| 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 |
| 10000.a.160000.1 |
10000.a |
\( 2^{4} \cdot 5^{4} \) |
\( - 2^{8} \cdot 5^{4} \) |
$0$ |
$0$ |
$\Z/5\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2$ |
$C_2$ |
$2$ |
$0$ |
2.60.2, 3.1080.9 |
✓ |
✓ |
$1$ |
\( 5 \) |
\(1.000000\) |
\(8.650088\) |
\(1.730018\) |
$[612,11325,1916325,20000]$ |
$[612,8056,110704,712928,160000]$ |
$[335364543972/625,7213296078/625,161966871/625]$ |
$y^2 + xy = x^6 - 2x^5 + 2x^4 - x^3 + 2x^2 - 3x + 2$ |
| 10000.b.800000.1 |
10000.b |
\( 2^{4} \cdot 5^{4} \) |
\( 2^{8} \cdot 5^{5} \) |
$0$ |
$1$ |
$\Z/10\Z$ |
\(\mathsf{CM}\) |
\(\Q\) |
|
$F_{ac}$ |
|
✓ |
✓ |
$C_2$ |
$C_{10}$ |
$4$ |
$2$ |
2.180.2, 3.1296.1 |
✓ |
✓ |
$1$ |
\( 2 \cdot 5 \) |
\(1.000000\) |
\(10.314071\) |
\(1.031407\) |
$[0,0,0,1]$ |
$[0,0,0,0,800000]$ |
$[0,0,0]$ |
$y^2 = x^5 + 1$ |
| 10005.a.50025.1 |
10005.a |
\( 3 \cdot 5 \cdot 23 \cdot 29 \) |
\( 3 \cdot 5^{2} \cdot 23 \cdot 29 \) |
$1$ |
$1$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$4$ |
$0$ |
2.20.2 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(0.034065\) |
\(10.892123\) |
\(0.742091\) |
$[356,7873,1025121,6403200]$ |
$[89,2,-4496,-100037,50025]$ |
$[5584059449/50025,1409938/50025,-35612816/50025]$ |
$y^2 + (x^3 + x + 1)y = x - 1$ |
| 10005.b.450225.1 |
10005.b |
\( 3 \cdot 5 \cdot 23 \cdot 29 \) |
\( 3^{3} \cdot 5^{2} \cdot 23 \cdot 29 \) |
$2$ |
$2$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$14$ |
$0$ |
2.20.2 |
✓ |
✓ |
$1$ |
\( 2 \cdot 3 \) |
\(0.003683\) |
\(16.517374\) |
\(0.365023\) |
$[444,108777,21372411,-57628800]$ |
$[111,-4019,-153925,-8309509,-450225]$ |
$[-624095613/16675,203574407/16675,8428933/2001]$ |
$y^2 + (x^3 + x + 1)y = -2x^4 + 3x^2 + x + 2$ |
| 10016.a.641024.1 |
10016.a |
\( 2^{5} \cdot 313 \) |
\( 2^{11} \cdot 313 \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$2$ |
$2$ |
2.180.3 |
✓ |
✓ |
$1$ |
\( 2^{2} \) |
\(1.000000\) |
\(3.556106\) |
\(0.889027\) |
$[7540,280537,678288235,80128]$ |
$[7540,2181792,781060880,282245675984,641024]$ |
$[23798893892678125/626,456664687571625/313,173455315333625/2504]$ |
$y^2 + xy = 8x^5 - 13x^4 - 19x^3 + 9x^2 - x$ |
| 10017.a.10017.1 |
10017.a |
\( 3^{3} \cdot 7 \cdot 53 \) |
\( 3^{3} \cdot 7 \cdot 53 \) |
$1$ |
$1$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
|
✓ |
✓ |
$C_2$ |
$C_2$ |
$4$ |
$0$ |
|
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.093885\) |
\(7.225875\) |
\(0.678402\) |
$[996,3825,1057257,1282176]$ |
$[249,2424,32076,527787,10017]$ |
$[35451365787/371,1386011688/371,73657188/371]$ |
$y^2 + (x^3 + x^2 + 1)y = -x^4 - 2x^3 - 2$ |
| 10020.a.160320.1 |
10020.a |
\( 2^{2} \cdot 3 \cdot 5 \cdot 167 \) |
\( - 2^{6} \cdot 3 \cdot 5 \cdot 167 \) |
$1$ |
$1$ |
$\Z/3\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$3$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$6$ |
$0$ |
3.80.1 |
✓ |
✓ |
$1$ |
\( 3 \) |
\(0.113712\) |
\(19.204492\) |
\(0.727926\) |
$[1436,278545,179457607,20520960]$ |
$[359,-6236,-1227984,-119933488,160320]$ |
$[5963102065799/160320,-72132246961/40080,-3297162623/3340]$ |
$y^2 + (x^3 + x + 1)y = -x^4 - 4x^3 + 7x + 4$ |
| 10023.a.30069.1 |
10023.a |
\( 3 \cdot 13 \cdot 257 \) |
\( 3^{2} \cdot 13 \cdot 257 \) |
$1$ |
$1$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$5$ |
$1$ |
2.6.1 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(0.027384\) |
\(11.964997\) |
\(0.655295\) |
$[280,-2048,-91928,120276]$ |
$[140,1158,3292,-220021,30069]$ |
$[53782400000/30069,1059184000/10023,64523200/30069]$ |
$y^2 + y = x^5 + 2x^4 + x^3 - 2x^2$ |
| 10025.a.10025.1 |
10025.a |
\( 5^{2} \cdot 401 \) |
\( 5^{2} \cdot 401 \) |
$1$ |
$1$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
|
✓ |
✓ |
$C_2$ |
$C_2$ |
$4$ |
$0$ |
|
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.041216\) |
\(22.572427\) |
\(0.930348\) |
$[336,1620,219240,-40100]$ |
$[168,906,-784,-238137,-10025]$ |
$[-133827821568/10025,-4295918592/10025,22127616/10025]$ |
$y^2 + y = x^6 - x^5 - x^4 + x^2 + x$ |
| 10028.a.641792.1 |
10028.a |
\( 2^{2} \cdot 23 \cdot 109 \) |
\( - 2^{8} \cdot 23 \cdot 109 \) |
$1$ |
$1$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
|
✓ |
✓ |
$C_2$ |
$C_2$ |
$6$ |
$0$ |
|
✓ |
✓ |
$1$ |
\( 13 \) |
\(0.007912\) |
\(7.935388\) |
\(0.816246\) |
$[3500,34537,37868843,82149376]$ |
$[875,30462,1374556,68700764,641792]$ |
$[512908935546875/641792,10203580078125/320896,263098609375/160448]$ |
$y^2 + (x^3 + x^2 + x)y = 2x^4 + 2x^3 + 6x^2 + 2x + 4$ |
| 10032.a.30096.1 |
10032.a |
\( 2^{4} \cdot 3 \cdot 11 \cdot 19 \) |
\( 2^{4} \cdot 3^{2} \cdot 11 \cdot 19 \) |
$1$ |
$1$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,3$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$2$ |
$0$ |
2.20.2, 3.40.1 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(0.084313\) |
\(5.626941\) |
\(0.948843\) |
$[136,2197,64119,-3762]$ |
$[136,-694,4160,21031,-30096]$ |
$[-2907867136/1881,109107904/1881,-4808960/1881]$ |
$y^2 + x^3y = -4x^4 - 8x^3 - 8x^2 - 4x - 1$ |
| 10036.a.642304.1 |
10036.a |
\( 2^{2} \cdot 13 \cdot 193 \) |
\( 2^{8} \cdot 13 \cdot 193 \) |
$1$ |
$1$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$5$ |
$1$ |
2.6.1 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(0.044840\) |
\(10.148310\) |
\(0.910105\) |
$[468,-27951,-4137687,82214912]$ |
$[117,1735,23325,-70300,642304]$ |
$[1686498489/49408,213753735/49408,24561225/49408]$ |
$y^2 + (x^2 + x + 1)y = -x^5 - 4x^3 - 2x^2$ |
| 10037.a.10037.1 |
10037.a |
\( 10037 \) |
\( 10037 \) |
$2$ |
$2$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$7$ |
$1$ |
2.6.1 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.026888\) |
\(16.218074\) |
\(0.436076\) |
$[0,1200,2304,-40148]$ |
$[0,-200,256,-10000,10037]$ |
$[0,-320000000000/100741369,-51200/10037]$ |
$y^2 + y = x^5 + x^2$ |
| 10040.a.20080.1 |
10040.a |
\( 2^{3} \cdot 5 \cdot 251 \) |
\( - 2^{4} \cdot 5 \cdot 251 \) |
$1$ |
$2$ |
$\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$4$ |
$2$ |
2.30.3 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(0.079534\) |
\(19.409052\) |
\(0.771844\) |
$[272,-620,-181772,-80320]$ |
$[136,874,22116,560975,-20080]$ |
$[-2907867136/1255,-137406784/1255,-25566096/1255]$ |
$y^2 + (x + 1)y = 2x^5 - x^4 - 2x^3$ |
| 10040.b.321280.1 |
10040.b |
\( 2^{3} \cdot 5 \cdot 251 \) |
\( - 2^{8} \cdot 5 \cdot 251 \) |
$1$ |
$2$ |
$\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$8$ |
$2$ |
2.30.3 |
✓ |
✓ |
$1$ |
\( 2 \cdot 7 \) |
\(0.018737\) |
\(16.510273\) |
\(1.082736\) |
$[776,8044,1792988,-1285120]$ |
$[388,4932,80484,1725792,-321280]$ |
$[-34349361028/1255,-1125325809/1255,-189318489/5020]$ |
$y^2 + (x + 1)y = 2x^5 - x^4 - 3x^3 + x^2 + x$ |
| 10040.c.502000.1 |
10040.c |
\( 2^{3} \cdot 5 \cdot 251 \) |
\( - 2^{4} \cdot 5^{3} \cdot 251 \) |
$1$ |
$2$ |
$\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$6$ |
$2$ |
2.30.3 |
✓ |
✓ |
$1$ |
\( 2 \cdot 3 \) |
\(0.045172\) |
\(11.060477\) |
\(0.749431\) |
$[16,-4076,38588,2008000]$ |
$[8,682,-5796,-127873,502000]$ |
$[2048/31375,21824/31375,-23184/31375]$ |
$y^2 + (x^2 + 1)y = x^5 - 3x^4 + 3x^3 - 2x$ |
| 10043.a.10043.1 |
10043.a |
\( 11^{2} \cdot 83 \) |
\( - 11^{2} \cdot 83 \) |
$1$ |
$1$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$3$ |
$1$ |
2.6.1 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.086103\) |
\(9.620048\) |
\(0.828315\) |
$[376,352,24200,-40172]$ |
$[188,1414,15756,240683,-10043]$ |
$[-234849287168/10043,-9395566208/10043,-556880064/10043]$ |
$y^2 + y = x^5 - 2x^4 - 3x^3 + x$ |
| 10044.a.40176.1 |
10044.a |
\( 2^{2} \cdot 3^{4} \cdot 31 \) |
\( - 2^{4} \cdot 3^{4} \cdot 31 \) |
$1$ |
$2$ |
$\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,3$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$3$ |
$1$ |
2.60.1, 3.90.2 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(0.141330\) |
\(13.036036\) |
\(0.921192\) |
$[108,-6543,-22041,5142528]$ |
$[27,303,-1693,-34380,40176]$ |
$[177147/496,73629/496,-15237/496]$ |
$y^2 + (x^2 + x + 1)y = -x^5 - 2x^2$ |
| 10048.a.10048.1 |
10048.a |
\( 2^{6} \cdot 157 \) |
\( - 2^{6} \cdot 157 \) |
$1$ |
$1$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$6$ |
$0$ |
2.10.1 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.041489\) |
\(17.159236\) |
\(0.711923\) |
$[460,16375,1900672,1256]$ |
$[460,-2100,-69264,-9067860,10048]$ |
$[321817150000/157,-3193837500/157,-229004100/157]$ |
$y^2 + (x^3 + x^2)y = 2x^4 - x^3 + x^2 - 4x + 2$ |
| 10048.b.160768.1 |
10048.b |
\( 2^{6} \cdot 157 \) |
\( - 2^{10} \cdot 157 \) |
$1$ |
$1$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$6$ |
$0$ |
2.10.1 |
✓ |
✓ |
$1$ |
\( 3^{2} \) |
\(0.009996\) |
\(12.047346\) |
\(1.083807\) |
$[172,679,25648,20096]$ |
$[172,780,10608,304044,160768]$ |
$[147008443/157,15503865/628,1225887/628]$ |
$y^2 + (x^3 + x^2)y = x^4 + 3x^3 + 5x^2 + 4x + 2$ |
| 10056.a.181008.1 |
10056.a |
\( 2^{3} \cdot 3 \cdot 419 \) |
\( 2^{4} \cdot 3^{3} \cdot 419 \) |
$1$ |
$2$ |
$\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$4$ |
$2$ |
2.30.3 |
✓ |
✓ |
$1$ |
\( 2 \cdot 3 \) |
\(0.055781\) |
\(8.723347\) |
\(0.729895\) |
$[368,4132,532068,724032]$ |
$[184,722,-9500,-567321,181008]$ |
$[13181630464/11313,281106368/11313,-20102000/11313]$ |
$y^2 + xy = 2x^5 - 3x^4 + 4x^3 - 2x^2 + x$ |
| 10064.a.10064.1 |
10064.a |
\( 2^{4} \cdot 17 \cdot 37 \) |
\( - 2^{4} \cdot 17 \cdot 37 \) |
$1$ |
$1$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$4$ |
$0$ |
2.10.1 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.034575\) |
\(22.394433\) |
\(0.774288\) |
$[104,9760,284236,40256]$ |
$[52,-1514,-7760,-673929,10064]$ |
$[23762752/629,-13305032/629,-1311440/629]$ |
$y^2 + (x^3 + x)y = -x^4 - 2x^3 + x^2 + 2x + 1$ |
| 10073.a.10073.1 |
10073.a |
\( 7 \cdot 1439 \) |
\( - 7 \cdot 1439 \) |
$2$ |
$2$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$11$ |
$1$ |
2.6.1 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.017404\) |
\(24.245966\) |
\(0.421984\) |
$[500,7801,1091757,-1289344]$ |
$[125,326,644,-6444,-10073]$ |
$[-30517578125/10073,-636718750/10073,-1437500/1439]$ |
$y^2 + (x^2 + x + 1)y = -x^5 + 2x^4 - 3x^2$ |
| 10075.a.10075.1 |
10075.a |
\( 5^{2} \cdot 13 \cdot 31 \) |
\( - 5^{2} \cdot 13 \cdot 31 \) |
$1$ |
$2$ |
$\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$4$ |
$2$ |
2.30.3 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.182151\) |
\(18.074402\) |
\(0.823066\) |
$[224,304,41431,-40300]$ |
$[112,472,225,-49396,-10075]$ |
$[-17623416832/10075,-663126016/10075,-112896/403]$ |
$y^2 + xy = x^5 - 4x^3 - 4x^2 - x$ |
| 10075.b.654875.1 |
10075.b |
\( 5^{2} \cdot 13 \cdot 31 \) |
\( - 5^{3} \cdot 13^{2} \cdot 31 \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$3$ |
$3$ |
2.120.3 |
✓ |
✓ |
$1$ |
\( 2^{2} \) |
\(1.000000\) |
\(3.336022\) |
\(0.834006\) |
$[1376,69520,22838615,-2619500]$ |
$[688,8136,430561,57507868,-654875]$ |
$[-154149525127168/654875,-2649575227392/654875,-203803465984/654875]$ |
$y^2 + xy = x^5 + 2x^4 - 4x^3 - 8x^2 - 1$ |
| 10075.c.654875.1 |
10075.c |
\( 5^{2} \cdot 13 \cdot 31 \) |
\( - 5^{3} \cdot 13^{2} \cdot 31 \) |
$0$ |
$4$ |
$\Z/2\Z\oplus\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$3$ |
$3$ |
2.120.3 |
✓ |
✓ |
$4$ |
\( 2^{2} \) |
\(1.000000\) |
\(1.535742\) |
\(1.535742\) |
$[144016,182644,6685568599,-2619500]$ |
$[72008,216017562,864154072025,3890604831488089,-654875]$ |
$[-1935992825145263554592768/654875,-80655002008707170079744/654875,-179230810806977336384/26195]$ |
$y^2 + xy = 5x^5 + 41x^4 + 88x^3 + 16x^2 + x$ |
| 10080.a.60480.1 |
10080.a |
\( 2^{5} \cdot 3^{2} \cdot 5 \cdot 7 \) |
\( 2^{6} \cdot 3^{3} \cdot 5 \cdot 7 \) |
$0$ |
$4$ |
$\Z/2\Z\oplus\Z/2\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$0$ |
$0$ |
2.180.7, 3.90.1 |
✓ |
✓ |
$4$ |
\( 2 \cdot 3 \) |
\(1.000000\) |
\(0.556034\) |
\(0.834051\) |
$[161296,406586887,19127473723714,7560]$ |
$[161296,812958726,4856153621760,30594066098964471,60480]$ |
$[1705838896690345318825984/945,17767980154611986862208/315,6266846885932235776/3]$ |
$y^2 + xy = -15x^6 + 58x^4 - 60x^2 + 7$ |
| 10080.b.60480.1 |
10080.b |
\( 2^{5} \cdot 3^{2} \cdot 5 \cdot 7 \) |
\( - 2^{6} \cdot 3^{3} \cdot 5 \cdot 7 \) |
$0$ |
$3$ |
$\Z/4\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$0$ |
$0$ |
2.90.5, 3.90.1 |
|
✓ |
$4$ |
\( 2 \) |
\(1.000000\) |
\(0.944615\) |
\(0.472308\) |
$[161296,406586887,19127473723714,7560]$ |
$[161296,812958726,4856153621760,30594066098964471,60480]$ |
$[1705838896690345318825984/945,17767980154611986862208/315,6266846885932235776/3]$ |
$y^2 + xy = -15x^6 - 58x^4 - 60x^2 - 7$ |
| 10080.c.141120.1 |
10080.c |
\( 2^{5} \cdot 3^{2} \cdot 5 \cdot 7 \) |
\( 2^{6} \cdot 3^{2} \cdot 5 \cdot 7^{2} \) |
$0$ |
$4$ |
$\Z/2\Z\oplus\Z/4\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$2$ |
$2$ |
2.180.3, 3.90.1 |
✓ |
✓ |
$4$ |
\( 2^{2} \) |
\(1.000000\) |
\(5.655296\) |
\(1.413824\) |
$[3388552,174712,197326050612,564480]$ |
$[1694276,119607102722,11258185829425920,1192153758196342556159,141120]$ |
$[218142768611210403574323981584/2205,9089279812657801356650662498/2205,229006686528379459553216]$ |
$y^2 + (x^3 + x)y = -x^6 + 35x^4 - 560x^2 + 2940$ |
| 10080.d.241920.1 |
10080.d |
\( 2^{5} \cdot 3^{2} \cdot 5 \cdot 7 \) |
\( 2^{8} \cdot 3^{3} \cdot 5 \cdot 7 \) |
$1$ |
$3$ |
$\Z/2\Z\oplus\Z/4\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$4$ |
$2$ |
2.180.3, 3.90.1 |
✓ |
✓ |
$1$ |
\( 2^{3} \) |
\(0.532647\) |
\(12.085488\) |
\(0.804662\) |
$[182588,82357,5005132713,30240]$ |
$[182588,1389044168,14089048001280,160761848950725104,241920]$ |
$[113246073358644668236004/135,4718399886030325759138/135,1941575745370456496]$ |
$y^2 + (x^3 + x)y = 2x^6 - 25x^4 + 88x^2 - 105$ |
| 10081.a.10081.1 |
10081.a |
\( 17 \cdot 593 \) |
\( - 17 \cdot 593 \) |
$1$ |
$1$ |
$\Z/3\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,3$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$4$ |
$0$ |
2.10.1, 3.80.1 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.569378\) |
\(13.178255\) |
\(0.833712\) |
$[876,8337,1989399,1290368]$ |
$[219,1651,17815,293921,10081]$ |
$[503756397099/10081,17341210809/10081,854425215/10081]$ |
$y^2 + (x^2 + x + 1)y = x^6 + 2x^4 + x^3 + x^2$ |
| 10082.a.20164.1 |
10082.a |
\( 2 \cdot 71^{2} \) |
\( - 2^{2} \cdot 71^{2} \) |
$1$ |
$2$ |
$\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$4$ |
$2$ |
2.30.3 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(0.137571\) |
\(14.062445\) |
\(0.967292\) |
$[484,-25631,-3305263,-2580992]$ |
$[121,1678,14112,-277033,-20164]$ |
$[-25937424601/20164,-1486339679/10082,-51653448/5041]$ |
$y^2 + (x^2 + x)y = -x^5 + x^3 - 2x^2 - x + 1$ |
| 10086.a.181548.1 |
10086.a |
\( 2 \cdot 3 \cdot 41^{2} \) |
\( 2^{2} \cdot 3^{3} \cdot 41^{2} \) |
$1$ |
$2$ |
$\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$6$ |
$2$ |
2.30.3 |
✓ |
✓ |
$1$ |
\( 2 \cdot 3 \) |
\(0.058561\) |
\(10.585028\) |
\(0.929797\) |
$[388,11521,1128033,23238144]$ |
$[97,-88,-620,-16971,181548]$ |
$[8587340257/181548,-20078806/45387,-1458395/45387]$ |
$y^2 + (x^2 + x)y = x^5 + x^4 + x^3 + 2x^2 + 2x + 1$ |
| 10086.b.413526.1 |
10086.b |
\( 2 \cdot 3 \cdot 41^{2} \) |
\( 2 \cdot 3 \cdot 41^{3} \) |
$0$ |
$3$ |
$\Z/6\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,3$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$0$ |
$0$ |
2.15.1, 3.80.1 |
✓ |
✓ |
$4$ |
\( 2 \) |
\(1.000000\) |
\(5.766529\) |
\(1.281451\) |
$[1208,136120,71419827,1654104]$ |
$[604,-7486,-3619151,-560501850,413526]$ |
$[40193395584512/206763,-824765797952/206763,-660162095608/206763]$ |
$y^2 + (x^3 + x)y = -x^6 - 4x^5 - 7x^4 - 6x^3 + 3x + 3$ |
| 10095.a.30285.1 |
10095.a |
\( 3 \cdot 5 \cdot 673 \) |
\( 3^{2} \cdot 5 \cdot 673 \) |
$1$ |
$2$ |
$\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$6$ |
$2$ |
2.30.3 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(0.073448\) |
\(19.185274\) |
\(0.704561\) |
$[408,1140,79287,121140]$ |
$[204,1544,21609,506075,30285]$ |
$[39256206336/3365,1456449024/3365,99920016/3365]$ |
$y^2 + (x^3 + x)y = -2x^4 + 4x^2 - 3x$ |
| 10097.a.10097.1 |
10097.a |
\( 23 \cdot 439 \) |
\( 23 \cdot 439 \) |
$1$ |
$1$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$4$ |
$0$ |
2.20.2 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.099172\) |
\(11.170733\) |
\(1.107828\) |
$[484,5761,1219457,1292416]$ |
$[121,370,-4768,-178457,10097]$ |
$[25937424601/10097,655477570/10097,-69808288/10097]$ |
$y^2 + (x^3 + x + 1)y = -x^4 + 2x^3 - 3x^2 + 2x - 1$ |
| 10098.a.272646.1 |
10098.a |
\( 2 \cdot 3^{3} \cdot 11 \cdot 17 \) |
\( - 2 \cdot 3^{6} \cdot 11 \cdot 17 \) |
$0$ |
$3$ |
$\Z/2\Z\oplus\Z/2\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$0$ |
$0$ |
2.90.6, 3.90.1 |
|
|
$2$ |
\( 2^{2} \) |
\(1.000000\) |
\(3.494509\) |
\(1.747254\) |
$[56004,288321,5331417537,143616]$ |
$[42003,73402380,170798965524,446539889810043,272646]$ |
$[179338702480653356667/374,3730727674118765970/187,1105214886926046]$ |
$y^2 + (x^3 + 1)y = -9x^6 + 16x^5 - 35x^4 + 33x^3 - 35x^2 + 16x - 9$ |
| 10102.a.323264.1 |
10102.a |
\( 2 \cdot 5051 \) |
\( - 2^{6} \cdot 5051 \) |
$1$ |
$2$ |
$\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$8$ |
$2$ |
2.30.3 |
✓ |
✓ |
$1$ |
\( 2 \cdot 3 \) |
\(0.025482\) |
\(17.571527\) |
\(0.671647\) |
$[472,8644,1089623,-1293056]$ |
$[236,880,3801,30659,-323264]$ |
$[-11438788784/5051,-180733520/5051,-13231281/20204]$ |
$y^2 + (x + 1)y = -x^5 + 3x^4 + x^3 - 3x^2$ |
| 10110.a.50550.2 |
10110.a |
\( 2 \cdot 3 \cdot 5 \cdot 337 \) |
\( - 2 \cdot 3 \cdot 5^{2} \cdot 337 \) |
$1$ |
$2$ |
$\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$1$ |
$1$ |
2.60.1 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(0.303674\) |
\(6.345414\) |
\(0.963468\) |
$[5467652,-306863,-559265218983,-6470400]$ |
$[1366913,77852144018,5912063482701400,505080025782601398469,-50550]$ |
$[-4772043231067501633914862225793/50550,-99417583641640068080475078473/25275,-655572807749456176591436/3]$ |
$y^2 + (x^2 + x)y = 39x^6 - 45x^5 - 62x^4 + 22x^3 + 69x^2 + 50x - 75$ |
| 10110.a.50550.1 |
10110.a |
\( 2 \cdot 3 \cdot 5 \cdot 337 \) |
\( 2 \cdot 3 \cdot 5^{2} \cdot 337 \) |
$1$ |
$2$ |
$\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$2$ |
$0$ |
2.15.1 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(0.303674\) |
\(6.345414\) |
\(0.963468\) |
$[20,16177,1232025,6470400]$ |
$[5,-673,-16175,-133451,50550]$ |
$[125/2022,-3365/2022,-16175/2022]$ |
$y^2 + (x^3 + 1)y = 2x^5 + 3x^4 + 2x^3 - x - 1$ |
| 10112.a.10112.1 |
10112.a |
\( 2^{7} \cdot 79 \) |
\( - 2^{7} \cdot 79 \) |
$1$ |
$2$ |
$\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$2$ |
$0$ |
2.15.1 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.265768\) |
\(11.091126\) |
\(0.736918\) |
$[592,493,90838,1264]$ |
$[592,14274,453568,16191295,10112]$ |
$[568065695744/79,23136669504/79,1241869184/79]$ |
$y^2 + (x^3 + x^2)y = 2x^4 + 2x^3 + 5x^2 + 2x + 3$ |
| 10114.a.262964.1 |
10114.a |
\( 2 \cdot 13 \cdot 389 \) |
\( 2^{2} \cdot 13^{2} \cdot 389 \) |
$0$ |
$1$ |
$\Z/6\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,3$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$2$ |
$2$ |
2.30.3, 3.80.1 |
✓ |
✓ |
$1$ |
\( 2^{2} \) |
\(1.000000\) |
\(14.310026\) |
\(1.590003\) |
$[1256,3016,-13131397,1051856]$ |
$[628,15930,2120049,269406468,262964]$ |
$[24419582094592/65741,986358327840/65741,209028351204/65741]$ |
$y^2 + (x^2 + 1)y = 2x^5 - 4x^4 - 2x^3 + 3x^2 + x + 1$ |
| 10115.a.10115.1 |
10115.a |
\( 5 \cdot 7 \cdot 17^{2} \) |
\( 5 \cdot 7 \cdot 17^{2} \) |
$1$ |
$2$ |
$\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$4$ |
$0$ |
2.15.1 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.269552\) |
\(11.751001\) |
\(0.791876\) |
$[1236,3825,1561977,1294720]$ |
$[309,3819,60281,1010517,10115]$ |
$[2817036000549/10115,112674359151/10115,5755690161/10115]$ |
$y^2 + (x^3 + x^2 + x)y = -x^4 + 3x^2 + x - 2$ |
| 10115.b.70805.1 |
10115.b |
\( 5 \cdot 7 \cdot 17^{2} \) |
\( 5 \cdot 7^{2} \cdot 17^{2} \) |
$0$ |
$1$ |
$\Z/10\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,5$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$4$ |
$2$ |
2.30.3 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(1.000000\) |
\(12.989455\) |
\(0.259789\) |
$[184,-45356,-3194113,283220]$ |
$[92,7912,163521,-11888953,70805]$ |
$[6590815232/70805,6160979456/70805,1384041744/70805]$ |
$y^2 + xy = 7x^5 - 12x^4 + 7x^3 - 3x^2 + x$ |
| 10115.c.70805.1 |
10115.c |
\( 5 \cdot 7 \cdot 17^{2} \) |
\( 5 \cdot 7^{2} \cdot 17^{2} \) |
$0$ |
$1$ |
$\Z/4\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$2$ |
$2$ |
2.30.3 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(1.000000\) |
\(9.537419\) |
\(1.192177\) |
$[176,-1292,-23681,283220]$ |
$[88,538,-1055,-95571,70805]$ |
$[5277319168/70805,366631936/70805,-1633984/14161]$ |
$y^2 + xy = x^5 - x^4 + x$ |
| 10121.a.293509.1 |
10121.a |
\( 29 \cdot 349 \) |
\( 29^{2} \cdot 349 \) |
$1$ |
$1$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$5$ |
$1$ |
2.6.1 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(0.042928\) |
\(10.777185\) |
\(0.925276\) |
$[640,-512,-234048,1174036]$ |
$[320,4352,94272,2806784,293509]$ |
$[3355443200000/293509,142606336000/293509,9653452800/293509]$ |
$y^2 + y = x^5 + 2x^4 + 4x + 3$ |
| 10125.a.10125.1 |
10125.a |
\( 3^{4} \cdot 5^{3} \) |
\( 3^{4} \cdot 5^{3} \) |
$1$ |
$1$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$5$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$2$ |
$0$ |
|
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.094033\) |
\(11.744269\) |
\(1.104351\) |
$[420,6705,902025,1296000]$ |
$[105,180,-1700,-52725,10125]$ |
$[1260525,20580,-16660/9]$ |
$y^2 + (x^3 + x + 1)y = -x^2 + x - 1$ |
| 10125.a.10125.2 |
10125.a |
\( 3^{4} \cdot 5^{3} \) |
\( 3^{4} \cdot 5^{3} \) |
$1$ |
$1$ |
$\Z/5\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$5$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$2$ |
$0$ |
|
✓ |
✓ |
$1$ |
\( 1 \) |
\(2.350830\) |
\(11.744269\) |
\(1.104351\) |
$[27780,151768305,775034217225,1296000]$ |
$[6945,-4313970,2210480200,-814638042975,10125]$ |
$[1595755016890725,-142724601457530,94771685998760/9]$ |
$y^2 + (x^3 + x^2 + 1)y = 9x^4 + 28x^3 - x^2 - 34x + 13$ |
| 10130.a.162080.1 |
10130.a |
\( 2 \cdot 5 \cdot 1013 \) |
\( 2^{5} \cdot 5 \cdot 1013 \) |
$1$ |
$1$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$3$ |
$1$ |
2.6.1 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.134122\) |
\(5.992174\) |
\(0.803683\) |
$[2144,5248,3753415,648320]$ |
$[1072,47008,2695089,169845836,162080]$ |
$[44240899506176/5065,1809698189312/5065,96786036168/5065]$ |
$y^2 + (x^3 + x^2)y = -x^4 + 3x^2 - 5x - 10$ |
| 10137.a.10137.1 |
10137.a |
\( 3 \cdot 31 \cdot 109 \) |
\( 3 \cdot 31 \cdot 109 \) |
$1$ |
$1$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$4$ |
$0$ |
2.20.2 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.057474\) |
\(12.967735\) |
\(0.745306\) |
$[2628,3417,2633517,1297536]$ |
$[657,17843,645873,26491478,10137]$ |
$[40804268165019/3379,1686718970433/3379,92930144859/3379]$ |
$y^2 + (x^3 + x + 1)y = -2x^4 + 4x^2 - x - 4$ |
