$ |
2.15.1 |
✓ |
✓ |
$1$ |
\( 2^{2} \) |
\(1.000000\) |
\(7.116022\) |
\(0.444751\) |
$[352,316,34242,74]$ |
$[1408,79232,5831680,483323904,606208]$ |
$[337748426752/37,13498597376/37,705633280/37]$ |
$y^2 = x^6 - 2x^5 + 5x^4 - 4x^3 + 6x^2 - 2x + 2$ |
| 1200.a.450000.1 |
1200.a |
\( 2^{4} \cdot 3 \cdot 5^{2} \) |
\( - 2^{4} \cdot 3^{2} \cdot 5^{5} \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/8\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$2$ |
$0$ |
2.180.7, 3.90.1 |
✓ |
✓ |
$1$ |
\( 2^{4} \) |
\(1.000000\) |
\(5.655371\) |
\(0.353461\) |
$[18072,38904,233095932,1800000]$ |
$[9036,3395570,1698206400,953774351375,450000]$ |
$[418329622965299904/3125,3479436045234936/625,38515932506304/125]$ |
$y^2 + (x^3 + x)y = 4x^4 + 25x^2 + 45$ |
| 1210.a.1210.1 |
1210.a |
\( 2 \cdot 5 \cdot 11^{2} \) |
\( 2 \cdot 5 \cdot 11^{2} \) |
$0$ |
$0$ |
$\Z/5\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2$ |
$C_2$ |
$2$ |
$0$ |
2.20.2, 3.90.1 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(8.627716\) |
\(0.345109\) |
$[208,75964,-1718663,-4840]$ |
$[104,-12210,559319,-22728731,-1210]$ |
$[-6083264512/605,124859904/11,-3024797152/605]$ |
$y^2 + (x^3 + x)y = 3x^3 - 2x^2 + 6x + 2$ |
| 1270.a.1270.1 |
1270.a |
\( 2 \cdot 5 \cdot 127 \) |
\( 2 \cdot 5 \cdot 127 \) |
$0$ |
$1$ |
$\Z/6\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,3$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$2$ |
$0$ |
2.15.1, 3.80.1 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(17.051434\) |
\(0.473651\) |
$[2612,-8063,-7006415,162560]$ |
$[653,18103,680921,29230701,1270]$ |
$[118731486838493/1270,5040691228931/1270,290350842689/1270]$ |
$y^2 + (x^3 + 1)y = -2x^4 + 5x^2 - 2x - 3$ |
| 1320.a.2640.1 |
1320.a |
\( 2^{3} \cdot 3 \cdot 5 \cdot 11 \) |
\( 2^{4} \cdot 3 \cdot 5 \cdot 11 \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/4\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$2$ |
$2$ |
2.180.3, 3.90.1 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(1.000000\) |
\(17.746741\) |
\(0.554586\) |
$[63768,10392,220729308,10560]$ |
$[31884,42356162,75020763840,149479393726079,2640]$ |
$[686471900571962215488/55,28601826290311163976/55,28888377841215936]$ |
$y^2 + (x^3 + x)y = -x^6 + 9x^4 - 40x^2 + 55$ |
| 1328.a.1328.1 |
1328.a |
\( 2^{4} \cdot 83 \) |
\( - 2^{4} \cdot 83 \) |
$0$ |
$1$ |
$\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$2$ |
$2$ |
2.30.3 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(2.234905\) |
\(0.558726\) |
$[424,348664,-49372844,-5312]$ |
$[212,-56238,8930000,-317388161,-1328]$ |
$[-26764511552/83,33490178904/83,-25084370000/83]$ |
$y^2 + x^2y = x^5 - 3x^4 - 9x^3 - 5x^2 - 4x - 5$ |
| 1344.a.4032.2 |
1344.a |
\( 2^{6} \cdot 3 \cdot 7 \) |
\( 2^{6} \cdot 3^{2} \cdot 7 \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/4\Z$ |
\(\mathsf{CM} \times \Q\) |
\(\Q \times \Q\) |
✓ |
$N(\mathrm{U}(1)\times\mathrm{SU}(2))$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$2$ |
$2$ |
2.180.3, 3.270.2 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(1.000000\) |
\(13.382426\) |
\(0.418201\) |
$[48576,2301,37257288,504]$ |
$[48576,98316290,265314615552,805457471422463,4032]$ |
$[469554780013829554176/7,19564477241823191040/7,155268783788507136]$ |
$y^2 + xy = -x^6 + 12x^4 - 48x^2 + 63$ |
| 1344.b.172032.1 |
1344.b |
\( 2^{6} \cdot 3 \cdot 7 \) |
\( 2^{13} \cdot 3 \cdot 7 \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/4\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$2$ |
$2$ |
2.180.3, 3.90.1 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(1.000000\) |
\(15.087817\) |
\(0.471494\) |
$[4248,2904,4071996,672]$ |
$[8496,2999840,1408899072,742741622528,172032]$ |
$[1801197437083776/7,74856652932240/7,591152665536]$ |
$y^2 = x^5 - 11x^4 + 32x^3 - 11x^2 + x$ |
| 1386.a.9702.1 |
1386.a |
\( 2 \cdot 3^{2} \cdot 7 \cdot 11 \) |
\( 2 \cdot 3^{2} \cdot 7^{2} \cdot 11 \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/2\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$2$ |
$2$ |
2.180.3, 3.90.1 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(1.000000\) |
\(3.977728\) |
\(0.497216\) |
$[472004,2486881,389970923697,1241856]$ |
$[118001,580072880,3801391710732,28020869286648083,9702]$ |
$[22878546973310459240590001/9702,476551267590924869796440/4851,5455728232578591266]$ |
$y^2 + (x^2 + x)y = x^5 + 20x^4 + 104x^3 + 20x^2 + x$ |
| 1440.a.116640.1 |
1440.a |
\( 2^{5} \cdot 3^{2} \cdot 5 \) |
\( - 2^{5} \cdot 3^{6} \cdot 5 \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/6\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$2$ |
$0$ |
2.90.6, 3.720.4 |
✓ |
✓ |
$1$ |
\( 2^{2} \cdot 3 \) |
\(1.000000\) |
\(5.650548\) |
\(0.470879\) |
$[35416,45688,537039964,466560]$ |
$[17708,13057938,12831384960,14177105014959,116640]$ |
$[54412363190235229024/3645,251762275020280012/405,310461362928064/9]$ |
$y^2 + (x^3 + x)y = 5x^4 + 39x^2 + 90$ |
| 1444.b.109744.1 |
1444.b |
\( 2^{2} \cdot 19^{2} \) |
\( 2^{4} \cdot 19^{3} \) |
$0$ |
$0$ |
$\Z/3\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$2$ |
$0$ |
2.60.2, 3.2160.20 |
✓ |
✓ |
$1$ |
\( 3 \) |
\(1.000000\) |
\(1.509904\) |
\(0.503301\) |
$[4328,28957,40080803,13718]$ |
$[4328,761178,175243840,44765847959,109744]$ |
$[94910940689819648/6859,202989886275264/361,568316258560/19]$ |
$y^2 + x^3y = -4x^4 + 16x^2 - 19$ |
| 1536.b.49152.2 |
1536.b |
\( 2^{9} \cdot 3 \) |
\( - 2^{14} \cdot 3 \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/4\Z$ |
\(\mathsf{CM} \times \Q\) |
\(\Q \times \Q\) |
✓ |
$N(\mathrm{U}(1)\times\mathrm{SU}(2))$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$2$ |
$0$ |
2.90.6, 3.270.2 |
✓ |
✓ |
$1$ |
\( 2^{2} \) |
\(1.000000\) |
\(7.996682\) |
\(0.499793\) |
$[624,141,29202,6]$ |
$[2496,258080,35377152,5424021248,49152]$ |
$[1970977701888,81648253440,4484054016]$ |
$y^2 + x^3y = 3x^4 + 11x^2 + 12$ |
| 1536.c.98304.1 |
1536.c |
\( 2^{9} \cdot 3 \) |
\( 2^{15} \cdot 3 \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/4\Z$ |
\(\mathsf{CM} \times \Q\) |
\(\Q \times \Q\) |
✓ |
$N(\mathrm{U}(1)\times\mathrm{SU}(2))$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$2$ |
$0$ |
2.180.7, 3.270.2 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(1.000000\) |
\(17.680538\) |
\(0.552517\) |
$[1068,38019,11064156,12]$ |
$[4272,354880,32280576,2990701568,98304]$ |
$[14473882091808,281451823560,5992838496]$ |
$y^2 + y = 4x^6 - 12x^5 + 3x^4 + 14x^3 - 5x^2 - 4x + 1$ |
| 1568.a.1568.1 |
1568.a |
\( 2^{5} \cdot 7^{2} \) |
\( - 2^{5} \cdot 7^{2} \) |
$0$ |
$1$ |
$\Z/6\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$2$ |
$0$ |
2.45.1, 3.2160.21 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(13.648740\) |
\(0.379132\) |
$[792,120,15228,6272]$ |
$[396,6514,144256,3673295,1568]$ |
$[304316815968/49,12641055372/49,14427072]$ |
$y^2 + (x^3 + x)y = x^4 + 3x^2 + 2$ |
| 1568.a.43904.1 |
1568.a |
\( 2^{5} \cdot 7^{2} \) |
\( 2^{7} \cdot 7^{3} \) |
$0$ |
$1$ |
$\Z/6\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$2$ |
$0$ |
2.45.1, 3.2160.20 |
✓ |
✓ |
$1$ |
\( 3 \) |
\(1.000000\) |
\(4.549580\) |
\(0.379132\) |
$[21288,3000,20891172,175616]$ |
$[10644,4720114,2790613504,1855953490895,43904]$ |
$[1067368445729034408/343,6352710665144931/49,50408453477952/7]$ |
$y^2 + (x^3 + x)y = -5x^4 + 27x^2 - 56$ |
| 1600.a.409600.1 |
1600.a |
\( 2^{6} \cdot 5^{2} \) |
\( 2^{14} \cdot 5^{2} \) |
$0$ |
$1$ |
$\Z/6\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$2$ |
$0$ |
2.90.2, 3.2160.21 |
✓ |
✓ |
$1$ |
\( 3 \) |
\(1.000000\) |
\(5.702147\) |
\(0.475179\) |
$[120,309,14889,50]$ |
$[480,6304,-151552,-28121344,409600]$ |
$[62208000,1702080,-85248]$ |
$y^2 = x^6 - 2x^2 - 1$ |
| 1649.a.159953.1 |
1649.a |
\( 17 \cdot 97 \) |
\( - 17 \cdot 97^{2} \) |
$0$ |
$1$ |
$\Z/6\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,3$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$2$ |
$0$ |
2.90.1, 3.80.1 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(1.000000\) |
\(9.711420\) |
\(0.539523\) |
$[1804,147073,69331343,20473984]$ |
$[451,2347,17119,553065,159953]$ |
$[18658757027251/159953,215299348297/159953,204824807/9409]$ |
$y^2 + (x^3 + x^2 + x)y = x^4 + 3x^3 + 4x^2 + 6x + 5$ |
| 1650.a.371250.1 |
1650.a |
\( 2 \cdot 3 \cdot 5^{2} \cdot 11 \) |
\( 2 \cdot 3^{3} \cdot 5^{4} \cdot 11 \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/6\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$2$ |
$2$ |
2.180.3, 3.720.4 |
✓ |
✓ |
$1$ |
\( 2 \cdot 3 \) |
\(1.000000\) |
\(13.792193\) |
\(0.574675\) |
$[30180,172689,1721884569,47520000]$ |
$[7545,2364764,985411548,460705338491,371250]$ |
$[1448946796623435/22,150474103581314/55,3777545308302/25]$ |
$y^2 + (x^2 + x)y = x^5 - 11x^4 + 30x^3 - 11x^2 + x$ |
| 1656.a.804816.1 |
1656.a |
\( 2^{3} \cdot 3^{2} \cdot 23 \) |
\( 2^{4} \cdot 3^{7} \cdot 23 \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/4\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$2$ |
$2$ |
2.180.3 |
✓ |
✓ |
$1$ |
\( 2^{3} \) |
\(1.000000\) |
\(5.200244\) |
\(0.650030\) |
$[680,19992,5459780,13248]$ |
$[1020,13362,-5426240,-1428326961,804816]$ |
$[283971400000/207,10941251000/621,-39204584000/5589]$ |
$y^2 + xy = 2x^5 - 6x^4 + 13x^3 - 13x^2 + 9x$ |
| 1665.a.1665.1 |
1665.a |
\( 3^{2} \cdot 5 \cdot 37 \) |
\( - 3^{2} \cdot 5 \cdot 37 \) |
$0$ |
$0$ |
$\Z/5\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,5$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$2$ |
$0$ |
2.10.1 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(16.175945\) |
\(0.647038\) |
$[572,1969,296919,213120]$ |
$[143,770,5904,62843,1665]$ |
$[59797108943/1665,450327878/333,13414544/185]$ |
$y^2 + (x^3 + x^2 + 1)y = x^4 + x^3 + 2x^2 + 2x + 1$ |
| 1680.b.215040.1 |
1680.b |
\( 2^{4} \cdot 3 \cdot 5 \cdot 7 \) |
\( 2^{11} \cdot 3 \cdot 5 \cdot 7 \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$2$ |
$2$ |
2.180.3 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(1.000000\) |
\(5.032776\) |
\(0.629097\) |
$[11352,175353,681849159,26880]$ |
$[11352,5252594,3148904976,2039156389679,215040]$ |
$[30683910352656528/35,2501322958040841/70,18870572179701/10]$ |
$y^2 + xy = 4x^5 + 25x^4 + 44x^3 + 15x^2 + x$ |
| 1680.c.241920.1 |
1680.c |
\( 2^{4} \cdot 3 \cdot 5 \cdot 7 \) |
\( 2^{8} \cdot 3^{3} \cdot 5 \cdot 7 \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/6\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$2$ |
$2$ |
2.180.3, 3.720.4 |
✓ |
✓ |
$1$ |
\( 2 \cdot 3 \) |
\(1.000000\) |
\(11.725763\) |
\(0.488573\) |
$[182340,50613,3073006935,30240]$ |
$[182340,1385294408,14032351630080,159904599848179184,241920]$ |
$[5832248478791381977500/7,243004434356588125950/7,1928513067842084400]$ |
$y^2 + (x^2 + 1)y = 135x^6 - 96x^4 + 22x^2 - 2$ |
| 1696.a.217088.1 |
1696.a |
\( 2^{5} \cdot 53 \) |
\( - 2^{12} \cdot 53 \) |
$0$ |
$1$ |
$\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$2$ |
$2$ |
2.30.3 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(1.000000\) |
\(1.270310\) |
\(0.635155\) |
$[3746,232693,328269020,848]$ |
$[7492,1718238,-69556676,-868365110309,217088]$ |
$[23050953088040593/212,5645035221351423/1696,-61003448054801/3392]$ |
$y^2 + (x^2 + 1)y = x^5 - 24x^4 - 28x^3 - 22x^2 - 7x - 1$ |
| 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 |
✓ |
✓ |
$1$ |
\( 3^{2} \) |
\(1.000000\) |
\(5.985343\) |
\(0.665038\) |
$[11236,7908289,22291799553,54272]$ |
$[11236,-11872,-76224768,-214150609408,434176]$ |
$[3299763591802133/8,-155150527903/4,-44328573381/2]$ |
$y^2 + xy = x^6 - 2x^5 + 2x^4 + 9x^3 - 12x^2 + 3x + 26$ |
