| 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 |
| 25913.a.25913.1 |
25913.a |
\( 25913 \) |
\( 25913 \) |
$3$ |
$3$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
|
✓ |
✓ |
$C_2$ |
$C_2$ |
$18$ |
$0$ |
|
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.019223\) |
\(20.351877\) |
\(0.391214\) |
$[36,4857,-524835,3316864]$ |
$[9,-199,7797,7643,25913]$ |
$[59049/25913,-145071/25913,631557/25913]$ |
$y^2 + (x^3 + x + 1)y = x^3 - x^2 - 2x$ |
| 35131.a.35131.1 |
35131.a |
\( 19 \cdot 43^{2} \) |
\( - 19 \cdot 43^{2} \) |
$3$ |
$3$ |
$\mathsf{trivial}$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$14$ |
$0$ |
2.15.2, 3.90.1 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.032194\) |
\(16.714784\) |
\(0.538120\) |
$[280,2452,209776,140524]$ |
$[140,408,-1064,-78856,35131]$ |
$[53782400000/35131,1119552000/35131,-1097600/1849]$ |
$y^2 + x^3y = x^4 - 3x^3 + 4x^2 - 3x + 1$ |
| 39017.a.39017.1 |
39017.a |
\( 11 \cdot 3547 \) |
\( - 11 \cdot 3547 \) |
$3$ |
$3$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
|
✓ |
✓ |
$C_2$ |
$C_2$ |
$16$ |
$0$ |
|
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.027877\) |
\(18.010487\) |
\(0.502077\) |
$[604,-1943,386715,4994176]$ |
$[151,1031,-797,-295827,39017]$ |
$[78502725751/39017,3549682481/39017,-18172397/39017]$ |
$y^2 + (x^3 + x + 1)y = -x^5 + x$ |
| 39497.a.39497.1 |
39497.a |
\( 127 \cdot 311 \) |
\( 127 \cdot 311 \) |
$3$ |
$3$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
|
✓ |
✓ |
$C_2$ |
$C_2$ |
$14$ |
$0$ |
|
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.039402\) |
\(14.578300\) |
\(0.574414\) |
$[120,1140,26304,-157988]$ |
$[60,-40,744,10760,-39497]$ |
$[-777600000/39497,8640000/39497,-2678400/39497]$ |
$y^2 + y = x^6 - x^5 + x^4 - x^3 + x^2 - x$ |
| 39701.a.39701.1 |
39701.a |
\( 29 \cdot 37^{2} \) |
\( 29 \cdot 37^{2} \) |
$3$ |
$3$ |
$\mathsf{trivial}$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$14$ |
$0$ |
2.15.2, 3.90.1 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.025568\) |
\(22.282995\) |
\(0.569732\) |
$[1320,23892,9358896,158804]$ |
$[660,14168,355656,8500184,39701]$ |
$[125233257600000/39701,4073243328000/39701,5342198400/1369]$ |
$y^2 + y = x^6 - 3x^5 + 5x^3 - x^2 - 2x$ |
| 39993.a.119979.1 |
39993.a |
\( 3 \cdot 13331 \) |
\( 3^{2} \cdot 13331 \) |
$3$ |
$3$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
|
✓ |
✓ |
$C_2$ |
$C_2$ |
$20$ |
$0$ |
|
✓ |
✓ |
$1$ |
\( 2 \) |
\(0.013479\) |
\(18.812189\) |
\(0.507136\) |
$[260,19033,674317,15357312]$ |
$[65,-617,5589,-4351,119979]$ |
$[1160290625/119979,-169443625/119979,2623725/13331]$ |
$y^2 + (x^3 + x^2 + 1)y = 2x^4 + x^3 - 2x^2 - x$ |
| 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 |
\( 61 \cdot 683 \) |
\( 61 \cdot 683 \) |
$3$ |
$3$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
|
✓ |
✓ |
$C_2$ |
$C_2$ |
$18$ |
$0$ |
|
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.022321\) |
\(21.884652\) |
\(0.488481\) |
$[1284,38841,14686365,5332864]$ |
$[321,2675,16893,-433243,41663]$ |
$[3408200705601/41663,88478730675/41663,1740671613/41663]$ |
$y^2 + (x^3 + x + 1)y = x^5 - x^4 - 4x^3 + 2x$ |
| 42439.a.42439.1 |
42439.a |
\( 31 \cdot 37^{2} \) |
\( - 31 \cdot 37^{2} \) |
$3$ |
$3$ |
$\mathsf{trivial}$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$14$ |
$0$ |
2.15.2, 3.90.1 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.029811\) |
\(19.960990\) |
\(0.595048\) |
$[504,3156,671472,169756]$ |
$[252,2120,-744,-1170472,42439]$ |
$[1016255020032/42439,33926376960/42439,-1524096/1369]$ |
$y^2 + y = x^6 - 3x^5 + 3x^4 - x^3 - x^2 + x$ |
| 44543.a.44543.1 |
44543.a |
\( 44543 \) |
\( 44543 \) |
$3$ |
$3$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
|
✓ |
✓ |
$C_2$ |
$C_2$ |
$16$ |
$0$ |
|
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.030217\) |
\(17.639210\) |
\(0.533002\) |
$[36,7497,-26955,5701504]$ |
$[9,-309,1157,-21267,44543]$ |
$[59049/44543,-225261/44543,93717/44543]$ |
$y^2 + (x^3 + x + 1)y = x^4 - x^2$ |
| 45413.a.45413.1 |
45413.a |
\( 45413 \) |
\( -45413 \) |
$3$ |
$3$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
|
✓ |
✓ |
$C_2$ |
$C_2$ |
$18$ |
$0$ |
|
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.025475\) |
\(19.997449\) |
\(0.509438\) |
$[548,9193,955301,-5812864]$ |
$[137,399,7261,208889,-45413]$ |
$[-48261724457/45413,-1025969847/45413,-136281709/45413]$ |
$y^2 + (x^3 + x + 1)y = -x^5 + 2x^2 - 3x$ |
| 46234.a.92468.1 |
46234.a |
\( 2 \cdot 23117 \) |
\( 2^{2} \cdot 23117 \) |
$3$ |
$3$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
|
✓ |
✓ |
$C_2$ |
$C_2$ |
$20$ |
$0$ |
|
✓ |
✓ |
$1$ |
\( 2 \) |
\(0.015896\) |
\(19.586115\) |
\(0.622689\) |
$[276,19257,789645,11835904]$ |
$[69,-604,5172,-1987,92468]$ |
$[1564031349/92468,-49604859/23117,6155973/23117]$ |
$y^2 + (x^3 + 1)y = -x^4 + 3x^2 - 2x$ |
| 49507.a.49507.1 |
49507.a |
\( 31 \cdot 1597 \) |
\( - 31 \cdot 1597 \) |
$3$ |
$3$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
|
✓ |
✓ |
$C_2$ |
$C_2$ |
$18$ |
$0$ |
|
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.040745\) |
\(15.858977\) |
\(0.646167\) |
$[300,8889,544659,6336896]$ |
$[75,-136,1128,16526,49507]$ |
$[2373046875/49507,-57375000/49507,6345000/49507]$ |
$y^2 + (x^3 + 1)y = 2x^4 + 3x^3 + 3x^2 + x$ |
| 51035.a.255175.1 |
51035.a |
\( 5 \cdot 59 \cdot 173 \) |
\( - 5^{2} \cdot 59 \cdot 173 \) |
$3$ |
$3$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
|
✓ |
✓ |
$C_2$ |
$C_2$ |
$20$ |
$0$ |
|
✓ |
✓ |
$1$ |
\( 2 \) |
\(0.014615\) |
\(18.563908\) |
\(0.542623\) |
$[1572,70521,31551645,-32662400]$ |
$[393,3497,23061,-791509,-255175]$ |
$[-9374815985193/255175,-212262504129/255175,-3561748389/255175]$ |
$y^2 + (x^3 + x + 1)y = -3x^4 + 5x^2 + 2x$ |
| 52498.a.104996.1 |
52498.a |
\( 2 \cdot 26249 \) |
\( 2^{2} \cdot 26249 \) |
$3$ |
$3$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
|
✓ |
✓ |
$C_2$ |
$C_2$ |
$18$ |
$0$ |
|
✓ |
✓ |
$1$ |
\( 2 \) |
\(0.020395\) |
\(16.217317\) |
\(0.661516\) |
$[588,6873,1630563,-13439488]$ |
$[147,614,-3600,-226549,-104996]$ |
$[-68641485507/104996,-975192561/52498,19448100/26249]$ |
$y^2 + (x^3 + x^2 + x)y = -2x^4 - x + 1$ |
| 53623.a.53623.1 |
53623.a |
\( 53623 \) |
\( -53623 \) |
$3$ |
$3$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
|
✓ |
✓ |
$C_2$ |
$C_2$ |
$16$ |
$0$ |
|
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.041051\) |
\(16.386560\) |
\(0.672678\) |
$[204,-24519,1305075,6863744]$ |
$[51,1130,-32292,-730948,53623]$ |
$[345025251/53623,149895630/53623,-83991492/53623]$ |
$y^2 + (x^2 + x + 1)y = x^6 - 2x^4 + x^3 - 2x$ |
| 54983.a.54983.1 |
54983.a |
\( 54983 \) |
\( -54983 \) |
$3$ |
$3$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
|
✓ |
✓ |
$C_2$ |
$C_2$ |
$18$ |
$0$ |
|
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.032929\) |
\(21.518437\) |
\(0.708583\) |
$[200,21076,648368,-219932]$ |
$[100,-3096,27848,-1700104,-54983]$ |
$[-10000000000/54983,3096000000/54983,-278480000/54983]$ |
$y^2 + y = x^6 - x^5 - 3x^4 + x^3 + 3x^2 + x$ |
| 55112.a.110224.1 |
55112.a |
\( 2^{3} \cdot 83^{2} \) |
\( - 2^{4} \cdot 83^{2} \) |
$3$ |
$3$ |
$\mathsf{trivial}$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$12$ |
$0$ |
2.15.2, 3.90.1 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(0.034280\) |
\(11.991605\) |
\(0.822141\) |
$[360,1032,31284,440896]$ |
$[180,1178,18624,491159,110224]$ |
$[11809800000/6889,429381000/6889,37713600/6889]$ |
$y^2 + (x^3 + x)y = x^4 + x^2 + 1$ |
| 56473.a.56473.1 |
56473.a |
\( 56473 \) |
\( 56473 \) |
$3$ |
$3$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
|
✓ |
✓ |
$C_2$ |
$C_2$ |
$16$ |
$0$ |
|
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.037876\) |
\(18.143501\) |
\(0.687194\) |
$[652,6841,1976179,-7228544]$ |
$[163,822,-4516,-352948,-56473]$ |
$[-115063617043/56473,-3559874034/56473,119985604/56473]$ |
$y^2 + (x^3 + x^2 + x)y = -2x^4 + x^3 - 2x + 1$ |
| 56629.a.56629.1 |
56629.a |
\( 56629 \) |
\( 56629 \) |
$3$ |
$3$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
|
✓ |
✓ |
$C_2$ |
$C_2$ |
$16$ |
$0$ |
|
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.049000\) |
\(14.841003\) |
\(0.727209\) |
$[460,10153,1182123,-7248512]$ |
$[115,128,616,13614,-56629]$ |
$[-20113571875/56629,-194672000/56629,-8146600/56629]$ |
$y^2 + (x^2 + x + 1)y = x^6 - x^2$ |
| 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 |
\( 59107 \) |
\( 59107 \) |
$3$ |
$3$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
|
✓ |
✓ |
$C_2$ |
$C_2$ |
$18$ |
$0$ |
|
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.027565\) |
\(20.504440\) |
\(0.565207\) |
$[452,20473,1298237,7565696]$ |
$[113,-321,12085,315641,59107]$ |
$[18424351793/59107,-463169937/59107,154313365/59107]$ |
$y^2 + (x^3 + x^2 + 1)y = 2x^4 - 3x^2 - x$ |
| 59411.a.59411.1 |
59411.a |
\( 11^{2} \cdot 491 \) |
\( - 11^{2} \cdot 491 \) |
$3$ |
$3$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
|
✓ |
✓ |
$C_2$ |
$C_2$ |
$16$ |
$0$ |
|
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.039854\) |
\(17.372656\) |
\(0.692363\) |
$[56,2068,17600,237644]$ |
$[28,-312,776,-18904,59411]$ |
$[17210368/59411,-6849024/59411,608384/59411]$ |
$y^2 + y = x^6 - x^5 - x^3 + 2x^2 - x$ |
| 59883.a.179649.1 |
59883.a |
\( 3 \cdot 19961 \) |
\( - 3^{2} \cdot 19961 \) |
$3$ |
$3$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
|
✓ |
✓ |
$C_2$ |
$C_2$ |
$20$ |
$0$ |
|
✓ |
✓ |
$1$ |
\( 2 \) |
\(0.018962\) |
\(17.104579\) |
\(0.648662\) |
$[100,16873,513893,-22995072]$ |
$[25,-677,-2219,-128451,-179649]$ |
$[-9765625/179649,10578125/179649,1386875/179649]$ |
$y^2 + (x^3 + x + 1)y = x^5 + x^4 - 2x^3$ |
| 59967.a.539703.1 |
59967.a |
\( 3^{3} \cdot 2221 \) |
\( - 3^{5} \cdot 2221 \) |
$3$ |
$3$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
|
✓ |
✓ |
$C_2$ |
$C_2$ |
$20$ |
$0$ |
|
✓ |
✓ |
$1$ |
\( 3 \) |
\(0.013599\) |
\(14.898743\) |
\(0.607808\) |
$[20,1281,78353,284288]$ |
$[15,-471,-27373,-158109,539703]$ |
$[3125/2221,-19625/6663,-684325/59967]$ |
$y^2 + (x^3 + x^2 + 1)y = x^4 + 2x^3 - x^2 - 2x$ |
| 60617.a.60617.1 |
60617.a |
\( 60617 \) |
\( 60617 \) |
$3$ |
$3$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
|
✓ |
✓ |
$C_2$ |
$C_2$ |
$18$ |
$0$ |
|
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.025722\) |
\(22.520707\) |
\(0.579286\) |
$[612,80025,8776845,7758976]$ |
$[153,-2359,28101,-316357,60617]$ |
$[83841135993/60617,-8448940143/60617,657816309/60617]$ |
$y^2 + (x^3 + x + 1)y = x^4 - 5x^3 + x^2 + x$ |
| 60916.a.243664.1 |
60916.a |
\( 2^{2} \cdot 97 \cdot 157 \) |
\( - 2^{4} \cdot 97 \cdot 157 \) |
$3$ |
$3$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
|
✓ |
✓ |
$C_2$ |
$C_2$ |
$20$ |
$0$ |
|
✓ |
✓ |
$1$ |
\( 3 \) |
\(0.014488\) |
\(16.659342\) |
\(0.724084\) |
$[72,933,50337,30458]$ |
$[72,-406,-31440,-607129,243664]$ |
$[120932352/15229,-9471168/15229,-10186560/15229]$ |
$y^2 + x^3y = 2x^3 - x^2 - 2x + 1$ |
| 61099.a.61099.1 |
61099.a |
\( 61099 \) |
\( -61099 \) |
$3$ |
$3$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
|
✓ |
✓ |
$C_2$ |
$C_2$ |
$16$ |
$0$ |
|
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.032786\) |
\(21.855339\) |
\(0.716544\) |
$[1236,54105,18692061,-7820672]$ |
$[309,1724,2184,-574330,-61099]$ |
$[-2817036000549/61099,-50864256396/61099,-208530504/61099]$ |
$y^2 + (x^3 + 1)y = -3x^4 + 3x^3 + 2x^2 - 2x$ |
| 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 |
\( 61553 \) |
\( -61553 \) |
$3$ |
$3$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
|
✓ |
✓ |
$C_2$ |
$C_2$ |
$18$ |
$0$ |
|
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.029514\) |
\(20.665839\) |
\(0.609927\) |
$[260,20089,257469,-7878784]$ |
$[65,-661,12173,88581,-61553]$ |
$[-1160290625/61553,181527125/61553,-51430925/61553]$ |
$y^2 + (x^3 + x + 1)y = -x^4 - 3x^3 + x^2 + x$ |
| 62233.a.62233.1 |
62233.a |
\( 62233 \) |
\( -62233 \) |
$3$ |
$3$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
|
✓ |
✓ |
$C_2$ |
$C_2$ |
$20$ |
$0$ |
|
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.026760\) |
\(21.721873\) |
\(0.581269\) |
$[1668,64473,30534477,-7965824]$ |
$[417,4559,54933,530645,-62233]$ |
$[-12608989261857/62233,-330580899567/62233,-9552244437/62233]$ |
$y^2 + (x^3 + x + 1)y = -3x^4 + x^3 + 5x^2 - 5x$ |
| 62411.b.62411.1 |
62411.b |
\( 139 \cdot 449 \) |
\( - 139 \cdot 449 \) |
$3$ |
$3$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$17$ |
$1$ |
2.6.1 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.052702\) |
\(14.170643\) |
\(0.746827\) |
$[160,-1280,-20480,249644]$ |
$[80,480,-1280,-83200,62411]$ |
$[3276800000/62411,245760000/62411,-8192000/62411]$ |
$y^2 + y = x^5 - x$ |
| 62563.a.62563.1 |
62563.a |
\( 62563 \) |
\( 62563 \) |
$3$ |
$3$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
|
✓ |
✓ |
$C_2$ |
$C_2$ |
$18$ |
$0$ |
|
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.029057\) |
\(21.403273\) |
\(0.621922\) |
$[1028,58585,13837773,8008064]$ |
$[257,311,21365,1348521,62563]$ |
$[1121154893057/62563,5279098423/62563,1411136885/62563]$ |
$y^2 + (x^3 + x + 1)y = -3x^4 + x^3 + 3x^2 - x$ |
| 62924.a.251696.1 |
62924.a |
\( 2^{2} \cdot 15731 \) |
\( 2^{4} \cdot 15731 \) |
$3$ |
$3$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
|
✓ |
✓ |
$C_2$ |
$C_2$ |
$20$ |
$0$ |
|
✓ |
✓ |
$1$ |
\( 3 \) |
\(0.013662\) |
\(17.731932\) |
\(0.726786\) |
$[120,1653,38967,31462]$ |
$[120,-502,6096,119879,251696]$ |
$[1555200000/15731,-54216000/15731,5486400/15731]$ |
$y^2 + x^3y = -x^4 - 2x^3 + 6x^2 - 4x + 1$ |
| 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 |
\( 64237 \) |
\( 64237 \) |
$3$ |
$3$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
|
✓ |
✓ |
$C_2$ |
$C_2$ |
$18$ |
$0$ |
|
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.034994\) |
\(18.153996\) |
\(0.635284\) |
$[508,4489,4345419,-8222336]$ |
$[127,485,-49013,-1614969,-64237]$ |
$[-33038369407/64237,-993465755/64237,790530677/64237]$ |
$y^2 + (x^3 + x^2 + 1)y = x^3 - 3x$ |
| 64829.a.64829.1 |
64829.a |
\( 241 \cdot 269 \) |
\( 241 \cdot 269 \) |
$3$ |
$3$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
|
✓ |
✓ |
$C_2$ |
$C_2$ |
$16$ |
$0$ |
|
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.042084\) |
\(13.638482\) |
\(0.573956\) |
$[252,8745,455643,-8298112]$ |
$[63,-199,627,-25,-64829]$ |
$[-992436543/64829,49759353/64829,-2488563/64829]$ |
$y^2 + (x^3 + x + 1)y = x^4 + x^3 + x^2 + x$ |
| 65167.b.65167.1 |
65167.b |
\( 65167 \) |
\( 65167 \) |
$3$ |
$3$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
|
✓ |
✓ |
$C_2$ |
$C_2$ |
$16$ |
$0$ |
|
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.031573\) |
\(19.721382\) |
\(0.622665\) |
$[1220,34009,12962829,8341376]$ |
$[305,2459,5693,-1077579,65167]$ |
$[2639363440625/65167,69768284875/65167,529591325/65167]$ |
$y^2 + (x^3 + x + 1)y = x^5 - x^4 - 5x^3 - 2x^2 + x$ |
| 65814.a.394884.1 |
65814.a |
\( 2 \cdot 3 \cdot 7 \cdot 1567 \) |
\( 2^{2} \cdot 3^{2} \cdot 7 \cdot 1567 \) |
$3$ |
$3$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
|
✓ |
✓ |
$C_2$ |
$C_2$ |
$22$ |
$0$ |
|
✓ |
✓ |
$1$ |
\( 2^{2} \) |
\(0.011922\) |
\(16.312533\) |
\(0.777941\) |
$[1900,55033,39721043,-50545152]$ |
$[475,7108,-1044,-12754891,-394884]$ |
$[-24180654296875/394884,-190444421875/98721,6543125/10969]$ |
$y^2 + (x^3 + 1)y = x^5 + x^4 - x^2 - 3x + 2$ |
| 65869.a.65869.1 |
65869.a |
\( 199 \cdot 331 \) |
\( 199 \cdot 331 \) |
$3$ |
$3$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
|
✓ |
✓ |
$C_2$ |
$C_2$ |
$14$ |
$0$ |
|
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.040474\) |
\(18.835224\) |
\(0.762328\) |
$[376,3220,570016,-263476]$ |
$[188,936,-19928,-1155640,-65869]$ |
$[-234849287168/65869,-6219412992/65869,704335232/65869]$ |
$y^2 + y = x^6 - x^5 - x^3 + x$ |
| 66161.a.66161.1 |
66161.a |
\( 66161 \) |
\( 66161 \) |
$3$ |
$3$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
|
✓ |
✓ |
$C_2$ |
$C_2$ |
$14$ |
$0$ |
|
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.042580\) |
\(18.103437\) |
\(0.770841\) |
$[312,5940,589248,-264644]$ |
$[156,24,-13784,-537720,-66161]$ |
$[-92389579776/66161,-91113984/66161,335447424/66161]$ |
$y^2 + y = x^6 - x^5 - x^4 - x^3 + x^2 + x$ |
| 66601.a.66601.1 |
66601.a |
\( 66601 \) |
\( 66601 \) |
$3$ |
$3$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
|
✓ |
✓ |
$C_2$ |
$C_2$ |
$16$ |
$0$ |
|
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.034274\) |
\(22.822020\) |
\(0.782194\) |
$[2420,465193,269934933,8524928]$ |
$[605,-4132,20936,-1101786,66601]$ |
$[81054451878125/66601,-915011256500/66601,7663099400/66601]$ |
$y^2 + (x^3 + 1)y = -x^4 + 5x^3 + 16x^2 + 11x + 2$ |
| 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 |
\( 3^{3} \cdot 19 \cdot 131 \) |
\( 3^{5} \cdot 19 \cdot 131 \) |
$3$ |
$3$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
|
✓ |
✓ |
$C_2$ |
$C_2$ |
$18$ |
$0$ |
|
✓ |
✓ |
$1$ |
\( 3 \) |
\(0.016859\) |
\(13.556935\) |
\(0.685653\) |
$[1116,27657,9938475,-77417856]$ |
$[279,2091,1547,-985167,-604827]$ |
$[-6956883693/2489,-186878943/2489,-1486667/7467]$ |
$y^2 + (x^3 + x + 1)y = -x^4 - x^2 + 2$ |
| 68209.a.68209.1 |
68209.a |
\( 68209 \) |
\( 68209 \) |
$3$ |
$3$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
|
✓ |
✓ |
$C_2$ |
$C_2$ |
$14$ |
$0$ |
|
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.044349\) |
\(18.004061\) |
\(0.798466\) |
$[148,4393,-738827,8730752]$ |
$[37,-126,12260,109436,68209]$ |
$[69343957/68209,-6382278/68209,16783940/68209]$ |
$y^2 + (x^3 + 1)y = x^5 - 3x^4 + 3x^3 - x$ |
| 70351.a.70351.1 |
70351.a |
\( 70351 \) |
\( 70351 \) |
$3$ |
$3$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
|
✓ |
✓ |
$C_2$ |
$C_2$ |
$14$ |
$0$ |
|
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.039543\) |
\(20.357524\) |
\(0.805002\) |
$[908,86953,32815403,-9004928]$ |
$[227,-1476,-200240,-11908264,-70351]$ |
$[-602738989907/70351,17264894508/70351,10318166960/70351]$ |
$y^2 + (x^3 + x^2 + x)y = -x^4 + x^3 + 3x^2 - 4x + 1$ |
| 70450.c.704500.1 |
70450.c |
\( 2 \cdot 5^{2} \cdot 1409 \) |
\( - 2^{2} \cdot 5^{3} \cdot 1409 \) |
$3$ |
$4$ |
$\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$22$ |
$0$ |
2.15.1 |
✓ |
✓ |
$1$ |
\( 2^{2} \) |
\(0.046458\) |
\(16.521294\) |
\(0.767540\) |
$[1012,58105,13468045,-90176000]$ |
$[253,246,20576,1286303,-704500]$ |
$[-1036579476493/704500,-1991896071/352250,-329262296/176125]$ |
$y^2 + (x^3 + 1)y = -2x^4 + x^3 + 4x^2 - 3x$ |
| 70469.a.70469.1 |
70469.a |
\( 7 \cdot 10067 \) |
\( - 7 \cdot 10067 \) |
$3$ |
$3$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
|
✓ |
✓ |
$C_2$ |
$C_2$ |
$10$ |
$0$ |
|
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.065676\) |
\(9.942305\) |
\(0.652967\) |
$[2108,21913,14810963,9020032]$ |
$[527,10659,266755,6741401,70469]$ |
$[40649300451407/70469,1560085167597/70469,74085599395/70469]$ |
$y^2 + (x^3 + x^2 + 1)y = 2x^4 + x^3 + 4x^2 + x + 2$ |
| 71407.a.71407.1 |
71407.a |
\( 7 \cdot 101^{2} \) |
\( - 7 \cdot 101^{2} \) |
$3$ |
$3$ |
$\mathsf{trivial}$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$14$ |
$0$ |
2.15.2, 3.90.1 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.037176\) |
\(19.804710\) |
\(0.736260\) |
$[104,3412,3776,-285628]$ |
$[52,-456,8120,53576,-71407]$ |
$[-380204032/71407,64117248/71407,-3136640/10201]$ |
$y^2 + x^3y = -2x^4 - 3x^3 + x^2 + 3x + 1$ |
