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 |
7662.b.45972.1 |
7662.b |
\( 2 \cdot 3 \cdot 1277 \) |
\( 2^{2} \cdot 3^{2} \cdot 1277 \) |
$2$ |
$2$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$15$ |
$1$ |
2.6.1 |
✓ |
✓ |
$1$ |
\( 2^{2} \) |
\(0.004195\) |
\(21.882491\) |
\(0.367167\) |
$[500,19129,2141869,5884416]$ |
$[125,-146,2448,71171,45972]$ |
$[30517578125/45972,-142578125/22986,1062500/1277]$ |
$y^2 + (x^3 + 1)y = -2x^4 + x^3 + 2x^2 - x$ |
9426.a.509004.1 |
9426.a |
\( 2 \cdot 3 \cdot 1571 \) |
\( 2^{2} \cdot 3^{4} \cdot 1571 \) |
$2$ |
$2$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$15$ |
$1$ |
2.6.1 |
✓ |
✓ |
$1$ |
\( 2^{3} \) |
\(0.003390\) |
\(15.791673\) |
\(0.428319\) |
$[468,25113,2276253,65152512]$ |
$[117,-476,6100,121781,509004]$ |
$[270672597/6284,-2352987/1571,257725/1571]$ |
$y^2 + (x^3 + 1)y = 3x^3 + 4x^2 + x$ |
12330.a.73980.1 |
12330.a |
\( 2 \cdot 3^{2} \cdot 5 \cdot 137 \) |
\( - 2^{2} \cdot 3^{3} \cdot 5 \cdot 137 \) |
$2$ |
$3$ |
$\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$15$ |
$1$ |
2.60.1 |
✓ |
✓ |
$1$ |
\( 2^{2} \) |
\(0.023790\) |
\(20.517399\) |
\(0.488101\) |
$[684,49833,15970923,9469440]$ |
$[171,-858,-111616,-4955625,73980]$ |
$[5415228513/2740,-79447797/1370,-30220032/685]$ |
$y^2 + (x^3 + x^2 + x)y = 2x^3 - 3x + 1$ |
14394.a.259092.1 |
14394.a |
\( 2 \cdot 3 \cdot 2399 \) |
\( 2^{2} \cdot 3^{3} \cdot 2399 \) |
$2$ |
$2$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$15$ |
$1$ |
2.6.1 |
✓ |
✓ |
$1$ |
\( 2 \cdot 3 \) |
\(0.005831\) |
\(14.890367\) |
\(0.520928\) |
$[468,8553,339381,33163776]$ |
$[117,214,10576,297899,259092]$ |
$[812017791/9596,6347133/4798,1340508/2399]$ |
$y^2 + (x^3 + 1)y = x^5 + x^4 + 3x^2 + 3x$ |
16824.a.403776.1 |
16824.a |
\( 2^{3} \cdot 3 \cdot 701 \) |
\( 2^{6} \cdot 3^{2} \cdot 701 \) |
$2$ |
$2$ |
$\Z/3\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,3$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$15$ |
$1$ |
2.6.1, 3.80.1 |
✓ |
✓ |
$1$ |
\( 2^{2} \cdot 3 \) |
\(0.030432\) |
\(16.471260\) |
\(0.668341\) |
$[136,8512,221804,1615104]$ |
$[68,-1226,2880,-326809,403776]$ |
$[22717712/6309,-6023338/6309,23120/701]$ |
$y^2 + (x^3 + x)y = x^5 + 3x^2 + 3x + 1$ |
28542.c.171252.1 |
28542.c |
\( 2 \cdot 3 \cdot 67 \cdot 71 \) |
\( 2^{2} \cdot 3^{2} \cdot 67 \cdot 71 \) |
$2$ |
$2$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$15$ |
$1$ |
2.6.1 |
✓ |
✓ |
$1$ |
\( 2^{2} \) |
\(0.010025\) |
\(17.341418\) |
\(0.695364\) |
$[148,14953,-685963,21920256]$ |
$[37,-566,16048,68355,171252]$ |
$[69343957/171252,-14334799/85626,5492428/42813]$ |
$y^2 + (x^3 + x^2 + x)y = x^4 + 2x^3 - x^2 - 2x$ |
33336.a.800064.1 |
33336.a |
\( 2^{3} \cdot 3^{2} \cdot 463 \) |
\( 2^{6} \cdot 3^{3} \cdot 463 \) |
$2$ |
$2$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$15$ |
$1$ |
2.6.1 |
✓ |
✓ |
$1$ |
\( 2^{2} \cdot 3 \) |
\(0.005190\) |
\(14.140967\) |
\(0.880744\) |
$[216,7920,689076,-3200256]$ |
$[108,-834,-34048,-1093185,-800064]$ |
$[-8503056/463,607986/463,229824/463]$ |
$y^2 + (x + 1)y = x^6 - 2x^5 - 2x^4 + x^3 + x^2$ |
35544.a.853056.1 |
35544.a |
\( 2^{3} \cdot 3 \cdot 1481 \) |
\( 2^{6} \cdot 3^{2} \cdot 1481 \) |
$2$ |
$2$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$15$ |
$1$ |
2.6.1 |
✓ |
✓ |
$1$ |
\( 2^{2} \cdot 3 \) |
\(0.005747\) |
\(13.532361\) |
\(0.933265\) |
$[128,2620,420388,-3412224]$ |
$[64,-266,-38340,-631129,-853056]$ |
$[-16777216/13329,1089536/13329,272640/1481]$ |
$y^2 + (x + 1)y = x^6 + x^4 - 2x^2$ |
38466.a.692388.1 |
38466.a |
\( 2 \cdot 3^{2} \cdot 2137 \) |
\( - 2^{2} \cdot 3^{4} \cdot 2137 \) |
$2$ |
$2$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$15$ |
$1$ |
2.6.1 |
✓ |
✓ |
$1$ |
\( 2 \cdot 5 \) |
\(0.005375\) |
\(16.794213\) |
\(0.902703\) |
$[2900,165049,138935309,-88625664]$ |
$[725,15024,337428,4728681,-692388]$ |
$[-200304189453125/692388,-477109812500/57699,-4926683125/19233]$ |
$y^2 + (x^2 + x + 1)y = 6x^5 + 9x^4 - 4x^2 - x$ |
40152.a.963648.1 |
40152.a |
\( 2^{3} \cdot 3 \cdot 7 \cdot 239 \) |
\( 2^{6} \cdot 3^{2} \cdot 7 \cdot 239 \) |
$2$ |
$2$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$15$ |
$1$ |
2.6.1 |
✓ |
✓ |
$1$ |
\( 2^{2} \cdot 3 \) |
\(0.007006\) |
\(12.668426\) |
\(1.065050\) |
$[32,4396,-95924,3854592]$ |
$[16,-722,13924,-74625,963648]$ |
$[16384/15057,-46208/15057,55696/15057]$ |
$y^2 + (x + 1)y = x^6 + 4x^5 + 3x^4$ |
83999.a.83999.1 |
83999.a |
\( 19 \cdot 4421 \) |
\( 19 \cdot 4421 \) |
$3$ |
$3$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$15$ |
$1$ |
2.6.1 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.043530\) |
\(20.005180\) |
\(0.870831\) |
$[1428,53145,22805757,10751872]$ |
$[357,3096,8168,-1667310,83999]$ |
$[5798839393557/83999,140865811128/83999,1041003432/83999]$ |
$y^2 + (x^3 + 1)y = 3x^5 + 9x^4 + 8x^3 - 2x$ |
91771.a.91771.1 |
91771.a |
\( 91771 \) |
\( -91771 \) |
$3$ |
$3$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$15$ |
$1$ |
2.6.1 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.065991\) |
\(13.220645\) |
\(0.872445\) |
$[96,-2160,-15984,367084]$ |
$[48,456,-2768,-85200,91771]$ |
$[254803968/91771,50429952/91771,-6377472/91771]$ |
$y^2 + y = x^5 + x^4 - x^2 - x$ |
94961.a.94961.1 |
94961.a |
\( 94961 \) |
\( -94961 \) |
$3$ |
$3$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$15$ |
$1$ |
2.6.1 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.050128\) |
\(18.325985\) |
\(0.918646\) |
$[980,22105,6915165,-12155008]$ |
$[245,1580,680,-582450,-94961]$ |
$[-882735153125/94961,-23235677500/94961,-40817000/94961]$ |
$y^2 + (x^2 + x + 1)y = x^5 + x^4 - 3x^3 - 2x^2 + x$ |
125237.a.125237.1 |
125237.a |
\( 7 \cdot 17891 \) |
\( 7 \cdot 17891 \) |
$3$ |
$3$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$15$ |
$1$ |
2.6.1 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.070147\) |
\(15.347551\) |
\(1.076581\) |
$[600,5760,1142136,500948]$ |
$[300,2790,15596,-776325,125237]$ |
$[2430000000000/125237,75330000000/125237,200520000/17891]$ |
$y^2 + y = x^5 - x^4 - 3x^3 + x^2 + 2x$ |
140615.a.703075.1 |
140615.a |
\( 5 \cdot 28123 \) |
\( - 5^{2} \cdot 28123 \) |
$3$ |
$3$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$15$ |
$1$ |
2.6.1 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(0.042024\) |
\(13.303488\) |
\(1.118137\) |
$[72,-1008,253656,2812300]$ |
$[36,222,-29756,-280125,703075]$ |
$[60466176/703075,10357632/703075,-38563776/703075]$ |
$y^2 + y = x^5 + 2x^4 - 3x^3 + x^2 - x$ |
141991.b.141991.1 |
141991.b |
\( 141991 \) |
\( -141991 \) |
$3$ |
$3$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$15$ |
$1$ |
2.6.1 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.067359\) |
\(16.292643\) |
\(1.097455\) |
$[660,5337,754461,-18174848]$ |
$[165,912,10112,209184,-141991]$ |
$[-122298103125/141991,-4096818000/141991,-275299200/141991]$ |
$y^2 + (x^2 + x + 1)y = x^5 - 2x^4 - 2x^3 + x^2$ |
143313.a.429939.1 |
143313.a |
\( 3 \cdot 23 \cdot 31 \cdot 67 \) |
\( - 3^{2} \cdot 23 \cdot 31 \cdot 67 \) |
$3$ |
$3$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$15$ |
$1$ |
2.6.1 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(0.043807\) |
\(13.786517\) |
\(1.207900\) |
$[40,-6080,642680,1719756]$ |
$[20,1030,-77020,-650325,429939]$ |
$[3200000/429939,8240000/429939,-30808000/429939]$ |
$y^2 + x^3y = x^5 - 5x^3 - 5x^2 + 5x + 6$ |
143482.a.286964.1 |
143482.a |
\( 2 \cdot 71741 \) |
\( 2^{2} \cdot 71741 \) |
$3$ |
$3$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$15$ |
$1$ |
2.6.1 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(0.039463\) |
\(17.054117\) |
\(1.345998\) |
$[24,7272,-144549,1147856]$ |
$[12,-1206,20105,-303294,286964]$ |
$[62208/71741,-520992/71741,723780/71741]$ |
$y^2 + (x + 1)y = x^6 + x^5 - 2x^4 - x^3 + x^2$ |
143849.a.143849.1 |
143849.a |
\( 19 \cdot 67 \cdot 113 \) |
\( 19 \cdot 67 \cdot 113 \) |
$3$ |
$3$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$15$ |
$1$ |
2.6.1 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.078082\) |
\(15.254400\) |
\(1.191100\) |
$[2964,-11895,-21353019,18412672]$ |
$[741,23374,1136380,73928426,143849]$ |
$[11758107837879/7571,500534552466/7571,32840245620/7571]$ |
$y^2 + (x^2 + x + 1)y = -x^5 + 3x^4 - 9x^2 + x + 6$ |
144203.a.144203.1 |
144203.a |
\( 144203 \) |
\( -144203 \) |
$3$ |
$3$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$15$ |
$1$ |
2.6.1 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.082592\) |
\(13.620120\) |
\(1.124911\) |
$[40,-1664,22552,576812]$ |
$[20,294,-4028,-41749,144203]$ |
$[3200000/144203,2352000/144203,-1611200/144203]$ |
$y^2 + y = x^5 - 2x^4 + x^3 + 2x^2 - 2x$ |
146594.a.293188.1 |
146594.a |
\( 2 \cdot 7 \cdot 37 \cdot 283 \) |
\( - 2^{2} \cdot 7 \cdot 37 \cdot 283 \) |
$3$ |
$3$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$15$ |
$1$ |
2.6.1 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(0.041793\) |
\(16.320596\) |
\(1.364186\) |
$[1320,22896,9789003,-1172752]$ |
$[660,14334,277433,-5589444,-293188]$ |
$[-31308314400000/73297,-1030241916000/73297,-30212453700/73297]$ |
$y^2 + xy = x^5 + 3x^4 - x^3 - 7x^2 + 4$ |
150443.a.150443.1 |
150443.a |
\( 23 \cdot 31 \cdot 211 \) |
\( - 23 \cdot 31 \cdot 211 \) |
$3$ |
$3$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$15$ |
$1$ |
2.6.1 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.069530\) |
\(16.214585\) |
\(1.127401\) |
$[280,1216,63768,-601772]$ |
$[140,614,7148,155931,-150443]$ |
$[-53782400000/150443,-1684816000/150443,-140100800/150443]$ |
$y^2 + y = x^5 - 2x^4 - x^3 + 2x^2$ |
151507.a.151507.1 |
151507.a |
\( 151507 \) |
\( 151507 \) |
$3$ |
$3$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$15$ |
$1$ |
2.6.1 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.088519\) |
\(13.459299\) |
\(1.191405\) |
$[20,7129,-207011,19392896]$ |
$[5,-296,3288,-17794,151507]$ |
$[3125/151507,-37000/151507,82200/151507]$ |
$y^2 + (x^2 + x + 1)y = x^5 - x^4 + x^2 - x$ |
153499.a.153499.1 |
153499.a |
\( 153499 \) |
\( 153499 \) |
$3$ |
$3$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$15$ |
$1$ |
2.6.1 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.067015\) |
\(16.869603\) |
\(1.130515\) |
$[1396,40441,18768877,19647872]$ |
$[349,3390,1076,-2779144,153499]$ |
$[5177583776749/153499,144103981110/153499,131057876/153499]$ |
$y^2 + (x^2 + x + 1)y = x^5 - 4x^3 - x^2 + 2x$ |
157137.a.471411.1 |
157137.a |
\( 3 \cdot 52379 \) |
\( - 3^{2} \cdot 52379 \) |
$3$ |
$3$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$15$ |
$1$ |
2.6.1 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(0.045011\) |
\(13.456946\) |
\(1.211434\) |
$[180,-15495,-3934035,-60340608]$ |
$[45,730,46780,393050,-471411]$ |
$[-20503125/52379,-7391250/52379,-10525500/52379]$ |
$y^2 + (x^3 + 1)y = 2x^3 - 5x^2 + 2x$ |
159482.a.318964.1 |
159482.a |
\( 2 \cdot 23 \cdot 3467 \) |
\( 2^{2} \cdot 23 \cdot 3467 \) |
$3$ |
$3$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$15$ |
$1$ |
2.6.1 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(0.069995\) |
\(10.250670\) |
\(1.434989\) |
$[104,2872,104963,1275856]$ |
$[52,-366,-4423,-90988,318964]$ |
$[95051008/79741,-12865632/79741,-2989948/79741]$ |
$y^2 + xy = x^5 + x^4 + x^3 + x^2 + x + 1$ |
160507.a.160507.1 |
160507.a |
\( 160507 \) |
\( -160507 \) |
$3$ |
$3$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$15$ |
$1$ |
2.6.1 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.067015\) |
\(18.054200\) |
\(1.209905\) |
$[224,3856,161264,-642028]$ |
$[112,-120,5328,145584,-160507]$ |
$[-17623416832/160507,168591360/160507,-66834432/160507]$ |
$y^2 + y = x^5 + 2x^4 - 2x^3 - x^2$ |
164326.a.328652.1 |
164326.a |
\( 2 \cdot 82163 \) |
\( - 2^{2} \cdot 82163 \) |
$3$ |
$3$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$15$ |
$1$ |
2.6.1 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(0.033199\) |
\(16.734081\) |
\(1.111093\) |
$[500,21049,1530861,-42067456]$ |
$[125,-226,13712,415731,-328652]$ |
$[-30517578125/328652,220703125/164326,-53562500/82163]$ |
$y^2 + (x^3 + 1)y = 2x^4 + x^3 - 2x^2 - x$ |
166319.a.166319.1 |
166319.a |
\( 166319 \) |
\( 166319 \) |
$3$ |
$3$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$15$ |
$1$ |
2.6.1 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.105549\) |
\(13.820656\) |
\(1.458762\) |
$[24,-3492,-159705,665276]$ |
$[12,588,15809,-39009,166319]$ |
$[248832/166319,1016064/166319,2276496/166319]$ |
$y^2 + xy = x^5 - x^3 - x^2 + 1$ |
168328.a.336656.1 |
168328.a |
\( 2^{3} \cdot 53 \cdot 397 \) |
\( - 2^{4} \cdot 53 \cdot 397 \) |
$3$ |
$3$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$15$ |
$1$ |
2.6.1 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(0.046316\) |
\(15.562706\) |
\(1.441611\) |
$[496,3172,816364,1346624]$ |
$[248,2034,-18980,-2211049,336656]$ |
$[58632501248/21041,1939036608/21041,-72959120/21041]$ |
$y^2 + (x^3 + x)y = x^5 - x^4 - x^3 + x^2 - 2x + 1$ |
183902.a.367804.1 |
183902.a |
\( 2 \cdot 91951 \) |
\( 2^{2} \cdot 91951 \) |
$3$ |
$3$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$15$ |
$1$ |
2.6.1 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(0.043391\) |
\(17.443835\) |
\(1.513794\) |
$[2144,70216,44820647,1471216]$ |
$[1072,36180,1356401,36267368,367804]$ |
$[353927196049408/91951,11142763868160/91951,389688581696/91951]$ |
$y^2 + xy = x^5 - 6x^3 - x^2 + 8x + 4$ |
184029.a.552087.1 |
184029.a |
\( 3 \cdot 61343 \) |
\( 3^{2} \cdot 61343 \) |
$3$ |
$3$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$15$ |
$1$ |
2.6.1 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(0.037048\) |
\(17.563116\) |
\(1.301367\) |
$[1396,77497,29789069,70667136]$ |
$[349,1846,-2300,-1052604,552087]$ |
$[5177583776749/552087,78470781454/552087,-280142300/552087]$ |
$y^2 + (x^2 + x + 1)y = x^5 + 3x^4 - 3x^3 - 3x^2$ |
191872.a.383744.1 |
191872.a |
\( 2^{7} \cdot 1499 \) |
\( 2^{8} \cdot 1499 \) |
$3$ |
$3$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$15$ |
$1$ |
2.6.1 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(0.051678\) |
\(13.170940\) |
\(1.361283\) |
$[6,102,-1236,1499]$ |
$[12,-266,9700,11411,383744]$ |
$[972/1499,-3591/2998,21825/5996]$ |
$y^2 + y = 2x^5 + x^4 - x^3$ |
197317.a.197317.1 |
197317.a |
\( 23^{2} \cdot 373 \) |
\( 23^{2} \cdot 373 \) |
$3$ |
$3$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$15$ |
$1$ |
2.6.1 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.070224\) |
\(19.575049\) |
\(1.374638\) |
$[1048,31648,8995208,789268]$ |
$[524,6166,101340,3770651,197317]$ |
$[39505397402624/197317,887150662784/197317,27825531840/197317]$ |
$y^2 + y = x^5 - 3x^4 - x^3 + 7x^2 - 2x$ |
206111.a.206111.1 |
206111.a |
\( 79 \cdot 2609 \) |
\( - 79 \cdot 2609 \) |
$3$ |
$3$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$15$ |
$1$ |
2.6.1 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.067873\) |
\(18.737287\) |
\(1.271754\) |
$[788,34153,6373269,-26382208]$ |
$[197,194,7052,337902,-206111]$ |
$[-296709280757/206111,-1483202362/206111,-273681068/206111]$ |
$y^2 + (x^3 + x^2 + x)y = 3x^4 + 3x^3 - x^2 - x$ |
209889.a.629667.1 |
209889.a |
\( 3^{2} \cdot 23321 \) |
\( 3^{3} \cdot 23321 \) |
$3$ |
$3$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$15$ |
$1$ |
2.6.1 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(0.051533\) |
\(13.266271\) |
\(1.367293\) |
$[300,30825,2650347,-80597376]$ |
$[75,-1050,-9076,-445800,-629667]$ |
$[-87890625/23321,16406250/23321,5672500/69963]$ |
$y^2 + (x^3 + x^2 + x)y = 2x^4 + 2x^3 + x^2 - x$ |
215851.a.215851.1 |
215851.a |
\( 215851 \) |
\( -215851 \) |
$3$ |
$3$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$15$ |
$1$ |
2.6.1 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.071732\) |
\(19.183686\) |
\(1.376092\) |
$[1108,50089,14937781,-27628928]$ |
$[277,1110,2316,-147642,-215851]$ |
$[-1630793025157/215851,-23591865630/215851,-177704364/215851]$ |
$y^2 + (x^2 + x + 1)y = x^5 + x^4 - 4x^3 - x^2 + x$ |
216423.a.649269.1 |
216423.a |
\( 3^{2} \cdot 139 \cdot 173 \) |
\( 3^{3} \cdot 139 \cdot 173 \) |
$3$ |
$3$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$15$ |
$1$ |
2.6.1 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(0.038909\) |
\(17.693290\) |
\(1.376857\) |
$[1056,43488,12553920,2597076]$ |
$[528,4368,8896,-3595584,649269]$ |
$[1519867920384/24047,23813357568/24047,1982464/519]$ |
$y^2 + y = x^5 - 8x^3 + 10x^2 - 3x$ |
225411.a.676233.1 |
225411.a |
\( 3 \cdot 227 \cdot 331 \) |
\( - 3^{2} \cdot 227 \cdot 331 \) |
$3$ |
$3$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$15$ |
$1$ |
2.6.1 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(0.039909\) |
\(17.921615\) |
\(1.430466\) |
$[1492,130105,48423725,-86557824]$ |
$[373,376,9256,827778,-676233]$ |
$[-7220115733093/676233,-19512563992/676233,-1287778024/676233]$ |
$y^2 + (x^3 + 1)y = x^5 - 5x^3 + x^2 + 2x$ |
226133.a.226133.1 |
226133.a |
\( 226133 \) |
\( 226133 \) |
$3$ |
$3$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$15$ |
$1$ |
2.6.1 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.067360\) |
\(18.465371\) |
\(1.243832\) |
$[192,10368,376272,904532]$ |
$[96,-1344,6320,-299904,226133]$ |
$[8153726976/226133,-1189085184/226133,58245120/226133]$ |
$y^2 + y = x^5 + 2x^4 - 6x^3 + 4x^2 - x$ |
233138.a.466276.1 |
233138.a |
\( 2 \cdot 17 \cdot 6857 \) |
\( 2^{2} \cdot 17 \cdot 6857 \) |
$3$ |
$3$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$15$ |
$1$ |
2.6.1 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(0.043379\) |
\(15.140829\) |
\(1.313597\) |
$[692,15193,901341,59683328]$ |
$[173,614,29888,1198407,466276]$ |
$[154963892093/466276,1589559119/233138,223629488/116569]$ |
$y^2 + (x^2 + x + 1)y = 2x^5 - x^4 - 3x^3$ |
233344.a.466688.1 |
233344.a |
\( 2^{7} \cdot 1823 \) |
\( 2^{8} \cdot 1823 \) |
$3$ |
$3$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$15$ |
$1$ |
2.6.1 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(0.042284\) |
\(15.889982\) |
\(1.343775\) |
$[150,450,15336,1823]$ |
$[300,2550,53444,2382675,466688]$ |
$[9492187500/1823,537890625/3646,75155625/7292]$ |
$y^2 + y = 2x^5 - x^4 - 3x^3 + x^2 + x$ |
235606.a.471212.1 |
235606.a |
\( 2 \cdot 7 \cdot 16829 \) |
\( - 2^{2} \cdot 7 \cdot 16829 \) |
$3$ |
$3$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$15$ |
$1$ |
2.6.1 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(0.057434\) |
\(14.521337\) |
\(1.668042\) |
$[208,1336,318649,1884848]$ |
$[104,228,-26369,-698590,471212]$ |
$[3041632256/117803,64117248/117803,-10185968/16829]$ |
$y^2 + (x + 1)y = x^6 - x^5 + x^4 - 2x^2$ |
249362.a.498724.1 |
249362.a |
\( 2 \cdot 41 \cdot 3041 \) |
\( - 2^{2} \cdot 41 \cdot 3041 \) |
$3$ |
$3$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$15$ |
$1$ |
2.6.1 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(0.044769\) |
\(16.477525\) |
\(1.475363\) |
$[4212,154569,192076389,-63836672]$ |
$[1053,39760,1918804,109910753,-498724]$ |
$[-1294618640600493/498724,-11605704217380/124681,-531896786109/124681]$ |
$y^2 + (x^2 + x + 1)y = 2x^5 - 9x^4 + 9x^3 - 2x$ |
249478.a.498956.1 |
249478.a |
\( 2 \cdot 124739 \) |
\( - 2^{2} \cdot 124739 \) |
$3$ |
$3$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$15$ |
$1$ |
2.6.1 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(0.066972\) |
\(12.899215\) |
\(1.727765\) |
$[1832,33760,22104779,-1995824]$ |
$[916,29334,754697,-42295276,-498956]$ |
$[-161219428390144/124739,-5636346933216/124739,-158308261508/124739]$ |
$y^2 + (x^2 + 1)y = 2x^5 + 5x^4 - 5x^2 + x$ |
251578.a.503156.1 |
251578.a |
\( 2 \cdot 125789 \) |
\( 2^{2} \cdot 125789 \) |
$3$ |
$3$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$15$ |
$1$ |
2.6.1 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(0.062424\) |
\(13.656941\) |
\(1.705034\) |
$[696,-4464,-2086677,2012624]$ |
$[348,5790,257489,14020518,503156]$ |
$[1275957556992/125789,61003717920/125789,7795736964/125789]$ |
$y^2 + xy = x^6 - x^5 - 2x^4 + 3x^3 + x^2 - 2x$ |
252040.b.504080.1 |
252040.b |
\( 2^{3} \cdot 5 \cdot 6301 \) |
\( - 2^{4} \cdot 5 \cdot 6301 \) |
$3$ |
$3$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$15$ |
$1$ |
2.6.1 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(0.048659\) |
\(17.502585\) |
\(1.703301\) |
$[272,28852,618836,-2016320]$ |
$[136,-4038,118724,-39745,-504080]$ |
$[-2907867136/31505,634838208/31505,-137244944/31505]$ |
$y^2 + (x + 1)y = -2x^5 + 3x^4 + 6x^3 + 2x^2$ |
253832.a.507664.1 |
253832.a |
\( 2^{3} \cdot 31729 \) |
\( 2^{4} \cdot 31729 \) |
$3$ |
$3$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$15$ |
$1$ |
2.6.1 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(0.052189\) |
\(16.230277\) |
\(1.694084\) |
$[976,22420,8941756,-2030656]$ |
$[488,6186,-217988,-36161185,-507664]$ |
$[-1729733224448/31729,-44931342912/31729,3244533392/31729]$ |
$y^2 + (x^3 + x^2)y = -2x^4 + 7x^2 - 10x + 4$ |
254848.b.509696.1 |
254848.b |
\( 2^{7} \cdot 11 \cdot 181 \) |
\( 2^{8} \cdot 11 \cdot 181 \) |
$3$ |
$3$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$15$ |
$1$ |
2.6.1 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(0.056217\) |
\(13.920164\) |
\(1.565105\) |
$[374,-62,-48328,1991]$ |
$[748,23478,1278084,101197587,509696]$ |
$[83152505348/181,6978518547/362,1015757259/724]$ |
$y^2 + y = 2x^5 - 7x^4 + 5x^3 + 2x^2$ |
261357.a.784071.1 |
261357.a |
\( 3 \cdot 87119 \) |
\( 3^{2} \cdot 87119 \) |
$3$ |
$3$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$15$ |
$1$ |
2.6.1 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(0.056267\) |
\(13.581035\) |
\(1.528322\) |
$[3604,88249,-5939923,100361088]$ |
$[901,30148,2695912,380028702,784071]$ |
$[593777798104501/784071,22051233069748/784071,2188544057512/784071]$ |
$y^2 + (x^2 + x + 1)y = x^5 - 6x^3 - 3x^2 + 6x + 6$ |