| 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 |
| 3319.a.3319.1 |
3319.a |
\( 3319 \) |
\( 3319 \) |
$2$ |
$2$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
|
✓ |
✓ |
$C_2$ |
$C_2$ |
$12$ |
$0$ |
|
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.007585\) |
\(25.359353\) |
\(0.192363\) |
$[68,3673,38093,424832]$ |
$[17,-141,205,-4099,3319]$ |
$[1419857/3319,-692733/3319,59245/3319]$ |
$y^2 + (x^3 + x + 1)y = x^5 + 2x^4 + x^3$ |
| 3391.b.3391.1 |
3391.b |
\( 3391 \) |
\( -3391 \) |
$2$ |
$2$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
|
✓ |
✓ |
$C_2$ |
$C_2$ |
$12$ |
$0$ |
|
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.008473\) |
\(22.961204\) |
\(0.194544\) |
$[252,105,105723,434048]$ |
$[63,161,-813,-19285,3391]$ |
$[992436543/3391,40257567/3391,-3226797/3391]$ |
$y^2 + (x^3 + x + 1)y = -x^5 - x^4$ |
| 3469.a.3469.1 |
3469.a |
\( 3469 \) |
\( 3469 \) |
$2$ |
$2$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
|
✓ |
✓ |
$C_2$ |
$C_2$ |
$14$ |
$0$ |
|
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.007740\) |
\(25.513186\) |
\(0.197472\) |
$[164,2905,2669,444032]$ |
$[41,-51,1501,14735,3469]$ |
$[115856201/3469,-3514971/3469,2523181/3469]$ |
$y^2 + (x^3 + x + 1)y = x^5 - x^4 - 2x^3$ |
| 3571.a.3571.1 |
3571.a |
\( 3571 \) |
\( -3571 \) |
$2$ |
$2$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
|
✓ |
✓ |
$C_2$ |
$C_2$ |
$14$ |
$0$ |
|
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.007530\) |
\(26.618205\) |
\(0.200441\) |
$[132,3849,30837,-457088]$ |
$[33,-115,1125,5975,-3571]$ |
$[-39135393/3571,4132755/3571,-1225125/3571]$ |
$y^2 + (x^3 + x + 1)y = -2x^4 + x^2 - x$ |
| 3721.a.3721.1 |
3721.a |
\( 61^{2} \) |
\( - 61^{2} \) |
$2$ |
$2$ |
$\mathsf{trivial}$ |
\(\mathrm{M}_2(\Q)\) |
\(\mathsf{CM}\) |
✓ |
$E_6$ |
|
✓ |
|
$C_6$ |
$D_6$ |
$12$ |
$0$ |
2.40.3, 3.480.12 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.007315\) |
\(28.081352\) |
\(0.205420\) |
$[196,6649,304573,-476288]$ |
$[49,-177,-187,-10123,-3721]$ |
$[-282475249/3721,20823873/3721,448987/3721]$ |
$y^2 + (x^3 + x + 1)y = -x^4 + x^3 + 3x^2 + x$ |
| 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 |
✓ |
✓ |
$1$ |
\( 3 \) |
\(0.003155\) |
\(23.234167\) |
\(0.219945\) |
$[268,2961,216951,18816]$ |
$[201,573,-563,-110373,35721]$ |
$[1350125107/147,57445733/441,-2527307/3969]$ |
$y^2 + (x^3 + x + 1)y = -2x^5 + 3x^4 - 3x^2$ |
| 4021.a.4021.1 |
4021.a |
\( 4021 \) |
\( -4021 \) |
$2$ |
$2$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
|
✓ |
✓ |
$C_2$ |
$C_2$ |
$12$ |
$0$ |
|
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.008454\) |
\(25.264530\) |
\(0.213597\) |
$[228,2697,96981,-514688]$ |
$[57,23,861,12137,-4021]$ |
$[-601692057/4021,-4259439/4021,-2797389/4021]$ |
$y^2 + (x^3 + x + 1)y = x^5 + 2x^2 + x$ |
| 4489.a.4489.1 |
4489.a |
\( 67^{2} \) |
\( 67^{2} \) |
$2$ |
$2$ |
$\mathsf{trivial}$ |
\(\mathsf{RM}\) |
\(\mathsf{RM}\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
✓ |
✓ |
$C_2$ |
$C_2$ |
$10$ |
$0$ |
2.12.2, 3.2160.18 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.011439\) |
\(20.465113\) |
\(0.234100\) |
$[284,1369,127187,-574592]$ |
$[71,153,187,-2533,-4489]$ |
$[-1804229351/4489,-54760383/4489,-942667/4489]$ |
$y^2 + (x^3 + x + 1)y = x^5 - x$ |
| 4673.a.4673.1 |
4673.a |
\( 4673 \) |
\( 4673 \) |
$2$ |
$2$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
|
✓ |
✓ |
$C_2$ |
$C_2$ |
$12$ |
$0$ |
|
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.010787\) |
\(25.100036\) |
\(0.270752\) |
$[216,2004,161568,-18692]$ |
$[108,152,-5016,-141208,-4673]$ |
$[-14693280768/4673,-191476224/4673,58506624/4673]$ |
$y^2 + x^3y = x^3 - x^2 - x + 1$ |
| 4925.b.4925.1 |
4925.b |
\( 5^{2} \cdot 197 \) |
\( 5^{2} \cdot 197 \) |
$2$ |
$2$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$3$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$12$ |
$0$ |
3.40.1 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.012038\) |
\(23.181407\) |
\(0.279065\) |
$[216,1140,86400,-19700]$ |
$[108,296,-984,-48472,-4925]$ |
$[-14693280768/4925,-372874752/4925,11477376/4925]$ |
$y^2 + x^3y = -x^4 - x^3 + x + 1$ |
| 4989.a.14967.1 |
4989.a |
\( 3 \cdot 1663 \) |
\( 3^{2} \cdot 1663 \) |
$2$ |
$2$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
|
✓ |
✓ |
$C_2$ |
$C_2$ |
$14$ |
$0$ |
|
✓ |
✓ |
$1$ |
\( 2 \) |
\(0.005446\) |
\(22.834120\) |
\(0.248711\) |
$[452,7129,732301,1915776]$ |
$[113,235,2493,56621,14967]$ |
$[18424351793/14967,339080795/14967,3537013/1663]$ |
$y^2 + (x^3 + x + 1)y = x^5 - 2x^3 + x$ |
| 5026.a.35182.1 |
5026.a |
\( 2 \cdot 7 \cdot 359 \) |
\( 2 \cdot 7^{2} \cdot 359 \) |
$2$ |
$3$ |
$\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$10$ |
$0$ |
2.15.1 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(0.031070\) |
\(18.252991\) |
\(0.283562\) |
$[31220,278329,2852760749,4503296]$ |
$[7805,2526654,1086135208,523326215681,35182]$ |
$[591110204777028125/718,12258530733232875/359,675155221982900/359]$ |
$y^2 + (x^3 + 1)y = 4x^5 + 22x^4 + 46x^3 + 28x^2 + 5x$ |
| 5113.a.5113.1 |
5113.a |
\( 5113 \) |
\( -5113 \) |
$2$ |
$2$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$12$ |
$0$ |
2.10.1 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.011558\) |
\(24.766371\) |
\(0.286246\) |
$[300,10329,1082211,654464]$ |
$[75,-196,-5088,-105004,5113]$ |
$[2373046875/5113,-82687500/5113,-28620000/5113]$ |
$y^2 + (x^2 + x + 1)y = x^6 - 2x^4 - x$ |
| 5170.b.10340.1 |
5170.b |
\( 2 \cdot 5 \cdot 11 \cdot 47 \) |
\( - 2^{2} \cdot 5 \cdot 11 \cdot 47 \) |
$2$ |
$3$ |
$\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$14$ |
$0$ |
2.15.1 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(0.024368\) |
\(23.616767\) |
\(0.287741\) |
$[460,9049,1961635,1323520]$ |
$[115,174,-11680,-343369,10340]$ |
$[4022714375/2068,26463225/1034,-7723400/517]$ |
$y^2 + (x^3 + x^2 + x)y = -2x^2 - x + 1$ |
| 5209.a.5209.1 |
5209.a |
\( 5209 \) |
\( -5209 \) |
$2$ |
$2$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
|
✓ |
✓ |
$C_2$ |
$C_2$ |
$12$ |
$0$ |
|
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.009447\) |
\(27.008148\) |
\(0.255151\) |
$[132,9657,203805,-666752]$ |
$[33,-357,941,-24099,-5209]$ |
$[-39135393/5209,12829509/5209,-1024749/5209]$ |
$y^2 + (x^3 + x + 1)y = x^4 + x^3 - x^2 - x$ |
| 5295.a.79425.1 |
5295.a |
\( 3 \cdot 5 \cdot 353 \) |
\( - 3^{2} \cdot 5^{2} \cdot 353 \) |
$2$ |
$2$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$14$ |
$0$ |
2.10.1 |
✓ |
✓ |
$1$ |
\( 2^{2} \) |
\(0.003932\) |
\(16.269634\) |
\(0.255908\) |
$[604,13993,2586683,10166400]$ |
$[151,367,-3501,-165835,79425]$ |
$[78502725751/79425,1263563017/79425,-8869589/8825]$ |
$y^2 + (x^3 + x^2 + 1)y = -x^3 + 3x + 2$ |
| 5329.b.5329.1 |
5329.b |
\( 73^{2} \) |
\( 73^{2} \) |
$2$ |
$2$ |
$\mathsf{trivial}$ |
\(\mathsf{RM}\) |
\(\mathsf{RM}\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
✓ |
✓ |
$C_2$ |
$C_2$ |
$10$ |
$0$ |
2.12.2, 3.2160.18 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.010713\) |
\(24.093314\) |
\(0.258121\) |
$[188,3721,413963,-682112]$ |
$[47,-63,-3485,-41941,-5329]$ |
$[-229345007/5329,6540849/5329,7698365/5329]$ |
$y^2 + (x^3 + x^2 + 1)y = x^3 - x$ |
| 5331.a.15993.1 |
5331.a |
\( 3 \cdot 1777 \) |
\( 3^{2} \cdot 1777 \) |
$2$ |
$2$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
|
✓ |
✓ |
$C_2$ |
$C_2$ |
$14$ |
$0$ |
|
✓ |
✓ |
$1$ |
\( 2 \) |
\(0.005864\) |
\(21.887650\) |
\(0.256680\) |
$[68,8329,84469,2047104]$ |
$[17,-335,477,-26029,15993]$ |
$[1419857/15993,-1645855/15993,15317/1777]$ |
$y^2 + (x^3 + x + 1)y = -x^4 + x^3 + x^2 - x$ |
| 5414.a.10828.1 |
5414.a |
\( 2 \cdot 2707 \) |
\( - 2^{2} \cdot 2707 \) |
$2$ |
$2$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
|
✓ |
✓ |
$C_2$ |
$C_2$ |
$12$ |
$0$ |
|
✓ |
✓ |
$1$ |
\( 2 \) |
\(0.007352\) |
\(20.103606\) |
\(0.295620\) |
$[108,3993,71523,1385984]$ |
$[27,-136,300,-2599,10828]$ |
$[14348907/10828,-669222/2707,54675/2707]$ |
$y^2 + (x^3 + 1)y = 2x^2 + x$ |
| 5449.b.5449.1 |
5449.b |
\( 5449 \) |
\( -5449 \) |
$2$ |
$2$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$12$ |
$0$ |
2.10.1 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.010593\) |
\(23.381067\) |
\(0.247684\) |
$[60,4857,73155,697472]$ |
$[15,-193,-165,-9931,5449]$ |
$[759375/5449,-651375/5449,-37125/5449]$ |
$y^2 + (x^3 + x + 1)y = x^4 + 2x^3 + x^2$ |
| 5476.b.21904.1 |
5476.b |
\( 2^{2} \cdot 37^{2} \) |
\( - 2^{4} \cdot 37^{2} \) |
$2$ |
$2$ |
$\mathsf{trivial}$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$12$ |
$0$ |
2.15.2, 3.90.1 |
✓ |
✓ |
$1$ |
\( 3 \) |
\(0.004919\) |
\(20.265680\) |
\(0.299062\) |
$[120,213,14793,2738]$ |
$[120,458,-4416,-184921,21904]$ |
$[1555200000/1369,49464000/1369,-3974400/1369]$ |
$y^2 + y = x^6 - x^2$ |
| 5501.a.5501.1 |
5501.a |
\( 5501 \) |
\( 5501 \) |
$2$ |
$2$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
|
✓ |
✓ |
$C_2$ |
$C_2$ |
$12$ |
$0$ |
|
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.010011\) |
\(26.164773\) |
\(0.261938\) |
$[732,22041,6292467,-704128]$ |
$[183,477,-26525,-1270401,-5501]$ |
$[-205236901143/5501,-2923288299/5501,888295725/5501]$ |
$y^2 + (x^3 + x^2 + 1)y = -2x^3 - 3x^2 + x + 2$ |
| 5547.b.16641.1 |
5547.b |
\( 3 \cdot 43^{2} \) |
\( 3^{2} \cdot 43^{2} \) |
$2$ |
$2$ |
$\mathsf{trivial}$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$14$ |
$0$ |
2.30.2, 3.90.1 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(0.006279\) |
\(24.460380\) |
\(0.307178\) |
$[520,6292,896816,66564]$ |
$[260,1768,16776,308984,16641]$ |
$[1188137600000/16641,31074368000/16641,126006400/1849]$ |
$y^2 + y = x^6 - 3x^5 + x^4 + 3x^3 - x^2 - x$ |
| 5599.a.5599.1 |
5599.a |
\( 11 \cdot 509 \) |
\( 11 \cdot 509 \) |
$2$ |
$2$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
|
✓ |
✓ |
$C_2$ |
$C_2$ |
$12$ |
$0$ |
|
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.012163\) |
\(21.606456\) |
\(0.262794\) |
$[28,937,106107,-716672]$ |
$[7,-37,-1397,-2787,-5599]$ |
$[-16807/5599,12691/5599,6223/509]$ |
$y^2 + (x^3 + x + 1)y = -x^4 + x^2 - 2x$ |
| 5618.a.11236.1 |
5618.a |
\( 2 \cdot 53^{2} \) |
\( - 2^{2} \cdot 53^{2} \) |
$2$ |
$2$ |
$\mathsf{trivial}$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$12$ |
$0$ |
2.60.2, 3.90.1 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(0.006408\) |
\(23.498592\) |
\(0.301139\) |
$[84,7305,129381,-1438208]$ |
$[21,-286,0,-20449,-11236]$ |
$[-4084101/11236,1324323/5618,0]$ |
$y^2 + (x^3 + 1)y = -x^5 + x^4 + x^2 - x$ |
| 5641.a.5641.1 |
5641.a |
\( 5641 \) |
\( 5641 \) |
$2$ |
$2$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
|
✓ |
✓ |
$C_2$ |
$C_2$ |
$12$ |
$0$ |
|
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.013760\) |
\(22.178341\) |
\(0.305182\) |
$[16,-380,-58424,22564]$ |
$[8,66,6352,11615,5641]$ |
$[32768/5641,33792/5641,406528/5641]$ |
$y^2 + y = x^6 - x^5 - x^4 + 2x^3 - x$ |
| 5705.a.5705.1 |
5705.a |
\( 5 \cdot 7 \cdot 163 \) |
\( - 5 \cdot 7 \cdot 163 \) |
$2$ |
$3$ |
$\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$12$ |
$0$ |
2.15.1 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.044428\) |
\(27.322834\) |
\(0.303472\) |
$[116,15673,-175603,-730240]$ |
$[29,-618,7756,-39250,-5705]$ |
$[-20511149/5705,15072402/5705,-931828/815]$ |
$y^2 + (x^3 + 1)y = x^5 + x^4 + x^3 + 4x^2 + 2x$ |
| 5769.b.17307.1 |
5769.b |
\( 3^{2} \cdot 641 \) |
\( - 3^{3} \cdot 641 \) |
$2$ |
$2$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
|
✓ |
✓ |
$C_2$ |
$C_2$ |
$14$ |
$0$ |
|
✓ |
✓ |
$1$ |
\( 2 \) |
\(0.005378\) |
\(24.769580\) |
\(0.266444\) |
$[324,19881,1386405,-2215296]$ |
$[81,-555,613,-64593,-17307]$ |
$[-129140163/641,10924065/641,-148959/641]$ |
$y^2 + (x^3 + x + 1)y = x^5 - 3x^3$ |
| 5819.a.5819.1 |
5819.a |
\( 11 \cdot 23^{2} \) |
\( - 11 \cdot 23^{2} \) |
$2$ |
$2$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$3$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$8$ |
$0$ |
3.40.1 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.021792\) |
\(14.497764\) |
\(0.315931\) |
$[344,1012,98256,23276]$ |
$[172,1064,8920,100536,5819]$ |
$[150536645632/5819,5414108672/5819,263889280/5819]$ |
$y^2 + x^3y = x^4 - x^3 + 2x^2 - x + 1$ |
| 5911.b.5911.1 |
5911.b |
\( 23 \cdot 257 \) |
\( - 23 \cdot 257 \) |
$2$ |
$2$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$12$ |
$0$ |
2.20.2 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.013645\) |
\(19.752008\) |
\(0.269521\) |
$[156,-3015,-9981,756608]$ |
$[39,189,-1085,-19509,5911]$ |
$[90224199/5911,11211291/5911,-1650285/5911]$ |
$y^2 + (x^3 + x + 1)y = -2x^4 + x^3 - x^2$ |
| 6081.b.164187.1 |
6081.b |
\( 3 \cdot 2027 \) |
\( 3^{4} \cdot 2027 \) |
$2$ |
$2$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
|
✓ |
✓ |
$C_2$ |
$C_2$ |
$16$ |
$0$ |
|
✓ |
✓ |
$1$ |
\( 2^{2} \) |
\(0.003504\) |
\(20.379079\) |
\(0.285654\) |
$[804,62697,11560485,21015936]$ |
$[201,-929,4093,-10087,164187]$ |
$[4050375321/2027,-279408827/6081,18373477/18243]$ |
$y^2 + (x^3 + x^2 + 1)y = -2x^4 - 5x^3 + 5x + 2$ |
| 6201.a.241839.1 |
6201.a |
\( 3^{2} \cdot 13 \cdot 53 \) |
\( - 3^{3} \cdot 13^{2} \cdot 53 \) |
$2$ |
$3$ |
$\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$14$ |
$0$ |
2.15.1 |
✓ |
✓ |
$1$ |
\( 2^{2} \) |
\(0.018010\) |
\(18.300731\) |
\(0.329589\) |
$[1260,869193,638706267,30955392]$ |
$[315,-32082,-5629636,-700647516,241839]$ |
$[114865340625/8957,-37138925250/8957,-20688912300/8957]$ |
$y^2 + (x^3 + 1)y = 2x^5 - 13x^3 + 21x^2 - 12x + 2$ |
| 6229.a.6229.1 |
6229.a |
\( 6229 \) |
\( 6229 \) |
$2$ |
$2$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
|
✓ |
✓ |
$C_2$ |
$C_2$ |
$12$ |
$0$ |
|
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.015603\) |
\(18.542125\) |
\(0.289308\) |
$[60,2793,63483,-797312]$ |
$[15,-107,-389,-4321,-6229]$ |
$[-759375/6229,361125/6229,87525/6229]$ |
$y^2 + (x^3 + x + 1)y = -2x^4 + 3x^3 - 3x^2$ |
| 6291.e.56619.1 |
6291.e |
\( 3^{3} \cdot 233 \) |
\( - 3^{5} \cdot 233 \) |
$2$ |
$2$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
|
✓ |
✓ |
$C_2$ |
$C_2$ |
$14$ |
$0$ |
|
✓ |
✓ |
$1$ |
\( 3 \) |
\(0.004819\) |
\(20.215601\) |
\(0.292232\) |
$[132,20745,608373,-7247232]$ |
$[33,-819,-443,-171345,-56619]$ |
$[-161051/233,121121/233,53603/6291]$ |
$y^2 + (x^3 + x + 1)y = 2x^4 - x^2 - x$ |
| 6400.f.64000.1 |
6400.f |
\( 2^{8} \cdot 5^{2} \) |
\( - 2^{9} \cdot 5^{3} \) |
$2$ |
$4$ |
$\Z/2\Z\oplus\Z/2\Z$ |
\(\mathrm{M}_2(\Q)\) |
\(\mathsf{CM}\) |
✓ |
$E_4$ |
|
✓ |
|
$C_4$ |
$D_4$ |
$16$ |
$0$ |
2.90.6, 3.540.6 |
✓ |
✓ |
$1$ |
\( 2^{2} \) |
\(0.067032\) |
\(19.455210\) |
\(0.326031\) |
$[154,310,19480,250]$ |
$[308,3126,-164,-2455597,64000]$ |
$[5413568314/125,713561079/500,-243089/1000]$ |
$y^2 + x^3y = -2x^4 - 3x^3 + x^2 + 6x + 4$ |
| 6437.a.6437.1 |
6437.a |
\( 41 \cdot 157 \) |
\( 41 \cdot 157 \) |
$2$ |
$2$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
|
✓ |
✓ |
$C_2$ |
$C_2$ |
$10$ |
$0$ |
|
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.013054\) |
\(25.574626\) |
\(0.333856\) |
$[120,2772,168912,-25748]$ |
$[60,-312,-10568,-182856,-6437]$ |
$[-777600000/6437,67392000/6437,38044800/6437]$ |
$y^2 + (x^3 + x^2 + x + 1)y = x^3 - 2x$ |
| 6443.a.6443.1 |
6443.a |
\( 17 \cdot 379 \) |
\( - 17 \cdot 379 \) |
$2$ |
$2$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$11$ |
$1$ |
2.6.1 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.013845\) |
\(24.118331\) |
\(0.333926\) |
$[320,1360,111776,-25772]$ |
$[160,840,7136,109040,-6443]$ |
$[-104857600000/6443,-3440640000/6443,-182681600/6443]$ |
$y^2 + y = x^5 - x^4 - 2x^3 + x^2 + x$ |
| 6463.a.6463.1 |
6463.a |
\( 23 \cdot 281 \) |
\( - 23 \cdot 281 \) |
$2$ |
$2$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
|
✓ |
✓ |
$C_2$ |
$C_2$ |
$12$ |
$0$ |
|
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.014972\) |
\(22.488471\) |
\(0.336705\) |
$[396,7497,936315,827264]$ |
$[99,96,-2168,-55962,6463]$ |
$[9509900499/6463,93148704/6463,-21248568/6463]$ |
$y^2 + (x^2 + x + 1)y = x^6 - x^4$ |
| 6511.a.6511.1 |
6511.a |
\( 17 \cdot 383 \) |
\( 17 \cdot 383 \) |
$2$ |
$2$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
|
✓ |
✓ |
$C_2$ |
$C_2$ |
$12$ |
$0$ |
|
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.010491\) |
\(27.158650\) |
\(0.284927\) |
$[292,12169,711445,833408]$ |
$[73,-285,1301,3437,6511]$ |
$[2073071593/6511,-110869845/6511,6933029/6511]$ |
$y^2 + (x^3 + x + 1)y = x^5 + 2x^4 - 2x^2 - x$ |
| 6718.a.13436.1 |
6718.a |
\( 2 \cdot 3359 \) |
\( - 2^{2} \cdot 3359 \) |
$2$ |
$2$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
|
✓ |
✓ |
$C_2$ |
$C_2$ |
$12$ |
$0$ |
|
✓ |
✓ |
$1$ |
\( 2 \) |
\(0.008000\) |
\(21.445453\) |
\(0.343120\) |
$[620,9913,2068403,1719808]$ |
$[155,588,-2324,-176491,13436]$ |
$[89466096875/13436,547409625/3359,-13958525/3359]$ |
$y^2 + (x^2 + x + 1)y = x^6 + x^5 - x^2 - x$ |
| 6845.a.6845.1 |
6845.a |
\( 5 \cdot 37^{2} \) |
\( 5 \cdot 37^{2} \) |
$2$ |
$2$ |
$\mathsf{trivial}$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$10$ |
$0$ |
2.15.2, 3.90.1 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.022546\) |
\(14.663073\) |
\(0.330594\) |
$[24,852,-14064,-27380]$ |
$[12,-136,2040,1496,-6845]$ |
$[-248832/6845,235008/6845,-58752/1369]$ |
$y^2 + x^3y = x^5 - 7x^3 - 16x^2 - 15x - 5$ |
| 6869.a.6869.1 |
6869.a |
\( 6869 \) |
\( 6869 \) |
$2$ |
$2$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
|
✓ |
✓ |
$C_2$ |
$C_2$ |
$12$ |
$0$ |
|
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.015090\) |
\(22.208533\) |
\(0.335132\) |
$[492,1689,502275,-879232]$ |
$[123,560,-264,-86518,-6869]$ |
$[-28153056843/6869,-1042085520/6869,3994056/6869]$ |
$y^2 + (x^2 + x + 1)y = x^6 - x^4 - x^2 - x$ |
| 6982.a.13964.1 |
6982.a |
\( 2 \cdot 3491 \) |
\( - 2^{2} \cdot 3491 \) |
$2$ |
$2$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$13$ |
$1$ |
2.6.1 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(0.007467\) |
\(23.525330\) |
\(0.351346\) |
$[820,12505,2944285,-1787392]$ |
$[205,1230,8720,68675,-13964]$ |
$[-362050628125/13964,-5298301875/6982,-91614500/3491]$ |
$y^2 + (x^3 + 1)y = x^5 - 3x^3 + 2x$ |
| 7004.a.28016.1 |
7004.a |
\( 2^{2} \cdot 17 \cdot 103 \) |
\( 2^{4} \cdot 17 \cdot 103 \) |
$2$ |
$2$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
|
✓ |
✓ |
$C_2$ |
$C_2$ |
$14$ |
$0$ |
|
✓ |
✓ |
$1$ |
\( 3 \) |
\(0.005073\) |
\(22.353874\) |
\(0.340195\) |
$[72,789,10647,3502]$ |
$[72,-310,1920,10535,28016]$ |
$[120932352/1751,-7231680/1751,622080/1751]$ |
$y^2 + y = x^6 - 4x^4 - 4x^3 + x$ |
| 7165.a.7165.1 |
7165.a |
\( 5 \cdot 1433 \) |
\( - 5 \cdot 1433 \) |
$2$ |
$3$ |
$\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$12$ |
$0$ |
2.15.1 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.058535\) |
\(23.252455\) |
\(0.340272\) |
$[244,3001,-262067,-917120]$ |
$[61,30,6284,95606,-7165]$ |
$[-844596301/7165,-1361886/1433,-23382764/7165]$ |
$y^2 + (x^3 + 1)y = x^4 + x^3 - 2x^2$ |
| 7211.a.7211.1 |
7211.a |
\( 7211 \) |
\( -7211 \) |
$2$ |
$2$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$11$ |
$1$ |
2.6.1 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.018551\) |
\(19.324188\) |
\(0.358483\) |
$[76,-1415,40659,923008]$ |
$[19,74,-860,-5454,7211]$ |
$[2476099/7211,507566/7211,-310460/7211]$ |
$y^2 + (x^3 + 1)y = -x^4 + 2x^3 - 2x^2$ |
| 7225.a.36125.1 |
7225.a |
\( 5^{2} \cdot 17^{2} \) |
\( - 5^{3} \cdot 17^{2} \) |
$2$ |
$3$ |
$\Z/2\Z$ |
\(\mathsf{RM}\) |
\(\mathsf{RM}\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
✓ |
✓ |
$C_2$ |
$C_2$ |
$12$ |
$0$ |
2.45.1, 3.72.2 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(0.037430\) |
\(18.345600\) |
\(0.343342\) |
$[980,-2039,-2619067,-4624000]$ |
$[245,2586,64636,2287106,-36125]$ |
$[-7061881225/289,-304240314/289,-155191036/1445]$ |
$y^2 + (x^3 + 1)y = -x^5 + 2x^4 - 3x^2 - x$ |
| 7389.a.22167.1 |
7389.a |
\( 3^{2} \cdot 821 \) |
\( 3^{3} \cdot 821 \) |
$2$ |
$3$ |
$\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$14$ |
$0$ |
2.15.1 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(0.039437\) |
\(18.389087\) |
\(0.362602\) |
$[588,9945,1746243,-2837376]$ |
$[147,486,20,-58314,-22167]$ |
$[-2542277241/821,-57177414/821,-48020/2463]$ |
$y^2 + (x^3 + x^2 + x)y = -2x^4 + x^2 - 2x + 1$ |
| 7396.a.29584.1 |
7396.a |
\( 2^{2} \cdot 43^{2} \) |
\( - 2^{4} \cdot 43^{2} \) |
$2$ |
$2$ |
$\Z/3\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$12$ |
$0$ |
2.60.2, 3.720.4 |
✓ |
✓ |
$1$ |
\( 3 \) |
\(0.047749\) |
\(21.927407\) |
\(0.349006\) |
$[56,1285,33089,3698]$ |
$[56,-726,-15680,-351289,29584]$ |
$[34420736/1849,-7968576/1849,-3073280/1849]$ |
$y^2 + y = x^6 - 2x^4 + x^2$ |
| 7403.a.7403.1 |
7403.a |
\( 11 \cdot 673 \) |
\( - 11 \cdot 673 \) |
$2$ |
$2$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$11$ |
$1$ |
2.6.1 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.015338\) |
\(23.405457\) |
\(0.358995\) |
$[320,2224,231584,-29612]$ |
$[160,696,224,-112144,-7403]$ |
$[-104857600000/7403,-2850816000/7403,-5734400/7403]$ |
$y^2 + y = x^5 + x^4 - 2x^3 - x^2 + x$ |
