| 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 |
| 3969.b.35721.1 |
3969.b |
\( 3^{4} \cdot 7^{2} \) |
\( 3^{6} \cdot 7^{2} \) |
$2$ |
$2$ |
$\mathsf{trivial}$ |
\(\mathrm{M}_2(\Q)\) |
\(\mathsf{CM}\) |
✓ |
$E_6$ |
|
✓ |
|
$C_6$ |
$D_6$ |
$18$ |
$0$ |
2.80.1, 3.480.12 |
✓ |
✓ |
$1$ |
\( 3 \) |
\(0.003155\) |
\(23.234167\) |
\(0.219945\) |
$[268,2961,216951,18816]$ |
$[201,573,-563,-110373,35721]$ |
$[1350125107/147,57445733/441,-2527307/3969]$ |
$y^2 + (x^3 + x + 1)y = -2x^5 + 3x^4 - 3x^2$ |
| 7884.b.283824.1 |
7884.b |
\( 2^{2} \cdot 3^{3} \cdot 73 \) |
\( 2^{4} \cdot 3^{5} \cdot 73 \) |
$2$ |
$2$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
|
✓ |
✓ |
$C_2$ |
$C_2$ |
$18$ |
$0$ |
|
✓ |
✓ |
$1$ |
\( 3^{2} \) |
\(0.002338\) |
\(17.885402\) |
\(0.376330\) |
$[40,237,1909,146]$ |
$[120,-822,5584,-1401,283824]$ |
$[6400000/73,-1096000/219,558400/1971]$ |
$y^2 + (x^3 + x^2 + x + 1)y = -x^4 + 4x^2 + 2x$ |
| 25913.a.25913.1 |
25913.a |
\( 25913 \) |
\( 25913 \) |
$3$ |
$3$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
|
✓ |
✓ |
$C_2$ |
$C_2$ |
$18$ |
$0$ |
|
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.019223\) |
\(20.351877\) |
\(0.391214\) |
$[36,4857,-524835,3316864]$ |
$[9,-199,7797,7643,25913]$ |
$[59049/25913,-145071/25913,631557/25913]$ |
$y^2 + (x^3 + x + 1)y = x^3 - x^2 - 2x$ |
| 41411.a.41411.1 |
41411.a |
\( 41411 \) |
\( 41411 \) |
$3$ |
$3$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
|
✓ |
✓ |
$C_2$ |
$C_2$ |
$18$ |
$0$ |
|
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.029860\) |
\(19.864180\) |
\(0.593148\) |
$[1044,16089,2664477,5300608]$ |
$[261,2168,52752,2267012,41411]$ |
$[1211162837301/41411,38546131608/41411,3593518992/41411]$ |
$y^2 + (x^3 + 1)y = -3x^4 + 7x^3 - 4x^2$ |
| 41663.b.41663.1 |
41663.b |
\( 61 \cdot 683 \) |
\( 61 \cdot 683 \) |
$3$ |
$3$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
|
✓ |
✓ |
$C_2$ |
$C_2$ |
$18$ |
$0$ |
|
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.022321\) |
\(21.884652\) |
\(0.488481\) |
$[1284,38841,14686365,5332864]$ |
$[321,2675,16893,-433243,41663]$ |
$[3408200705601/41663,88478730675/41663,1740671613/41663]$ |
$y^2 + (x^3 + x + 1)y = x^5 - x^4 - 4x^3 + 2x$ |
| 45413.a.45413.1 |
45413.a |
\( 45413 \) |
\( -45413 \) |
$3$ |
$3$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
|
✓ |
✓ |
$C_2$ |
$C_2$ |
$18$ |
$0$ |
|
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.025475\) |
\(19.997449\) |
\(0.509438\) |
$[548,9193,955301,-5812864]$ |
$[137,399,7261,208889,-45413]$ |
$[-48261724457/45413,-1025969847/45413,-136281709/45413]$ |
$y^2 + (x^3 + x + 1)y = -x^5 + 2x^2 - 3x$ |
| 49507.a.49507.1 |
49507.a |
\( 31 \cdot 1597 \) |
\( - 31 \cdot 1597 \) |
$3$ |
$3$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
|
✓ |
✓ |
$C_2$ |
$C_2$ |
$18$ |
$0$ |
|
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.040745\) |
\(15.858977\) |
\(0.646167\) |
$[300,8889,544659,6336896]$ |
$[75,-136,1128,16526,49507]$ |
$[2373046875/49507,-57375000/49507,6345000/49507]$ |
$y^2 + (x^3 + 1)y = 2x^4 + 3x^3 + 3x^2 + x$ |
| 52498.a.104996.1 |
52498.a |
\( 2 \cdot 26249 \) |
\( 2^{2} \cdot 26249 \) |
$3$ |
$3$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
|
✓ |
✓ |
$C_2$ |
$C_2$ |
$18$ |
$0$ |
|
✓ |
✓ |
$1$ |
\( 2 \) |
\(0.020395\) |
\(16.217317\) |
\(0.661516\) |
$[588,6873,1630563,-13439488]$ |
$[147,614,-3600,-226549,-104996]$ |
$[-68641485507/104996,-975192561/52498,19448100/26249]$ |
$y^2 + (x^3 + x^2 + x)y = -2x^4 - x + 1$ |
| 54983.a.54983.1 |
54983.a |
\( 54983 \) |
\( -54983 \) |
$3$ |
$3$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
|
✓ |
✓ |
$C_2$ |
$C_2$ |
$18$ |
$0$ |
|
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.032929\) |
\(21.518437\) |
\(0.708583\) |
$[200,21076,648368,-219932]$ |
$[100,-3096,27848,-1700104,-54983]$ |
$[-10000000000/54983,3096000000/54983,-278480000/54983]$ |
$y^2 + y = x^6 - x^5 - 3x^4 + x^3 + 3x^2 + x$ |
| 57065.a.285325.1 |
57065.a |
\( 5 \cdot 101 \cdot 113 \) |
\( - 5^{2} \cdot 101 \cdot 113 \) |
$3$ |
$3$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
|
✓ |
✓ |
$C_2$ |
$C_2$ |
$18$ |
$0$ |
|
✓ |
✓ |
$1$ |
\( 2 \) |
\(0.016343\) |
\(17.235344\) |
\(0.563352\) |
$[228,28617,1483701,-36521600]$ |
$[57,-1057,-1299,-297823,-285325]$ |
$[-601692057/285325,195749001/285325,4220451/285325]$ |
$y^2 + (x^3 + x + 1)y = x^4 - 4x^3 + x^2$ |
| 59107.a.59107.1 |
59107.a |
\( 59107 \) |
\( 59107 \) |
$3$ |
$3$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
|
✓ |
✓ |
$C_2$ |
$C_2$ |
$18$ |
$0$ |
|
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.027565\) |
\(20.504440\) |
\(0.565207\) |
$[452,20473,1298237,7565696]$ |
$[113,-321,12085,315641,59107]$ |
$[18424351793/59107,-463169937/59107,154313365/59107]$ |
$y^2 + (x^3 + x^2 + 1)y = 2x^4 - 3x^2 - x$ |
| 60617.a.60617.1 |
60617.a |
\( 60617 \) |
\( 60617 \) |
$3$ |
$3$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
|
✓ |
✓ |
$C_2$ |
$C_2$ |
$18$ |
$0$ |
|
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.025722\) |
\(22.520707\) |
\(0.579286\) |
$[612,80025,8776845,7758976]$ |
$[153,-2359,28101,-316357,60617]$ |
$[83841135993/60617,-8448940143/60617,657816309/60617]$ |
$y^2 + (x^3 + x + 1)y = x^4 - 5x^3 + x^2 + x$ |
| 61127.a.61127.1 |
61127.a |
\( 11 \cdot 5557 \) |
\( - 11 \cdot 5557 \) |
$3$ |
$3$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
|
✓ |
✓ |
$C_2$ |
$C_2$ |
$18$ |
$0$ |
|
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.029475\) |
\(19.614389\) |
\(0.578137\) |
$[548,10489,1460957,-7824256]$ |
$[137,345,2293,48779,-61127]$ |
$[-48261724457/61127,-887116785/61127,-43037317/61127]$ |
$y^2 + (x^3 + x + 1)y = 2x^5 + 3x^4 - x^2$ |
| 61553.a.61553.1 |
61553.a |
\( 61553 \) |
\( -61553 \) |
$3$ |
$3$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
|
✓ |
✓ |
$C_2$ |
$C_2$ |
$18$ |
$0$ |
|
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.029514\) |
\(20.665839\) |
\(0.609927\) |
$[260,20089,257469,-7878784]$ |
$[65,-661,12173,88581,-61553]$ |
$[-1160290625/61553,181527125/61553,-51430925/61553]$ |
$y^2 + (x^3 + x + 1)y = -x^4 - 3x^3 + x^2 + x$ |
| 62563.a.62563.1 |
62563.a |
\( 62563 \) |
\( 62563 \) |
$3$ |
$3$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
|
✓ |
✓ |
$C_2$ |
$C_2$ |
$18$ |
$0$ |
|
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.029057\) |
\(21.403273\) |
\(0.621922\) |
$[1028,58585,13837773,8008064]$ |
$[257,311,21365,1348521,62563]$ |
$[1121154893057/62563,5279098423/62563,1411136885/62563]$ |
$y^2 + (x^3 + x + 1)y = -3x^4 + x^3 + 3x^2 - x$ |
| 63506.a.127012.1 |
63506.a |
\( 2 \cdot 113 \cdot 281 \) |
\( - 2^{2} \cdot 113 \cdot 281 \) |
$3$ |
$3$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$18$ |
$0$ |
2.10.1 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(0.018715\) |
\(19.161053\) |
\(0.717203\) |
$[180,29049,814221,-16257536]$ |
$[45,-1126,4032,-271609,-127012]$ |
$[-184528125/127012,51303375/63506,-2041200/31753]$ |
$y^2 + (x^3 + 1)y = 2x^3 + 2x^2 - x$ |
| 63707.a.445949.1 |
63707.a |
\( 7 \cdot 19 \cdot 479 \) |
\( - 7^{2} \cdot 19 \cdot 479 \) |
$3$ |
$3$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
|
✓ |
✓ |
$C_2$ |
$C_2$ |
$18$ |
$0$ |
|
✓ |
✓ |
$1$ |
\( 2 \) |
\(0.018083\) |
\(17.460609\) |
\(0.631480\) |
$[388,94297,-541043,-57081472]$ |
$[97,-3537,115493,-326887,-445949]$ |
$[-8587340257/445949,3228124401/445949,-22177013/9101]$ |
$y^2 + (x^3 + x + 1)y = x^5 + x^3 + 6x^2 + 2x$ |
| 64237.a.64237.1 |
64237.a |
\( 64237 \) |
\( 64237 \) |
$3$ |
$3$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
|
✓ |
✓ |
$C_2$ |
$C_2$ |
$18$ |
$0$ |
|
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.034994\) |
\(18.153996\) |
\(0.635284\) |
$[508,4489,4345419,-8222336]$ |
$[127,485,-49013,-1614969,-64237]$ |
$[-33038369407/64237,-993465755/64237,790530677/64237]$ |
$y^2 + (x^3 + x^2 + 1)y = x^3 - 3x$ |
| 67006.a.134012.1 |
67006.a |
\( 2 \cdot 33503 \) |
\( 2^{2} \cdot 33503 \) |
$3$ |
$3$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
|
✓ |
✓ |
$C_2$ |
$C_2$ |
$18$ |
$0$ |
|
✓ |
✓ |
$1$ |
\( 2 \) |
\(0.019104\) |
\(19.351847\) |
\(0.739388\) |
$[372,31641,2506749,17153536]$ |
$[93,-958,1104,-203773,134012]$ |
$[6956883693/134012,-385287003/67006,2387124/33503]$ |
$y^2 + (x^3 + 1)y = 3x^4 + x^3 - x^2$ |
| 67203.c.604827.1 |
67203.c |
\( 3^{3} \cdot 19 \cdot 131 \) |
\( 3^{5} \cdot 19 \cdot 131 \) |
$3$ |
$3$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
|
✓ |
✓ |
$C_2$ |
$C_2$ |
$18$ |
$0$ |
|
✓ |
✓ |
$1$ |
\( 3 \) |
\(0.016859\) |
\(13.556935\) |
\(0.685653\) |
$[1116,27657,9938475,-77417856]$ |
$[279,2091,1547,-985167,-604827]$ |
$[-6956883693/2489,-186878943/2489,-1486667/7467]$ |
$y^2 + (x^3 + x + 1)y = -x^4 - x^2 + 2$ |
| 71446.a.142892.1 |
71446.a |
\( 2 \cdot 139 \cdot 257 \) |
\( - 2^{2} \cdot 139 \cdot 257 \) |
$3$ |
$3$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
|
✓ |
✓ |
$C_2$ |
$C_2$ |
$18$ |
$0$ |
|
✓ |
✓ |
$1$ |
\( 2 \) |
\(0.023695\) |
\(15.995218\) |
\(0.758019\) |
$[172,-1031,1120531,18290176]$ |
$[43,120,-15892,-174439,142892]$ |
$[147008443/142892,2385210/35723,-7346077/35723]$ |
$y^2 + (x^3 + 1)y = 2x^5 - 4x^4 + 3x^3 - x$ |
| 79154.a.158308.1 |
79154.a |
\( 2 \cdot 19 \cdot 2083 \) |
\( - 2^{2} \cdot 19 \cdot 2083 \) |
$3$ |
$3$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
|
✓ |
✓ |
$C_2$ |
$C_2$ |
$18$ |
$0$ |
|
✓ |
✓ |
$1$ |
\( 2 \) |
\(0.021341\) |
\(18.354204\) |
\(0.783381\) |
$[180,31929,1243629,-20263424]$ |
$[45,-1246,-432,-392989,-158308]$ |
$[-184528125/158308,56770875/79154,218700/39577]$ |
$y^2 + (x^3 + 1)y = 2x^4 + 2x^3 - x$ |
| 82413.a.247239.1 |
82413.a |
\( 3^{2} \cdot 9157 \) |
\( 3^{3} \cdot 9157 \) |
$3$ |
$3$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
|
✓ |
✓ |
$C_2$ |
$C_2$ |
$18$ |
$0$ |
|
✓ |
✓ |
$1$ |
\( 2 \) |
\(0.020590\) |
\(17.049342\) |
\(0.702096\) |
$[612,19017,2370933,31646592]$ |
$[153,183,9037,337293,247239]$ |
$[3105227259/9157,24275133/9157,7835079/9157]$ |
$y^2 + (x^3 + x + 1)y = -x^5 + 2x^4 - 2x^2 - x$ |
| 83422.a.166844.1 |
83422.a |
\( 2 \cdot 53 \cdot 787 \) |
\( 2^{2} \cdot 53 \cdot 787 \) |
$3$ |
$3$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
|
✓ |
✓ |
$C_2$ |
$C_2$ |
$18$ |
$0$ |
|
✓ |
✓ |
$1$ |
\( 2 \) |
\(0.025289\) |
\(16.098251\) |
\(0.814204\) |
$[876,12345,4168563,-21356032]$ |
$[219,1484,-2292,-676051,-166844]$ |
$[-503756397099/166844,-73524213/787,27481653/41711]$ |
$y^2 + (x^3 + 1)y = -x^5 + x^4 + x^2 - 7x + 6$ |
| 84685.a.423425.1 |
84685.a |
\( 5 \cdot 16937 \) |
\( 5^{2} \cdot 16937 \) |
$3$ |
$3$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
|
✓ |
✓ |
$C_2$ |
$C_2$ |
$18$ |
$0$ |
|
✓ |
✓ |
$1$ |
\( 2 \) |
\(0.029187\) |
\(14.395548\) |
\(0.840333\) |
$[204,34377,1726779,-54198400]$ |
$[51,-1324,-3384,-481390,-423425]$ |
$[-345025251/423425,175629924/423425,8801784/423425]$ |
$y^2 + (x^3 + x^2 + x)y = x^4 + 2x + 1$ |
| 85403.a.85403.1 |
85403.a |
\( 41 \cdot 2083 \) |
\( - 41 \cdot 2083 \) |
$3$ |
$3$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
|
✓ |
✓ |
$C_2$ |
$C_2$ |
$18$ |
$0$ |
|
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.049862\) |
\(16.941228\) |
\(0.844731\) |
$[16,-1676,-416552,-341612]$ |
$[8,282,45664,71447,-85403]$ |
$[-32768/85403,-144384/85403,-2922496/85403]$ |
$y^2 + y = x^6 - x^5 + 2x^3 - x^2 - x$ |
| 86365.a.431825.1 |
86365.a |
\( 5 \cdot 23 \cdot 751 \) |
\( 5^{2} \cdot 23 \cdot 751 \) |
$3$ |
$3$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$18$ |
$0$ |
2.20.2 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(0.022023\) |
\(16.311869\) |
\(0.718477\) |
$[252,65097,7313067,-55273600]$ |
$[63,-2547,-53525,-2464821,-431825]$ |
$[-992436543/431825,636869709/431825,8497629/17273]$ |
$y^2 + (x^3 + x + 1)y = x^5 + 2x^4 + x^3 - 2x^2 + 2$ |
| 90963.d.818667.1 |
90963.d |
\( 3^{4} \cdot 1123 \) |
\( - 3^{6} \cdot 1123 \) |
$3$ |
$3$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
|
✓ |
✓ |
$C_2$ |
$C_2$ |
$18$ |
$0$ |
|
✓ |
✓ |
$1$ |
\( 3 \) |
\(0.017320\) |
\(14.021215\) |
\(0.728562\) |
$[20,3105,3969,431232]$ |
$[15,-1155,3371,-320865,818667]$ |
$[3125/3369,-48125/10107,84275/90963]$ |
$y^2 + (x^3 + x + 1)y = x^5 + 3x^4$ |
| 94533.a.283599.1 |
94533.a |
\( 3 \cdot 31511 \) |
\( - 3^{2} \cdot 31511 \) |
$3$ |
$3$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
|
✓ |
✓ |
$C_2$ |
$C_2$ |
$18$ |
$0$ |
|
✓ |
✓ |
$1$ |
\( 2 \) |
\(0.037653\) |
\(12.557814\) |
\(0.945684\) |
$[16,-13148,-387256,-1134396]$ |
$[8,2194,38160,-1127089,-283599]$ |
$[-32768/283599,-1123328/283599,-271360/31511]$ |
$y^2 + y = x^6 - x^5 - 3x^4 + 3x^2 + 2x$ |
| 96677.a.676739.1 |
96677.a |
\( 7^{2} \cdot 1973 \) |
\( - 7^{3} \cdot 1973 \) |
$3$ |
$3$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
|
✓ |
✓ |
$C_2$ |
$C_2$ |
$18$ |
$0$ |
|
✓ |
✓ |
$1$ |
\( 2 \) |
\(0.028686\) |
\(12.957698\) |
\(0.743413\) |
$[988,49945,13920627,86622592]$ |
$[247,461,-15677,-1021185,676739]$ |
$[919358226007/676739,6946911803/676739,-956438093/676739]$ |
$y^2 + (x^3 + x + 1)y = 2x^3 + 3x^2 + 3x + 2$ |
| 101679.a.305037.1 |
101679.a |
\( 3 \cdot 33893 \) |
\( 3^{2} \cdot 33893 \) |
$3$ |
$3$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
|
✓ |
✓ |
$C_2$ |
$C_2$ |
$18$ |
$0$ |
|
✓ |
✓ |
$1$ |
\( 2 \) |
\(0.031749\) |
\(12.849864\) |
\(0.815942\) |
$[380,-19511,-1340309,-39044736]$ |
$[95,1189,-853,-373689,-305037]$ |
$[-7737809375/305037,-1019418875/305037,7698325/305037]$ |
$y^2 + (x^3 + x + 1)y = 2x^5 - x^4 + x^3 - x^2 - x$ |
| 103767.a.311301.1 |
103767.a |
\( 3 \cdot 34589 \) |
\( 3^{2} \cdot 34589 \) |
$3$ |
$3$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
|
✓ |
✓ |
$C_2$ |
$C_2$ |
$18$ |
$0$ |
|
✓ |
✓ |
$1$ |
\( 2 \) |
\(0.026885\) |
\(14.936419\) |
\(0.803120\) |
$[860,14233,4746547,-39846528]$ |
$[215,1333,-7501,-847401,-311301]$ |
$[-459401384375/311301,-13247853875/311301,346733725/311301]$ |
$y^2 + (x^3 + x + 1)y = x^5 + x^4 + x^3 - 3x$ |
| 104363.b.730541.1 |
104363.b |
\( 7 \cdot 17 \cdot 877 \) |
\( - 7^{2} \cdot 17 \cdot 877 \) |
$3$ |
$3$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
|
✓ |
✓ |
$C_2$ |
$C_2$ |
$18$ |
$0$ |
|
✓ |
✓ |
$1$ |
\( 2 \) |
\(0.022360\) |
\(17.415065\) |
\(0.778818\) |
$[1060,153097,36827221,-93509248]$ |
$[265,-3453,1157,-2904151,-730541]$ |
$[-1306860915625/730541,64259035125/730541,-81250325/730541]$ |
$y^2 + (x^3 + x + 1)y = x^5 + 5x^4 + x^3 - 2x^2 - x$ |
| 104482.a.208964.1 |
104482.a |
\( 2 \cdot 7 \cdot 17 \cdot 439 \) |
\( 2^{2} \cdot 7 \cdot 17 \cdot 439 \) |
$3$ |
$3$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
|
✓ |
✓ |
$C_2$ |
$C_2$ |
$18$ |
$0$ |
|
✓ |
✓ |
$1$ |
\( 2 \) |
\(0.030275\) |
\(14.427198\) |
\(0.873573\) |
$[108,14937,608067,-26747392]$ |
$[27,-592,-3732,-112807,-208964]$ |
$[-14348907/208964,2913084/52241,680157/52241]$ |
$y^2 + (x^3 + 1)y = 2x^4 + x$ |
| 104996.a.419984.1 |
104996.a |
\( 2^{2} \cdot 26249 \) |
\( - 2^{4} \cdot 26249 \) |
$3$ |
$3$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
|
✓ |
✓ |
$C_2$ |
$C_2$ |
$18$ |
$0$ |
|
✓ |
✓ |
$1$ |
\( 3 \) |
\(0.017278\) |
\(17.037099\) |
\(0.883101\) |
$[200,2293,100967,-52498]$ |
$[200,138,13696,680039,-419984]$ |
$[-20000000000/26249,-69000000/26249,-34240000/26249]$ |
$y^2 + y = x^6 - 2x^5 - 5x^4 + 4x^2 + 2x$ |
| 110848.b.221696.1 |
110848.b |
\( 2^{8} \cdot 433 \) |
\( - 2^{9} \cdot 433 \) |
$3$ |
$4$ |
$\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$18$ |
$0$ |
2.15.1 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(0.101663\) |
\(18.434702\) |
\(0.937066\) |
$[26,1138,27176,866]$ |
$[52,-2922,-149092,-4072717,221696]$ |
$[742586/433,-3209817/1732,-6299137/3464]$ |
$y^2 + x^3y = x^5 + x^4 - 3x^3 - 5x^2 + 2x + 4$ |
| 112529.a.112529.1 |
112529.a |
\( 131 \cdot 859 \) |
\( 131 \cdot 859 \) |
$3$ |
$3$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
|
✓ |
✓ |
$C_2$ |
$C_2$ |
$18$ |
$0$ |
|
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.051367\) |
\(19.306450\) |
\(0.991711\) |
$[852,22617,4802013,14403712]$ |
$[213,948,11432,384078,112529]$ |
$[438427732293/112529,9161089956/112529,518658408/112529]$ |
$y^2 + (x^3 + 1)y = -3x^4 + 4x^3 - x$ |
| 113675.a.568375.1 |
113675.a |
\( 5^{2} \cdot 4547 \) |
\( - 5^{3} \cdot 4547 \) |
$3$ |
$3$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
|
✓ |
✓ |
$C_2$ |
$C_2$ |
$18$ |
$0$ |
|
✓ |
✓ |
$1$ |
\( 2 \) |
\(0.027480\) |
\(13.271808\) |
\(0.729424\) |
$[612,2265,469485,-72752000]$ |
$[153,881,5781,27083,-568375]$ |
$[-83841135993/568375,-3155369337/568375,-135327429/568375]$ |
$y^2 + (x^3 + x + 1)y = -2x^5 + x^4 + x^2 - 2x$ |
| 115735.a.578675.1 |
115735.a |
\( 5 \cdot 79 \cdot 293 \) |
\( 5^{2} \cdot 79 \cdot 293 \) |
$3$ |
$3$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
|
✓ |
✓ |
$C_2$ |
$C_2$ |
$18$ |
$0$ |
|
✓ |
✓ |
$1$ |
\( 2 \) |
\(0.022775\) |
\(16.991225\) |
\(0.773941\) |
$[1596,669753,541410147,-74070400]$ |
$[399,-21273,-4279589,-540024135,-578675]$ |
$[-10112638401999/578675,1351286466327/578675,681314848389/578675]$ |
$y^2 + (x^3 + x + 1)y = x^4 + x^3 - 7x^2 - 3x + 6$ |
| 115784.a.231568.1 |
115784.a |
\( 2^{3} \cdot 41 \cdot 353 \) |
\( - 2^{4} \cdot 41 \cdot 353 \) |
$3$ |
$3$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
|
✓ |
✓ |
$C_2$ |
$C_2$ |
$18$ |
$0$ |
|
✓ |
✓ |
$1$ |
\( 2 \) |
\(0.025254\) |
\(18.043251\) |
\(0.911330\) |
$[456,4677,640695,-28946]$ |
$[456,5546,44928,-2567737,-231568]$ |
$[-1232265332736/14473,-32866572096/14473,-583884288/14473]$ |
$y^2 + x^3y = -4x^4 - 4x^3 + 3x^2 + 4x + 1$ |
| 117231.a.351693.1 |
117231.a |
\( 3 \cdot 23 \cdot 1699 \) |
\( - 3^{2} \cdot 23 \cdot 1699 \) |
$3$ |
$3$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
|
✓ |
✓ |
$C_2$ |
$C_2$ |
$18$ |
$0$ |
|
✓ |
✓ |
$1$ |
\( 2 \) |
\(0.024026\) |
\(16.203841\) |
\(0.778642\) |
$[1412,34009,8524621,-45016704]$ |
$[353,3775,122373,7236761,-351693]$ |
$[-5481173216993/351693,-166050838175/351693,-1694308573/39077]$ |
$y^2 + (x^3 + x + 1)y = -4x^4 - 5x^3 + x^2$ |
| 120436.a.481744.1 |
120436.a |
\( 2^{2} \cdot 30109 \) |
\( - 2^{4} \cdot 30109 \) |
$3$ |
$3$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
|
✓ |
✓ |
$C_2$ |
$C_2$ |
$18$ |
$0$ |
|
✓ |
✓ |
$1$ |
\( 3 \) |
\(0.018135\) |
\(17.820999\) |
\(0.969564\) |
$[312,4677,368463,-60218]$ |
$[312,938,13008,794663,-481744]$ |
$[-184779159552/30109,-1780519104/30109,-79140672/30109]$ |
$y^2 + x^3y = 6x^3 + 11x^2 + 6x + 1$ |
| 121994.a.243988.1 |
121994.a |
\( 2 \cdot 181 \cdot 337 \) |
\( - 2^{2} \cdot 181 \cdot 337 \) |
$3$ |
$3$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
|
✓ |
✓ |
$C_2$ |
$C_2$ |
$18$ |
$0$ |
|
✓ |
✓ |
$1$ |
\( 2 \) |
\(0.042220\) |
\(13.983698\) |
\(1.180780\) |
$[744,-24744,-724587,975952]$ |
$[372,9890,-226473,-45515014,243988]$ |
$[1780962225408/60997,127281451680/60997,-7835059908/60997]$ |
$y^2 + (x + 1)y = x^6 - 3x^5 + 3x^3 + x^2 + x$ |
| 122084.a.244168.1 |
122084.a |
\( 2^{2} \cdot 23 \cdot 1327 \) |
\( - 2^{3} \cdot 23 \cdot 1327 \) |
$3$ |
$3$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
|
✓ |
✓ |
$C_2$ |
$C_2$ |
$18$ |
$0$ |
|
✓ |
✓ |
$1$ |
\( 3 \) |
\(0.023630\) |
\(18.106386\) |
\(1.283543\) |
$[1284,56817,17284905,-31253504]$ |
$[321,1926,47588,2891568,-244168]$ |
$[-3408200705601/244168,-31852343043/122084,-1225878777/61042]$ |
$y^2 + (x^3 + x + 1)y = -x^5 + 3x^4 - 3x^2 - x$ |
| 123171.a.369513.1 |
123171.a |
\( 3 \cdot 41057 \) |
\( - 3^{2} \cdot 41057 \) |
$3$ |
$3$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
|
✓ |
✓ |
$C_2$ |
$C_2$ |
$18$ |
$0$ |
|
✓ |
✓ |
$1$ |
\( 2 \) |
\(0.036755\) |
\(14.910383\) |
\(1.096058\) |
$[716,28777,6576715,47297664]$ |
$[179,136,-18448,-830172,369513]$ |
$[183765996899/369513,780006104/369513,-591092368/369513]$ |
$y^2 + (x^3 + x^2 + x)y = x^3 - 2x + 1$ |
| 125201.a.125201.1 |
125201.a |
\( 125201 \) |
\( 125201 \) |
$3$ |
$3$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
|
✓ |
✓ |
$C_2$ |
$C_2$ |
$18$ |
$0$ |
|
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.040238\) |
\(18.926669\) |
\(0.761570\) |
$[996,31929,6976317,16025728]$ |
$[249,1253,30861,1528595,125201]$ |
$[957186876249/125201,19344125997/125201,1913412861/125201]$ |
$y^2 + (x^3 + x + 1)y = 5x^5 + 8x^4 + 3x^3$ |
| 130105.b.650525.1 |
130105.b |
\( 5 \cdot 26021 \) |
\( 5^{2} \cdot 26021 \) |
$3$ |
$3$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
|
✓ |
✓ |
$C_2$ |
$C_2$ |
$18$ |
$0$ |
|
✓ |
✓ |
$1$ |
\( 2 \) |
\(0.033640\) |
\(13.922053\) |
\(0.936689\) |
$[864,3408,454032,2602100]$ |
$[432,7208,204336,9079472,650525]$ |
$[15045919506432/650525,581120262144/650525,38134001664/650525]$ |
$y^2 + x^3y = 4x^3 + 5x^2 - x - 2$ |
| 131074.a.262148.1 |
131074.a |
\( 2 \cdot 65537 \) |
\( - 2^{2} \cdot 65537 \) |
$3$ |
$3$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
|
✓ |
✓ |
$C_2$ |
$C_2$ |
$18$ |
$0$ |
|
✓ |
✓ |
$1$ |
\( 2 \) |
\(0.032963\) |
\(15.751497\) |
\(1.038423\) |
$[940,32425,9977067,33554944]$ |
$[235,950,-20336,-1420365,262148]$ |
$[716703146875/262148,6164490625/131074,-280763900/65537]$ |
$y^2 + (x^3 + 1)y = -x^4 + x^2 - 2x + 2$ |
| 131169.b.393507.1 |
131169.b |
\( 3 \cdot 23 \cdot 1901 \) |
\( 3^{2} \cdot 23 \cdot 1901 \) |
$3$ |
$3$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
|
✓ |
✓ |
$C_2$ |
$C_2$ |
$18$ |
$0$ |
|
✓ |
✓ |
$1$ |
\( 2 \) |
\(0.032863\) |
\(15.969050\) |
\(1.049593\) |
$[20,27433,-930251,50368896]$ |
$[5,-1142,14508,-307906,393507]$ |
$[3125/393507,-142750/393507,40300/43723]$ |
$y^2 + (x^3 + x^2 + x)y = -2x^3 - x^2 + 2x + 1$ |
| 132206.b.264412.1 |
132206.b |
\( 2 \cdot 66103 \) |
\( - 2^{2} \cdot 66103 \) |
$3$ |
$3$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
|
✓ |
✓ |
$C_2$ |
$C_2$ |
$18$ |
$0$ |
|
✓ |
✓ |
$1$ |
\( 2 \) |
\(0.027621\) |
\(17.777314\) |
\(0.982052\) |
$[276,32505,-45267,-33844736]$ |
$[69,-1156,27348,137669,-264412]$ |
$[-1564031349/264412,94939101/66103,-32550957/66103]$ |
$y^2 + (x^3 + 1)y = 2x^5 + 4x^4 - 2x^2 - x$ |
