| 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 |
| 1070.a.2140.1 |
1070.a |
\( 2 \cdot 5 \cdot 107 \) |
\( - 2^{2} \cdot 5 \cdot 107 \) |
$1$ |
$2$ |
$\Z/4\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$9$ |
$1$ |
2.60.1 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(0.054349\) |
\(27.743934\) |
\(0.188481\) |
$[12,3321,141939,273920]$ |
$[3,-138,-1856,-6153,2140]$ |
$[243/2140,-1863/1070,-4176/535]$ |
$y^2 + (x^3 + 1)y = x^3 - x$ |
| 1094.a.2188.1 |
1094.a |
\( 2 \cdot 547 \) |
\( 2^{2} \cdot 547 \) |
$1$ |
$1$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$9$ |
$1$ |
2.6.1 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(0.003585\) |
\(26.605542\) |
\(0.190768\) |
$[20,3001,-30387,280064]$ |
$[5,-124,596,-3099,2188]$ |
$[3125/2188,-3875/547,3725/547]$ |
$y^2 + (x^3 + 1)y = x^4 - x^2$ |
| 1198.a.2396.1 |
1198.a |
\( 2 \cdot 599 \) |
\( 2^{2} \cdot 599 \) |
$1$ |
$1$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$9$ |
$1$ |
2.6.1 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(0.004486\) |
\(22.435716\) |
\(0.201311\) |
$[108,729,55683,-306688]$ |
$[27,0,-500,-3375,-2396]$ |
$[-14348907/2396,0,91125/599]$ |
$y^2 + (x^3 + 1)y = -x$ |
| 1383.a.4149.1 |
1383.a |
\( 3 \cdot 461 \) |
\( 3^{2} \cdot 461 \) |
$1$ |
$1$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$9$ |
$1$ |
2.6.1 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(0.005877\) |
\(19.046404\) |
\(0.223864\) |
$[0,192,3600,-16596]$ |
$[0,-32,400,-256,4149]$ |
$[0,-33554432/17214201,-12800/4149]$ |
$y^2 + y = x^5 + x^4$ |
| 1385.a.6925.1 |
1385.a |
\( 5 \cdot 277 \) |
\( 5^{2} \cdot 277 \) |
$1$ |
$1$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$9$ |
$1$ |
2.6.1 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(0.006508\) |
\(16.829506\) |
\(0.219038\) |
$[56,-2576,-46840,27700]$ |
$[28,462,1916,-39949,6925]$ |
$[17210368/6925,10141824/6925,1502144/6925]$ |
$y^2 + y = x^5 + 3x^4 + 3x^3 - x$ |
| 1636.a.6544.1 |
1636.a |
\( 2^{2} \cdot 409 \) |
\( 2^{4} \cdot 409 \) |
$1$ |
$1$ |
$\Z/3\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,3$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$9$ |
$1$ |
2.6.1, 3.80.1 |
✓ |
✓ |
$1$ |
\( 3 \) |
\(0.035894\) |
\(23.355555\) |
\(0.279445\) |
$[64,748,-3780,26176]$ |
$[32,-82,1604,11151,6544]$ |
$[2097152/409,-167936/409,102656/409]$ |
$y^2 + (x^3 + x)y = -x^4 - x^3 + x^2 + x$ |
| 1664.a.3328.1 |
1664.a |
\( 2^{7} \cdot 13 \) |
\( - 2^{8} \cdot 13 \) |
$1$ |
$2$ |
$\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$9$ |
$1$ |
2.60.1 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(0.020704\) |
\(27.242879\) |
\(0.282012\) |
$[276,810,65178,-416]$ |
$[276,2634,32132,482619,-3328]$ |
$[-6256125396/13,-432646353/26,-38245113/52]$ |
$y^2 + xy = x^6 - 2x^5 - x^4 + 3x^3 - x$ |
| 1791.a.5373.1 |
1791.a |
\( 3^{2} \cdot 199 \) |
\( 3^{3} \cdot 199 \) |
$1$ |
$1$ |
$\Z/5\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,5$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$9$ |
$1$ |
2.6.1 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(0.123952\) |
\(26.794751\) |
\(0.265700\) |
$[480,5904,740016,21492]$ |
$[240,1416,15376,421296,5373]$ |
$[29491200000/199,724992000/199,98406400/597]$ |
$y^2 + y = 3x^5 + 6x^4 + 2x^3 - x^2$ |
| 1899.a.5697.1 |
1899.a |
\( 3^{2} \cdot 211 \) |
\( 3^{3} \cdot 211 \) |
$1$ |
$2$ |
$\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$9$ |
$1$ |
2.60.1 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(0.027932\) |
\(19.045771\) |
\(0.265996\) |
$[108,-2727,-18909,-729216]$ |
$[27,144,-544,-8856,-5697]$ |
$[-531441/211,-104976/211,14688/211]$ |
$y^2 + (x^3 + 1)y = -x^5 + x^4 - 3x + 2$ |
| 1952.a.15616.1 |
1952.a |
\( 2^{5} \cdot 61 \) |
\( 2^{8} \cdot 61 \) |
$1$ |
$1$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,3$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$9$ |
$1$ |
2.6.1, 3.40.1 |
✓ |
✓ |
$1$ |
\( 2^{2} \) |
\(0.004205\) |
\(18.538536\) |
\(0.311842\) |
$[8,208,-822,1952]$ |
$[8,-136,1040,-2544,15616]$ |
$[128/61,-272/61,260/61]$ |
$y^2 + (x^3 + x)y = x^3 - x$ |
| 1982.a.63424.1 |
1982.a |
\( 2 \cdot 991 \) |
\( 2^{6} \cdot 991 \) |
$1$ |
$1$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$9$ |
$1$ |
2.6.1 |
✓ |
✓ |
$1$ |
\( 2 \cdot 3 \) |
\(0.003712\) |
\(14.109787\) |
\(0.314289\) |
$[136,220,-2399,-253696]$ |
$[68,156,1687,22595,-63424]$ |
$[-22717712/991,-766428/991,-487543/3964]$ |
$y^2 + (x + 1)y = -x^5 + x^4 - x^3 + x^2$ |
| 2102.a.33632.1 |
2102.a |
\( 2 \cdot 1051 \) |
\( 2^{5} \cdot 1051 \) |
$1$ |
$1$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$9$ |
$1$ |
2.6.1 |
✓ |
✓ |
$1$ |
\( 5 \) |
\(0.003479\) |
\(18.677811\) |
\(0.324935\) |
$[48,1548,5463,134528]$ |
$[24,-234,1145,-6819,33632]$ |
$[248832/1051,-101088/1051,20610/1051]$ |
$y^2 + (x + 1)y = x^5 + 2x^4$ |
| 2218.a.70976.1 |
2218.a |
\( 2 \cdot 1109 \) |
\( 2^{6} \cdot 1109 \) |
$1$ |
$1$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$9$ |
$1$ |
2.6.1 |
✓ |
✓ |
$1$ |
\( 2 \cdot 3 \) |
\(0.002735\) |
\(20.413673\) |
\(0.335046\) |
$[24,6948,250065,-283904]$ |
$[12,-1152,-23921,-403539,-70976]$ |
$[-3888/1109,31104/1109,215289/4436]$ |
$y^2 + (x^3 + x)y = -2x^4 + 2x^2 - x + 1$ |
| 2312.a.4624.1 |
2312.a |
\( 2^{3} \cdot 17^{2} \) |
\( 2^{4} \cdot 17^{2} \) |
$1$ |
$1$ |
$\Z/3\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,3$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$9$ |
$1$ |
2.12.1, 3.320.1 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(0.080045\) |
\(19.235783\) |
\(0.342160\) |
$[184,-3332,-264180,18496]$ |
$[92,908,16964,184056,4624]$ |
$[411925952/289,44190544/289,8973956/289]$ |
$y^2 + xy = x^6 - 2x^4 - x^3 + x^2 + x$ |
| 2312.a.18496.1 |
2312.a |
\( 2^{3} \cdot 17^{2} \) |
\( 2^{6} \cdot 17^{2} \) |
$1$ |
$1$ |
$\Z/3\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,3$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$9$ |
$1$ |
2.12.1, 3.2880.4 |
✓ |
✓ |
$1$ |
\( 2 \cdot 3 \) |
\(0.026682\) |
\(19.235783\) |
\(0.342160\) |
$[224,748,69972,-73984]$ |
$[112,398,-644,-57633,-18496]$ |
$[-275365888/289,-8736896/289,126224/289]$ |
$y^2 + (x + 1)y = x^6 - x^4$ |
| 2432.a.19456.1 |
2432.a |
\( 2^{7} \cdot 19 \) |
\( - 2^{10} \cdot 19 \) |
$1$ |
$2$ |
$\Z/4\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$9$ |
$1$ |
2.60.1 |
✓ |
✓ |
$1$ |
\( 2^{2} \) |
\(0.059374\) |
\(23.728445\) |
\(0.352211\) |
$[120,792,22860,-2432]$ |
$[120,72,1280,37104,-19456]$ |
$[-24300000/19,-121500/19,-18000/19]$ |
$y^2 + (x + 1)y = x^6 + 2x^5 + 2x^2 + x$ |
| 2528.a.20224.1 |
2528.a |
\( 2^{5} \cdot 79 \) |
\( - 2^{8} \cdot 79 \) |
$1$ |
$2$ |
$\Z/4\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$9$ |
$1$ |
2.60.1 |
✓ |
✓ |
$1$ |
\( 2^{2} \) |
\(0.081851\) |
\(17.463105\) |
\(0.357342\) |
$[84,-171,-873,2528]$ |
$[84,408,-512,-52368,20224]$ |
$[16336404/79,944622/79,-14112/79]$ |
$y^2 + (x^2 + 1)y = x^5 - x$ |
| 2602.a.41632.1 |
2602.a |
\( 2 \cdot 1301 \) |
\( 2^{5} \cdot 1301 \) |
$1$ |
$1$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$9$ |
$1$ |
2.6.1 |
✓ |
✓ |
$1$ |
\( 5 \) |
\(0.003548\) |
\(20.501012\) |
\(0.363667\) |
$[88,2668,-441,166528]$ |
$[44,-364,5681,29367,41632]$ |
$[5153632/1301,-968968/1301,687401/2602]$ |
$y^2 + (x^3 + x)y = x^5 - 2x^3 + 6x + 4$ |
| 2950.a.472000.1 |
2950.a |
\( 2 \cdot 5^{2} \cdot 59 \) |
\( - 2^{6} \cdot 5^{3} \cdot 59 \) |
$1$ |
$2$ |
$\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$9$ |
$1$ |
2.60.1 |
✓ |
✓ |
$1$ |
\( 2^{2} \cdot 3 \) |
\(0.012025\) |
\(12.655077\) |
\(0.456548\) |
$[108,-11295,823455,60416000]$ |
$[27,501,-14921,-163467,472000]$ |
$[14348907/472000,9861183/472000,-10877409/472000]$ |
$y^2 + (x^3 + 1)y = x^5 + x^4 + x^3 + 2x^2 - x - 1$ |
| 2985.a.134325.1 |
2985.a |
\( 3 \cdot 5 \cdot 199 \) |
\( 3^{3} \cdot 5^{2} \cdot 199 \) |
$1$ |
$1$ |
$\Z/3\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,3$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$9$ |
$1$ |
2.6.1, 3.80.1 |
✓ |
✓ |
$1$ |
\( 2 \cdot 3 \) |
\(0.039633\) |
\(13.595742\) |
\(0.359230\) |
$[128,2848,98832,-537300]$ |
$[64,-304,-1936,-54080,-134325]$ |
$[-1073741824/134325,79691776/134325,7929856/134325]$ |
$y^2 + y = x^5 + x^4 + 2x^2$ |
| 3003.b.819819.1 |
3003.b |
\( 3 \cdot 7 \cdot 11 \cdot 13 \) |
\( - 3^{2} \cdot 7^{2} \cdot 11 \cdot 13^{2} \) |
$1$ |
$3$ |
$\Z/2\Z\oplus\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$9$ |
$3$ |
2.120.3 |
✓ |
✓ |
$1$ |
\( 2^{3} \) |
\(0.060530\) |
\(13.204144\) |
\(0.399621\) |
$[240,-60,-206121,-3279276]$ |
$[120,610,26569,704045,-819819]$ |
$[-2764800000/91091,-117120000/91091,-42510400/91091]$ |
$y^2 + (x^2 + 1)y = x^5 + 4x^4 + 3x^3 + x$ |
| 3008.a.24064.1 |
3008.a |
\( 2^{6} \cdot 47 \) |
\( 2^{9} \cdot 47 \) |
$1$ |
$1$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$9$ |
$1$ |
2.6.1 |
✓ |
✓ |
$1$ |
\( 2^{2} \) |
\(0.004506\) |
\(21.723618\) |
\(0.391523\) |
$[124,529,14869,3008]$ |
$[124,288,3344,82928,24064]$ |
$[57258302/47,1072476/47,200849/94]$ |
$y^2 + (x^2 + 1)y = x^5 - 2x^3 + x$ |
| 3105.b.27945.1 |
3105.b |
\( 3^{3} \cdot 5 \cdot 23 \) |
\( 3^{5} \cdot 5 \cdot 23 \) |
$1$ |
$2$ |
$\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$9$ |
$1$ |
2.60.1 |
✓ |
✓ |
$1$ |
\( 3 \) |
\(0.026987\) |
\(18.479119\) |
\(0.374016\) |
$[508,2913,509999,14720]$ |
$[381,4956,52384,-1150908,27945]$ |
$[33038369407/115,3383928716/345,844901536/3105]$ |
$y^2 + (x^2 + x + 1)y = x^5 + 3x^4 - 4x^2$ |
| 3142.b.201088.1 |
3142.b |
\( 2 \cdot 1571 \) |
\( 2^{7} \cdot 1571 \) |
$1$ |
$1$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$9$ |
$1$ |
2.6.1 |
✓ |
✓ |
$1$ |
\( 7 \) |
\(0.002836\) |
\(19.988464\) |
\(0.396841\) |
$[440,16204,1672703,804352]$ |
$[220,-684,3833,93851,201088]$ |
$[4026275000/1571,-56900250/1571,11594825/12568]$ |
$y^2 + (x^3 + x)y = x^5 + 6x^2 + 10x + 4$ |
| 3153.a.9459.1 |
3153.a |
\( 3 \cdot 1051 \) |
\( - 3^{2} \cdot 1051 \) |
$1$ |
$1$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$9$ |
$1$ |
2.6.1 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(0.006145\) |
\(27.610007\) |
\(0.339353\) |
$[504,11568,1545192,-37836]$ |
$[252,718,316,-108973,-9459]$ |
$[-112917224448/1051,-1276684416/1051,-2229696/1051]$ |
$y^2 + y = x^5 + 2x^4 - 3x^3 - x^2 + x$ |
| 3226.a.12904.1 |
3226.a |
\( 2 \cdot 1613 \) |
\( 2^{3} \cdot 1613 \) |
$1$ |
$1$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$9$ |
$1$ |
2.6.1 |
✓ |
✓ |
$1$ |
\( 3 \) |
\(0.006372\) |
\(21.139598\) |
\(0.404133\) |
$[368,796,23687,51616]$ |
$[184,1278,18569,445853,12904]$ |
$[26363260928/1613,995163264/1613,78584008/1613]$ |
$y^2 + (x + 1)y = -x^5 - 4x^4 - 4x^3$ |
| 3298.b.844288.1 |
3298.b |
\( 2 \cdot 17 \cdot 97 \) |
\( 2^{9} \cdot 17 \cdot 97 \) |
$1$ |
$1$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$9$ |
$1$ |
2.6.1 |
✓ |
✓ |
$1$ |
\( 3^{2} \) |
\(0.002996\) |
\(15.054105\) |
\(0.405902\) |
$[80,13828,203567,3377152]$ |
$[40,-2238,3137,-1220791,844288]$ |
$[200000/1649,-279750/1649,78425/13192]$ |
$y^2 + (x^3 + x)y = x^5 + 3x^4 + 3x^3 + x + 1$ |
| 3327.a.9981.1 |
3327.a |
\( 3 \cdot 1109 \) |
\( 3^{2} \cdot 1109 \) |
$1$ |
$1$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$9$ |
$1$ |
2.6.1 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(0.009360\) |
\(19.911665\) |
\(0.372752\) |
$[168,-480,3144,-39924]$ |
$[84,374,-844,-52693,-9981]$ |
$[-464679936/1109,-24630144/1109,661696/1109]$ |
$y^2 + (x^3 + x^2 + x + 1)y = -x^4 - x^3 - 2x$ |
| 3328.b.13312.1 |
3328.b |
\( 2^{8} \cdot 13 \) |
\( - 2^{10} \cdot 13 \) |
$1$ |
$2$ |
$\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$9$ |
$1$ |
2.60.1 |
✓ |
✓ |
$1$ |
\( 2^{2} \) |
\(0.018374\) |
\(22.306262\) |
\(0.409858\) |
$[108,378,21366,1664]$ |
$[108,234,-8516,-243621,13312]$ |
$[14348907/13,177147/8,-1552041/208]$ |
$y^2 + (x + 1)y = x^6 - x^3 - x^2$ |
| 3578.a.57248.1 |
3578.a |
\( 2 \cdot 1789 \) |
\( - 2^{5} \cdot 1789 \) |
$1$ |
$1$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$9$ |
$1$ |
2.6.1 |
✓ |
✓ |
$1$ |
\( 5 \) |
\(0.004303\) |
\(19.663898\) |
\(0.423076\) |
$[16,2500,109153,228992]$ |
$[8,-414,-11201,-65251,57248]$ |
$[1024/1789,-6624/1789,-22402/1789]$ |
$y^2 + (x + 1)y = -x^5 + 2x^4 + 2x^3$ |
| 3622.a.463616.1 |
3622.a |
\( 2 \cdot 1811 \) |
\( - 2^{8} \cdot 1811 \) |
$1$ |
$1$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$9$ |
$1$ |
2.6.1 |
✓ |
✓ |
$1$ |
\( 2^{3} \) |
\(0.004245\) |
\(14.983536\) |
\(0.508829\) |
$[1108,11569,-1775207,-59342848]$ |
$[277,2715,110945,5840135,-463616]$ |
$[-1630793025157/463616,-57704428095/463616,-8512698905/463616]$ |
$y^2 + (x^3 + 1)y = -x^5 + x^3 + 3x^2 - 2x - 1$ |
| 3644.b.58304.1 |
3644.b |
\( 2^{2} \cdot 911 \) |
\( - 2^{6} \cdot 911 \) |
$1$ |
$1$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$9$ |
$1$ |
2.6.1 |
✓ |
✓ |
$1$ |
\( 3^{2} \) |
\(0.003614\) |
\(15.924885\) |
\(0.518021\) |
$[428,-2807,41723,7462912]$ |
$[107,594,-1220,-120844,58304]$ |
$[14025517307/58304,363837771/29152,-3491945/14576]$ |
$y^2 + (x^3 + 1)y = x^5 - x$ |
| 3675.a.385875.1 |
3675.a |
\( 3 \cdot 5^{2} \cdot 7^{2} \) |
\( - 3^{2} \cdot 5^{3} \cdot 7^{3} \) |
$1$ |
$3$ |
$\Z/2\Z\oplus\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$9$ |
$3$ |
2.120.3 |
✓ |
✓ |
$1$ |
\( 2^{3} \) |
\(0.093653\) |
\(9.686161\) |
\(0.453571\) |
$[1536,-11760,-6032145,-1543500]$ |
$[768,26536,1300681,73690928,-385875]$ |
$[-29686813949952/42875,-1335600611328/42875,-85241430016/42875]$ |
$y^2 + (x^3 + x^2)y = x^5 + 2x^4 + x^2 + x - 6$ |
| 3712.b.118784.1 |
3712.b |
\( 2^{7} \cdot 29 \) |
\( 2^{12} \cdot 29 \) |
$1$ |
$2$ |
$\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$9$ |
$1$ |
2.60.1 |
✓ |
✓ |
$1$ |
\( 2^{3} \) |
\(0.019100\) |
\(13.589168\) |
\(0.519112\) |
$[48,72,756,-464]$ |
$[96,192,1792,33792,-118784]$ |
$[-1990656/29,-41472/29,-4032/29]$ |
$y^2 + (x^3 + x^2 + x + 1)y = x^5 - x$ |
| 3746.c.239744.1 |
3746.c |
\( 2 \cdot 1873 \) |
\( - 2^{7} \cdot 1873 \) |
$1$ |
$1$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$9$ |
$1$ |
2.6.1 |
✓ |
✓ |
$1$ |
\( 7 \) |
\(0.004769\) |
\(12.924809\) |
\(0.431440\) |
$[176,-5132,-144447,958976]$ |
$[88,1178,-3281,-419103,239744]$ |
$[41229056/1873,6271672/1873,-397001/3746]$ |
$y^2 + (x + 1)y = -x^5 + 2x^4 - 2x^3 + x$ |
| 3788.b.242432.1 |
3788.b |
\( 2^{2} \cdot 947 \) |
\( - 2^{8} \cdot 947 \) |
$1$ |
$1$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$9$ |
$1$ |
2.6.1 |
✓ |
✓ |
$1$ |
\( 13 \) |
\(0.002895\) |
\(14.096947\) |
\(0.530568\) |
$[620,-3335,378803,31031296]$ |
$[155,1140,-2624,-426580,242432]$ |
$[89466096875/242432,1061304375/60608,-985025/3788]$ |
$y^2 + (x^3 + 1)y = x^5 + x^4 - x^2 - 2x$ |
| 3807.a.925101.1 |
3807.a |
\( 3^{4} \cdot 47 \) |
\( 3^{9} \cdot 47 \) |
$1$ |
$1$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$9$ |
$1$ |
2.6.1 |
✓ |
✓ |
$1$ |
\( 2 \cdot 3 \) |
\(0.005278\) |
\(12.461964\) |
\(0.394668\) |
$[456,26928,2933208,-3700404]$ |
$[228,-2322,-14236,-2159373,-925101]$ |
$[-2535525376/3807,37751936/1269,82227136/102789]$ |
$y^2 + y = x^5 + 7x^4 + 7x^3 + 4x^2 + x$ |
| 3984.a.47808.1 |
3984.a |
\( 2^{4} \cdot 3 \cdot 83 \) |
\( - 2^{6} \cdot 3^{2} \cdot 83 \) |
$1$ |
$3$ |
$\Z/2\Z\oplus\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$9$ |
$3$ |
2.120.3 |
✓ |
✓ |
$1$ |
\( 2^{3} \) |
\(0.053578\) |
\(17.574492\) |
\(0.470802\) |
$[136,-632,64820,191232]$ |
$[68,298,-8464,-166089,47808]$ |
$[22717712/747,1464074/747,-611524/747]$ |
$y^2 + (x + 1)y = -2x^5 + x^3$ |
| 4150.a.41500.1 |
4150.a |
\( 2 \cdot 5^{2} \cdot 83 \) |
\( - 2^{2} \cdot 5^{3} \cdot 83 \) |
$1$ |
$2$ |
$\Z/4\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$9$ |
$1$ |
2.60.1 |
✓ |
✓ |
$1$ |
\( 2^{2} \) |
\(0.150550\) |
\(14.516989\) |
\(0.546385\) |
$[756,-35631,-9830871,-5312000]$ |
$[189,2973,74225,1297449,-41500]$ |
$[-241162079949/41500,-20071522737/41500,-106055649/1660]$ |
$y^2 + (x^2 + x + 1)y = x^6 + 3x^5 + 2x^4 - x - 1$ |
| 4252.a.68032.1 |
4252.a |
\( 2^{2} \cdot 1063 \) |
\( 2^{6} \cdot 1063 \) |
$1$ |
$1$ |
$\Z/3\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,3$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$9$ |
$1$ |
2.6.1, 3.80.1 |
✓ |
✓ |
$1$ |
\( 3^{2} \) |
\(0.033894\) |
\(16.519099\) |
\(0.559900\) |
$[20,6745,-157347,8708096]$ |
$[5,-280,2576,-16380,68032]$ |
$[3125/68032,-4375/8504,4025/4252]$ |
$y^2 + (x^3 + 1)y = x^4 - x^2 - x$ |
| 4276.a.273664.1 |
4276.a |
\( 2^{2} \cdot 1069 \) |
\( 2^{8} \cdot 1069 \) |
$1$ |
$1$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$9$ |
$1$ |
2.6.1 |
✓ |
✓ |
$1$ |
\( 2 \cdot 5 \) |
\(0.003352\) |
\(16.845413\) |
\(0.564663\) |
$[820,21577,3581701,35028992]$ |
$[205,852,21392,914864,273664]$ |
$[362050628125/273664,1835021625/68416,56187425/17104]$ |
$y^2 + (x^2 + x + 1)y = 4x^5 + 8x^4 + 4x^3$ |
| 4580.a.293120.1 |
4580.a |
\( 2^{2} \cdot 5 \cdot 229 \) |
\( 2^{8} \cdot 5 \cdot 229 \) |
$1$ |
$2$ |
$\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$9$ |
$1$ |
2.60.1 |
✓ |
✓ |
$1$ |
\( 2 \cdot 5 \) |
\(0.012742\) |
\(18.214383\) |
\(0.580220\) |
$[1236,53433,18749997,37519360]$ |
$[309,1752,-1024,-846480,293120]$ |
$[2817036000549/293120,6461294751/36640,-381924/1145]$ |
$y^2 + (x^3 + 1)y = x^5 - x^4 - 4x^3 + x^2 + 2x$ |
| 4706.a.150592.1 |
4706.a |
\( 2 \cdot 13 \cdot 181 \) |
\( 2^{6} \cdot 13 \cdot 181 \) |
$1$ |
$1$ |
$\Z/3\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,3$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$9$ |
$1$ |
2.6.1, 3.80.1 |
✓ |
✓ |
$1$ |
\( 2 \cdot 3 \) |
\(0.045409\) |
\(15.693624\) |
\(0.475084\) |
$[16,3172,-10737,602368]$ |
$[8,-526,2369,-64431,150592]$ |
$[512/2353,-4208/2353,2369/2353]$ |
$y^2 + (x + 1)y = -x^5 + 2x^3 + 2x^2$ |
| 4992.a.119808.1 |
4992.a |
\( 2^{7} \cdot 3 \cdot 13 \) |
\( 2^{10} \cdot 3^{2} \cdot 13 \) |
$1$ |
$2$ |
$\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,3$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$9$ |
$1$ |
2.60.1, 3.40.1 |
✓ |
✓ |
$1$ |
\( 2^{3} \) |
\(0.016424\) |
\(15.951657\) |
\(0.523991\) |
$[200,928,59572,-14976]$ |
$[200,1048,-64,-277776,-119808]$ |
$[-312500000/117,-8187500/117,2500/117]$ |
$y^2 + (x + 1)y = x^6 - 2x^5$ |
| 4992.c.958464.1 |
4992.c |
\( 2^{7} \cdot 3 \cdot 13 \) |
\( - 2^{13} \cdot 3^{2} \cdot 13 \) |
$1$ |
$3$ |
$\Z/2\Z\oplus\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$9$ |
$3$ |
2.120.3 |
✓ |
✓ |
$1$ |
\( 2^{3} \) |
\(0.077604\) |
\(12.807874\) |
\(0.496970\) |
$[130,-365,-1261,3744]$ |
$[260,3790,-20644,-4932885,958464]$ |
$[89253125/72,40031875/576,-1677325/1152]$ |
$y^2 + (x^2 + 1)y = 3x^5 + x^4 - x$ |
| 5004.a.960768.1 |
5004.a |
\( 2^{2} \cdot 3^{2} \cdot 139 \) |
\( 2^{8} \cdot 3^{3} \cdot 139 \) |
$1$ |
$2$ |
$\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$9$ |
$1$ |
2.60.1 |
✓ |
✓ |
$1$ |
\( 2^{2} \cdot 5 \) |
\(0.009113\) |
\(13.974534\) |
\(0.636737\) |
$[780,27369,9665739,-122978304]$ |
$[195,444,-55312,-2745744,-960768]$ |
$[-10442615625/35584,-30483375/8896,14605825/6672]$ |
$y^2 + (x^3 + 1)y = -2x^4 + 2x^3 - 2x + 2$ |
| 5012.c.320768.1 |
5012.c |
\( 2^{2} \cdot 7 \cdot 179 \) |
\( 2^{8} \cdot 7 \cdot 179 \) |
$1$ |
$1$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$9$ |
$1$ |
2.6.1 |
✓ |
✓ |
$1$ |
\( 13 \) |
\(0.003178\) |
\(14.812966\) |
\(0.612030\) |
$[84,16137,-38907,41058304]$ |
$[21,-654,4484,-83388,320768]$ |
$[583443/45824,-432621/22912,70623/11456]$ |
$y^2 + (x^3 + 1)y = x^5 - 2x^4 + 2x^2 - x$ |
| 5103.a.15309.1 |
5103.a |
\( 3^{6} \cdot 7 \) |
\( 3^{7} \cdot 7 \) |
$1$ |
$1$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$9$ |
$1$ |
2.6.1 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(0.008812\) |
\(25.187414\) |
\(0.443913\) |
$[72,576,8664,252]$ |
$[108,-378,2844,41067,15309]$ |
$[6718464/7,-31104,15168/7]$ |
$y^2 + x^3y = x^5 - 3x^3 - x^2 + 3x + 2$ |
| 5184.c.995328.1 |
5184.c |
\( 2^{6} \cdot 3^{4} \) |
\( - 2^{12} \cdot 3^{5} \) |
$1$ |
$3$ |
$\Z/2\Z\oplus\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$9$ |
$3$ |
2.120.3 |
✓ |
✓ |
$1$ |
\( 2^{3} \) |
\(0.080335\) |
\(11.039824\) |
\(0.443441\) |
$[2,-128,-400,-16]$ |
$[12,3078,66564,-2168829,-995328]$ |
$[-1/4,-171/32,-1849/192]$ |
$y^2 + y = 4x^5 - x^3 - x^2$ |
| 5416.a.173312.1 |
5416.a |
\( 2^{3} \cdot 677 \) |
\( 2^{8} \cdot 677 \) |
$1$ |
$1$ |
$\Z/7\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,7$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$9$ |
$1$ |
2.6.1 |
✓ |
✓ |
$1$ |
\( 2 \cdot 7 \) |
\(0.182387\) |
\(14.525935\) |
\(0.756955\) |
$[240,1296,127332,-693248]$ |
$[120,384,-2948,-125304,-173312]$ |
$[-97200000/677,-2592000/677,165825/677]$ |
$y^2 + (x + 1)y = x^6 - x^2$ |
