| 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 |
| 196.a.21952.1 |
196.a |
\( 2^{2} \cdot 7^{2} \) |
\( - 2^{6} \cdot 7^{3} \) |
$0$ |
$2$ |
$\Z/6\Z\oplus\Z/6\Z$ |
\(\mathrm{M}_2(\Q)\) |
\(\mathrm{M}_2(\Q)\) |
|
$E_1$ |
|
|
|
$D_6$ |
$D_6$ |
$6$ |
$0$ |
2.360.3, 3.17280.1 |
✓ |
✓ |
$1$ |
\( 2^{2} \cdot 3 \) |
\(1.000000\) |
\(11.777148\) |
\(0.109048\) |
$[1340,1345,149855,2809856]$ |
$[335,4620,90160,2214800,21952]$ |
$[\frac{4219140959375}{21952},\frac{6203236875}{784},\frac{12905875}{28}]$ |
$y^2 + (x^2 + x)y = x^6 + 3x^5 + 6x^4 + 7x^3 + 6x^2 + 3x + 1$ |
| 363.a.11979.1 |
363.a |
\( 3 \cdot 11^{2} \) |
\( - 3^{2} \cdot 11^{3} \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/10\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2$ |
$C_2$ |
$5$ |
$3$ |
2.120.3, 3.80.4 |
✓ |
✓ |
$1$ |
\( 2^{2} \) |
\(1.000000\) |
\(18.970596\) |
\(0.189706\) |
$[344,-3068,-526433,-47916]$ |
$[172,1744,45841,1210779,-11979]$ |
$[-\frac{150536645632}{11979},-\frac{8874253312}{11979},-\frac{1356160144}{11979}]$ |
$y^2 + (x^2 + 1)y = x^5 + 2x^3 + 4x^2 + 2x$ |
| 363.a.43923.1 |
363.a |
\( 3 \cdot 11^{2} \) |
\( - 3 \cdot 11^{4} \) |
$0$ |
$1$ |
$\Z/10\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2$ |
$C_2$ |
$3$ |
$1$ |
2.60.1, 3.80.4 |
✓ |
✓ |
$1$ |
\( 5 \) |
\(1.000000\) |
\(3.794119\) |
\(0.189706\) |
$[11096,25612,88274095,-175692]$ |
$[5548,1278244,392069161,135322995423,-43923]$ |
$[-\frac{5256325630316243968}{43923},-\frac{1804005053317888}{363},-\frac{99735603013264}{363}]$ |
$y^2 + x^2y = 11x^5 - 13x^4 - 7x^3 + 10x^2 + x - 2$ |
| 450.a.36450.1 |
450.a |
\( 2 \cdot 3^{2} \cdot 5^{2} \) |
\( 2 \cdot 3^{6} \cdot 5^{2} \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/12\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$4$ |
$0$ |
2.180.7, 3.720.4 |
✓ |
✓ |
$1$ |
\( 2 \cdot 3 \) |
\(1.000000\) |
\(18.778996\) |
\(0.195615\) |
$[23444,212089,1627179821,4665600]$ |
$[5861,1422468,457836300,164990835819,36450]$ |
$[\frac{6916057684302385301}{36450},\frac{5303516319500302}{675},\frac{1294426477922}{3}]$ |
$y^2 + (x^3 + 1)y = x^5 - 4x^4 - 9x^3 + 28x^2 - 6x - 16$ |
| 464.a.29696.1 |
464.a |
\( 2^{4} \cdot 29 \) |
\( - 2^{10} \cdot 29 \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/8\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$5$ |
$3$ |
2.120.3 |
✓ |
✓ |
$1$ |
\( 2^{2} \) |
\(1.000000\) |
\(14.421431\) |
\(0.225335\) |
$[680,-5255,-1253953,-3712]$ |
$[680,22770,1180736,71106895,-29696]$ |
$[-\frac{141985700000}{29},-\frac{6991813125}{29},-\frac{533176100}{29}]$ |
$y^2 + (x + 1)y = 8x^5 + 3x^4 - 4x^3 - 2x^2$ |
| 464.a.29696.2 |
464.a |
\( 2^{4} \cdot 29 \) |
\( - 2^{10} \cdot 29 \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$3$ |
$3$ |
2.120.3 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(1.000000\) |
\(1.802679\) |
\(0.225335\) |
$[45368,202225,3012190355,-3712]$ |
$[45368,85625826,215176422416,607585463496703,-29696]$ |
$[-\frac{187693059992988715232}{29},-\frac{7808250185554819143}{29},-\frac{432507850151022641}{29}]$ |
$y^2 + xy = 4x^5 + 33x^4 + 72x^3 + 16x^2 + x$ |
| 472.a.60416.1 |
472.a |
\( 2^{3} \cdot 59 \) |
\( 2^{10} \cdot 59 \) |
$0$ |
$1$ |
$\Z/8\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$3$ |
$1$ |
2.60.1 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(1.000000\) |
\(7.278318\) |
\(0.227447\) |
$[152,17065,1592025,7552]$ |
$[152,-10414,-926656,-62325777,60416]$ |
$[\frac{79235168}{59},-\frac{35714813}{59},-\frac{20907676}{59}]$ |
$y^2 + (x + 1)y = 8x^5 + 5x^4 + 4x^3 + 2x^2$ |
| 504.a.27216.1 |
504.a |
\( 2^{3} \cdot 3^{2} \cdot 7 \) |
\( - 2^{4} \cdot 3^{5} \cdot 7 \) |
$0$ |
$2$ |
$\Z/4\Z\oplus\Z/4\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$2$ |
$0$ |
2.90.6, 3.90.1 |
✓ |
✓ |
$1$ |
\( 2^{3} \) |
\(1.000000\) |
\(7.782699\) |
\(0.243209\) |
$[8456,9496,26675348,108864]$ |
$[4228,743250,173847744,45651924783,27216]$ |
$[\frac{12063042849801664}{243},\frac{167186257609000}{81},\frac{3083035208512}{27}]$ |
$y^2 + (x^3 + x)y = 3x^4 + 15x^2 + 21$ |
| 588.a.18816.1 |
588.a |
\( 2^{2} \cdot 3 \cdot 7^{2} \) |
\( - 2^{7} \cdot 3 \cdot 7^{2} \) |
$0$ |
$1$ |
$\Z/24\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$6$ |
$0$ |
2.45.1, 3.720.4 |
✓ |
✓ |
$1$ |
\( 2^{3} \) |
\(1.000000\) |
\(20.658150\) |
\(0.286919\) |
$[748,11545,2902787,2408448]$ |
$[187,976,-192,-247120,18816]$ |
$[\frac{228669389707}{18816},\frac{398891383}{1176},-\frac{34969}{98}]$ |
$y^2 + (x^3 + 1)y = x^5 + x^4 + 5x^2 + 12x + 8$ |
| 600.a.18000.1 |
600.a |
\( 2^{3} \cdot 3 \cdot 5^{2} \) |
\( 2^{4} \cdot 3^{2} \cdot 5^{3} \) |
$0$ |
$3$ |
$\Z/2\Z\oplus\Z/2\Z\oplus\Z/6\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2$ |
$C_2$ |
$6$ |
$4$ |
2.360.2, 3.640.2 |
✓ |
✓ |
$1$ |
\( 2^{3} \) |
\(1.000000\) |
\(18.934319\) |
\(0.262977\) |
$[1376,23824,11410044,72000]$ |
$[688,15752,244900,-19908576,18000]$ |
$[\frac{9634345320448}{1125},\frac{320612931584}{1125},\frac{289804864}{45}]$ |
$y^2 + xy = 10x^5 - 18x^4 + 8x^3 + x^2 - x$ |
| 600.a.96000.1 |
600.a |
\( 2^{3} \cdot 3 \cdot 5^{2} \) |
\( 2^{8} \cdot 3 \cdot 5^{3} \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/6\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2$ |
$C_2$ |
$4$ |
$2$ |
2.180.3, 3.640.2 |
✓ |
✓ |
$1$ |
\( 2^{2} \) |
\(1.000000\) |
\(9.467159\) |
\(0.262977\) |
$[92,4981,43947,-12000]$ |
$[92,-2968,47600,-1107456,-96000]$ |
$[-\frac{25745372}{375},\frac{9027914}{375},-\frac{62951}{15}]$ |
$y^2 + (x + 1)y = 4x^5 + 5x^4 + 3x^3 + 2x^2$ |
| 600.b.30000.1 |
600.b |
\( 2^{3} \cdot 3 \cdot 5^{2} \) |
\( 2^{4} \cdot 3 \cdot 5^{4} \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/8\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$4$ |
$2$ |
2.180.3, 3.90.1 |
✓ |
✓ |
$1$ |
\( 2^{3} \) |
\(1.000000\) |
\(8.316291\) |
\(0.259884\) |
$[600,18744,4690524,120000]$ |
$[300,626,-198336,-14973169,30000]$ |
$[81000000,563400,-595008]$ |
$y^2 + (x^3 + x)y = x^4 + x^2 - 3$ |
| 630.a.34020.1 |
630.a |
\( 2 \cdot 3^{2} \cdot 5 \cdot 7 \) |
\( 2^{2} \cdot 3^{5} \cdot 5 \cdot 7 \) |
$0$ |
$3$ |
$\Z/2\Z\oplus\Z/2\Z\oplus\Z/4\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$4$ |
$4$ |
2.360.2, 3.90.1 |
✓ |
✓ |
$1$ |
\( 2^{2} \) |
\(1.000000\) |
\(19.470889\) |
\(0.304233\) |
$[24100,969793,7474503265,4354560]$ |
$[6025,1472118,470090880,166291536519,34020]$ |
$[\frac{1587871127345703125}{6804},\frac{10732293030978125}{1134},\frac{13543327580000}{27}]$ |
$y^2 + (x^2 + x)y = 3x^5 + 10x^4 - 23x^2 - 6x + 15$ |
| 640.a.81920.1 |
640.a |
\( 2^{7} \cdot 5 \) |
\( - 2^{14} \cdot 5 \) |
$0$ |
$1$ |
$\Z/12\Z$ |
\(\mathsf{CM} \times \Q\) |
\(\Q \times \Q\) |
✓ |
$N(\mathrm{U}(1)\times\mathrm{SU}(2))$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$2$ |
$0$ |
2.90.1, 3.2160.5 |
✓ |
✓ |
$1$ |
\( 2 \cdot 3 \) |
\(1.000000\) |
\(7.405674\) |
\(0.308570\) |
$[912,147,44562,10]$ |
$[3648,552928,111431680,25193348864,81920]$ |
$[\frac{39432490647552}{5},\frac{1638374321664}{5},18102076416]$ |
$y^2 + x^3y = 3x^4 + 13x^2 + 20$ |
| 640.a.81920.2 |
640.a |
\( 2^{7} \cdot 5 \) |
\( 2^{14} \cdot 5 \) |
$0$ |
$1$ |
$\Z/12\Z$ |
\(\mathsf{CM} \times \Q\) |
\(\Q \times \Q\) |
✓ |
$N(\mathrm{U}(1)\times\mathrm{SU}(2))$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$4$ |
$2$ |
2.90.3, 3.2160.5 |
✓ |
✓ |
$1$ |
\( 2 \cdot 3 \) |
\(1.000000\) |
\(7.405674\) |
\(0.308570\) |
$[912,147,44562,10]$ |
$[3648,552928,111431680,25193348864,81920]$ |
$[\frac{39432490647552}{5},\frac{1638374321664}{5},18102076416]$ |
$y^2 + x^3y = -3x^4 + 13x^2 - 20$ |
| 644.b.14812.1 |
644.b |
\( 2^{2} \cdot 7 \cdot 23 \) |
\( - 2^{2} \cdot 7 \cdot 23^{2} \) |
$0$ |
$1$ |
$\Z/10\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,5$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$4$ |
$2$ |
2.90.3 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(1.000000\) |
\(15.435107\) |
\(0.308702\) |
$[1268,-40511,-17688719,-1895936]$ |
$[317,5875,170781,4905488,-14812]$ |
$[-\frac{3201078401357}{14812},-\frac{187148201375}{14812},-\frac{17161611909}{14812}]$ |
$y^2 + (x^3 + 1)y = x^5 - x^4 - 4x^3 + 5x^2 - x - 1$ |
| 676.b.17576.1 |
676.b |
\( 2^{2} \cdot 13^{2} \) |
\( - 2^{3} \cdot 13^{3} \) |
$0$ |
$0$ |
$\Z/3\Z\oplus\Z/3\Z$ |
\(\mathrm{M}_2(\Q)\) |
\(\mathrm{M}_2(\Q)\) |
|
$E_1$ |
|
|
|
$D_6$ |
$D_6$ |
$0$ |
$0$ |
2.120.4, 3.17280.1 |
|
✓ |
$1$ |
\( 3 \) |
\(1.000000\) |
\(7.177121\) |
\(0.265819\) |
$[1244,1249,129167,2249728]$ |
$[311,3978,72332,1667692,17576]$ |
$[\frac{2909390022551}{17576},\frac{4602275343}{676},\frac{10349147}{26}]$ |
$y^2 + (x^2 + x)y = -x^6 + 3x^5 - 6x^4 + 6x^3 - 6x^2 + 3x - 1$ |
| 704.a.45056.1 |
704.a |
\( 2^{6} \cdot 11 \) |
\( - 2^{12} \cdot 11 \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/6\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,3$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$5$ |
$3$ |
2.120.3, 3.80.1 |
✓ |
✓ |
$1$ |
\( 2^{2} \) |
\(1.000000\) |
\(11.976027\) |
\(0.332667\) |
$[134,-464,-15328,-176]$ |
$[268,4230,61444,-356477,-45056]$ |
$[-\frac{1350125107}{44},-\frac{636113745}{352},-\frac{68955529}{704}]$ |
$y^2 + y = 4x^5 + 4x^4 - x^3 - 2x^2$ |
| 708.a.19116.1 |
708.a |
\( 2^{2} \cdot 3 \cdot 59 \) |
\( - 2^{2} \cdot 3^{4} \cdot 59 \) |
$0$ |
$1$ |
$\Z/10\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,5$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$4$ |
$2$ |
2.30.3 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(1.000000\) |
\(16.267181\) |
\(0.325344\) |
$[908,-132815,8426215,2446848]$ |
$[227,7681,-438901,-39657072,19116]$ |
$[\frac{602738989907}{19116},\frac{89845294523}{19116},-\frac{383324231}{324}]$ |
$y^2 + (x^3 + 1)y = -x^5 + 4x^2 + 4x - 1$ |
| 731.a.12427.1 |
731.a |
\( 17 \cdot 43 \) |
\( - 17^{2} \cdot 43 \) |
$0$ |
$1$ |
$\Z/10\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,5$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$4$ |
$2$ |
2.30.3 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(1.000000\) |
\(14.926779\) |
\(0.298536\) |
$[480,-21564,-3373785,-49708]$ |
$[240,5994,167265,1053891,-12427]$ |
$[-\frac{796262400000}{12427},-\frac{82861056000}{12427},-\frac{9634464000}{12427}]$ |
$y^2 + (x^3 + x^2)y = x^5 + 2x^4 - x - 3$ |
| 741.a.28899.1 |
741.a |
\( 3 \cdot 13 \cdot 19 \) |
\( - 3^{2} \cdot 13^{2} \cdot 19 \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/8\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$5$ |
$3$ |
2.120.3 |
✓ |
✓ |
$1$ |
\( 2^{2} \) |
\(1.000000\) |
\(18.756843\) |
\(0.293076\) |
$[576,-840,740385,115596]$ |
$[288,3596,-38169,-5980972,28899]$ |
$[\frac{220150628352}{3211},\frac{9544531968}{3211},-\frac{351765504}{3211}]$ |
$y^2 + (x + 1)y = -3x^5 - x^4 + 2x^2 + x$ |
| 762.a.82296.1 |
762.a |
\( 2 \cdot 3 \cdot 127 \) |
\( 2^{3} \cdot 3^{4} \cdot 127 \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/12\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,3$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$5$ |
$3$ |
2.120.3, 3.80.1 |
✓ |
✓ |
$1$ |
\( 2^{2} \cdot 3 \) |
\(1.000000\) |
\(16.733449\) |
\(0.348614\) |
$[12004,205249,810020577,10533888]$ |
$[3001,366698,58441312,10228738527,82296]$ |
$[\frac{243405270090015001}{82296},\frac{4955375073324349}{41148},\frac{65790314289164}{10287}]$ |
$y^2 + (x^2 + x)y = x^5 - 8x^4 + 14x^3 + 2x^2 - x$ |
| 784.a.43904.1 |
784.a |
\( 2^{4} \cdot 7^{2} \) |
\( - 2^{7} \cdot 7^{3} \) |
$0$ |
$1$ |
$\Z/12\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$2$ |
$0$ |
2.90.1, 3.2160.20 |
✓ |
✓ |
$1$ |
\( 2 \cdot 3 \) |
\(1.000000\) |
\(6.931117\) |
\(0.288797\) |
$[21288,3000,20891172,175616]$ |
$[10644,4720114,2790613504,1855953490895,43904]$ |
$[\frac{1067368445729034408}{343},\frac{6352710665144931}{49},\frac{50408453477952}{7}]$ |
$y^2 + (x^3 + x)y = 4x^4 + 27x^2 + 56$ |
| 784.b.12544.1 |
784.b |
\( 2^{4} \cdot 7^{2} \) |
\( 2^{8} \cdot 7^{2} \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/6\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$4$ |
$2$ |
2.360.1, 3.720.4 |
✓ |
✓ |
$1$ |
\( 2^{2} \) |
\(1.000000\) |
\(11.270100\) |
\(0.313058\) |
$[116,445,16259,1568]$ |
$[116,264,-1280,-54544,12544]$ |
$[\frac{82044596}{49},\frac{1609674}{49},-\frac{67280}{49}]$ |
$y^2 + (x^3 + x)y = -1$ |
| 784.b.25088.1 |
784.b |
\( 2^{4} \cdot 7^{2} \) |
\( - 2^{9} \cdot 7^{2} \) |
$0$ |
$2$ |
$\Z/2\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2$ |
$C_2$ |
$0$ |
$0$ |
2.45.1, 3.720.5 |
|
|
$2$ |
\( 1 \) |
\(1.000000\) |
\(0.626117\) |
\(0.313058\) |
$[2740,15382525,36170522453,3136]$ |
$[2740,-9942200,-24298750736,-41356479464160,25088]$ |
$[\frac{301635777856250}{49},-\frac{399451653071875}{49},-\frac{712598832131225}{98}]$ |
$y^2 + (x^2 + 1)y = -x^6 - 3x^5 + 7x^4 + 2x^3 - 49x^2 + 41x - 9$ |
| 784.b.76832.1 |
784.b |
\( 2^{4} \cdot 7^{2} \) |
\( - 2^{5} \cdot 7^{4} \) |
$0$ |
$1$ |
$\Z/6\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2$ |
$C_2$ |
$0$ |
$0$ |
2.45.1, 3.2160.20 |
|
✓ |
$1$ |
\( 3 \) |
\(1.000000\) |
\(3.756700\) |
\(0.313058\) |
$[1520,132280,50979316,307328]$ |
$[760,2020,6076,134340,76832]$ |
$[\frac{7923516800000}{2401},\frac{27710360000}{2401},\frac{2238200}{49}]$ |
$y^2 + (x + 1)y = -x^6 + 4x^5 - 4x^4 - 2x^3 + 10x - 9$ |
| 816.a.13872.1 |
816.a |
\( 2^{4} \cdot 3 \cdot 17 \) |
\( - 2^{4} \cdot 3 \cdot 17^{2} \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/6\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,3$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$4$ |
$2$ |
2.180.3, 3.80.1 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(1.000000\) |
\(22.166697\) |
\(0.307871\) |
$[688,9592,2944404,55488]$ |
$[344,3332,-80164,-9669660,13872]$ |
$[\frac{301073291264}{867},\frac{498667904}{51},-\frac{592892944}{867}]$ |
$y^2 + (x^3 + x^2)y = -2x^4 + 6x^2 - 8x + 3$ |
| 816.a.39168.1 |
816.a |
\( 2^{4} \cdot 3 \cdot 17 \) |
\( 2^{8} \cdot 3^{2} \cdot 17 \) |
$0$ |
$3$ |
$\Z/2\Z\oplus\Z/2\Z\oplus\Z/6\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,3$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$6$ |
$4$ |
2.360.2, 3.80.1 |
✓ |
✓ |
$1$ |
\( 2^{3} \) |
\(1.000000\) |
\(22.166697\) |
\(0.307871\) |
$[436,3373,434667,4896]$ |
$[436,5672,77824,439920,39168]$ |
$[\frac{61544958196}{153},\frac{1836351122}{153},\frac{57789184}{153}]$ |
$y^2 + (x^2 + 1)y = 3x^5 - 4x^3 - x^2 + x$ |
| 816.b.52224.1 |
816.b |
\( 2^{4} \cdot 3 \cdot 17 \) |
\( - 2^{10} \cdot 3 \cdot 17 \) |
$0$ |
$2$ |
$\Z/6\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$0$ |
$0$ |
2.45.1, 3.720.4 |
|
|
$2$ |
\( 3 \) |
\(1.000000\) |
\(2.423742\) |
\(0.403957\) |
$[15964,2380825,11444690699,6528]$ |
$[15964,9031504,6282991104,4683401370560,52224]$ |
$[\frac{1012531723491160951}{51},\frac{35882713644370099}{51},30660536527816]$ |
$y^2 + (x^3 + x)y = -x^6 - 12x^4 - 27x^2 - 17$ |
| 826.a.11564.1 |
826.a |
\( 2 \cdot 7 \cdot 59 \) |
\( - 2^{2} \cdot 7^{2} \cdot 59 \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/6\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,3$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$5$ |
$3$ |
2.120.3, 3.80.1 |
✓ |
✓ |
$1$ |
\( 2^{2} \) |
\(1.000000\) |
\(13.174483\) |
\(0.365958\) |
$[92,-554591,-3126961,1480192]$ |
$[23,23130,-104176,-134348237,11564]$ |
$[\frac{6436343}{11564},\frac{140711355}{5782},-\frac{13777276}{2891}]$ |
$y^2 + (x^2 + x)y = x^5 + x^4 + 3x^3 - 4x^2 - 4x + 3$ |
| 882.a.63504.1 |
882.a |
\( 2 \cdot 3^{2} \cdot 7^{2} \) |
\( 2^{4} \cdot 3^{4} \cdot 7^{2} \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/8\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$4$ |
$2$ |
2.360.1, 3.90.1 |
✓ |
✓ |
$1$ |
\( 2^{3} \) |
\(1.000000\) |
\(12.542623\) |
\(0.391957\) |
$[548,6049,662961,8128512]$ |
$[137,530,6336,146783,63504]$ |
$[\frac{48261724457}{63504},\frac{681408545}{31752},\frac{825836}{441}]$ |
$y^2 + (x^2 + x)y = x^5 + x^4 + x^3 + 3x^2 + 3x + 1$ |
| 925.a.23125.1 |
925.a |
\( 5^{2} \cdot 37 \) |
\( 5^{4} \cdot 37 \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/8\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$5$ |
$3$ |
2.120.3 |
✓ |
✓ |
$1$ |
\( 2^{2} \) |
\(1.000000\) |
\(20.878934\) |
\(0.326233\) |
$[3496,50536,55764955,92500]$ |
$[1748,118890,10257041,948618892,23125]$ |
$[\frac{16319511005139968}{23125},\frac{126998797147776}{4625},\frac{31340429803664}{23125}]$ |
$y^2 + xy = 5x^5 + x^4 - 19x^3 + 18x^2 - 5x$ |
| 975.a.63375.1 |
975.a |
\( 3 \cdot 5^{2} \cdot 13 \) |
\( - 3 \cdot 5^{3} \cdot 13^{2} \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/6\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,3$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$4$ |
$2$ |
2.180.3, 3.80.1 |
✓ |
✓ |
$1$ |
\( 2^{2} \) |
\(1.000000\) |
\(14.356290\) |
\(0.398786\) |
$[148,-48575,-4076175,-8112000]$ |
$[37,2081,35929,-750297,-63375]$ |
$[-\frac{69343957}{63375},-\frac{105408893}{63375},-\frac{49186801}{63375}]$ |
$y^2 + (x^3 + 1)y = -x^5 + x^3 + 2x^2 + x - 1$ |
| 1008.a.27216.1 |
1008.a |
\( 2^{4} \cdot 3^{2} \cdot 7 \) |
\( 2^{4} \cdot 3^{5} \cdot 7 \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/8\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$4$ |
$2$ |
2.180.3, 3.90.1 |
✓ |
✓ |
$1$ |
\( 2^{3} \) |
\(1.000000\) |
\(12.167487\) |
\(0.380234\) |
$[8456,9496,26675348,108864]$ |
$[4228,743250,173847744,45651924783,27216]$ |
$[\frac{12063042849801664}{243},\frac{167186257609000}{81},\frac{3083035208512}{27}]$ |
$y^2 + (x^3 + x)y = -4x^4 + 15x^2 - 21$ |
| 1083.a.20577.1 |
1083.a |
\( 3 \cdot 19^{2} \) |
\( 3 \cdot 19^{3} \) |
$1$ |
$1$ |
$\Z/3\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$4$ |
$0$ |
2.15.2, 3.2160.20 |
✓ |
✓ |
$1$ |
\( 3 \) |
\(0.075149\) |
\(7.554151\) |
\(0.189229\) |
$[904,13684,4578992,82308]$ |
$[452,6232,-8664,-10688488,20577]$ |
$[\frac{18866536236032}{20577},\frac{30289293824}{1083},-\frac{1634432}{19}]$ |
$y^2 + x^3y = x^5 - 5x^4 + 11x^3 - 13x^2 + 9x - 3$ |
| 1083.b.87723.1 |
1083.b |
\( 3 \cdot 19^{2} \) |
\( - 3^{5} \cdot 19^{2} \) |
$0$ |
$1$ |
$\Z/15\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$0$ |
$0$ |
2.15.2, 3.720.4 |
|
|
$2$ |
\( 5 \) |
\(1.000000\) |
\(5.981341\) |
\(0.265837\) |
$[5464,8692,15768656,350892]$ |
$[2732,309544,46549080,7838649656,87723]$ |
$[\frac{152196082896530432}{87723},\frac{6311963449851392}{87723},\frac{1429770125440}{361}]$ |
$y^2 + y = -x^6 - 3x^5 - 8x^4 - 11x^3 - 14x^2 - 9x - 6$ |
| 1104.a.17664.1 |
1104.a |
\( 2^{4} \cdot 3 \cdot 23 \) |
\( 2^{8} \cdot 3 \cdot 23 \) |
$0$ |
$1$ |
$\Z/10\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,5$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$3$ |
$1$ |
2.60.1 |
✓ |
✓ |
$1$ |
\( 5 \) |
\(1.000000\) |
\(8.907497\) |
\(0.445375\) |
$[88,160,4888,69]$ |
$[176,864,-1280,-242944,17664]$ |
$[\frac{659664896}{69},\frac{6133248}{23},-\frac{154880}{69}]$ |
$y^2 = x^5 - 2x^4 + 4x^3 - 4x^2 + 3x - 1$ |
| 1147.a.35557.1 |
1147.a |
\( 31 \cdot 37 \) |
\( 31^{2} \cdot 37 \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/4\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$3$ |
$3$ |
2.120.3 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(1.000000\) |
\(11.458568\) |
\(0.358080\) |
$[3712,11944,14677639,142228]$ |
$[1856,141540,14195057,1578113548,35557]$ |
$[\frac{22023678539595776}{35557},\frac{904926084464640}{35557},\frac{48898223869952}{35557}]$ |
$y^2 + xy = x^5 + 8x^4 + 18x^3 + 8x^2 + x$ |
| 1147.a.35557.2 |
1147.a |
\( 31 \cdot 37 \) |
\( 31^{2} \cdot 37 \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$3$ |
$3$ |
2.120.3 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(1.000000\) |
\(2.864642\) |
\(0.358080\) |
$[12352,2309104,8338761079,142228]$ |
$[6176,1204440,279006977,68117844088,35557]$ |
$[\frac{8985379753611493376}{35557},\frac{283731159059005440}{35557},\frac{10642156427543552}{35557}]$ |
$y^2 + xy = x^5 + 6x^4 - 32x^2 + x$ |
| 1148.a.47068.1 |
1148.a |
\( 2^{2} \cdot 7 \cdot 41 \) |
\( - 2^{2} \cdot 7 \cdot 41^{2} \) |
$0$ |
$1$ |
$\Z/10\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,5$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$4$ |
$2$ |
2.90.3 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(1.000000\) |
\(22.531311\) |
\(0.450626\) |
$[1236,129537,36025137,-6024704]$ |
$[309,-1419,31221,1908432,-47068]$ |
$[-\frac{2817036000549}{47068},\frac{41865649551}{47068},-\frac{2981012301}{47068}]$ |
$y^2 + (x^2 + x + 1)y = x^5 + 2x^4 - 5x^3 + x$ |
| 1170.a.10530.1 |
1170.a |
\( 2 \cdot 3^{2} \cdot 5 \cdot 13 \) |
\( - 2 \cdot 3^{4} \cdot 5 \cdot 13 \) |
$0$ |
$4$ |
$\Z/2\Z\oplus\Z/6\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$0$ |
$0$ |
2.90.6, 3.720.4 |
✓ |
✓ |
$4$ |
\( 3 \) |
\(1.000000\) |
\(5.542030\) |
\(0.461836\) |
$[507196,192673,32552199279,1347840]$ |
$[126799,669908072,4718980180980,37396285759331459,10530]$ |
$[\frac{32777750301275239538233999}{10530},\frac{682861614668954802420364}{5265},7205289570406928666]$ |
$y^2 + (x^2 + x)y = 15x^6 + 28x^5 + 62x^4 + 59x^3 + 62x^2 + 28x + 15$ |
| 1176.b.16464.1 |
1176.b |
\( 2^{3} \cdot 3 \cdot 7^{2} \) |
\( 2^{4} \cdot 3 \cdot 7^{3} \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/6\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2$ |
$C_2$ |
$4$ |
$2$ |
2.180.3, 3.640.2 |
✓ |
✓ |
$1$ |
\( 2^{2} \) |
\(1.000000\) |
\(13.019302\) |
\(0.361647\) |
$[160,4720,130020,-65856]$ |
$[80,-520,4220,16800,-16464]$ |
$[-\frac{204800000}{1029},\frac{16640000}{1029},-\frac{1688000}{1029}]$ |
$y^2 + (x + 1)y = -2x^5 + x^2$ |
| 1180.a.18880.1 |
1180.a |
\( 2^{2} \cdot 5 \cdot 59 \) |
\( - 2^{6} \cdot 5 \cdot 59 \) |
$0$ |
$1$ |
$\Z/18\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,3$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$5$ |
$1$ |
2.60.1, 3.80.1 |
✓ |
✓ |
$1$ |
\( 2 \cdot 3 \) |
\(1.000000\) |
\(24.170512\) |
\(0.447602\) |
$[916,23257,5960477,-2416640]$ |
$[229,1216,6656,11392,-18880]$ |
$[-\frac{629763392149}{18880},-\frac{228170791}{295},-\frac{5453864}{295}]$ |
$y^2 + (x^3 + 1)y = -2x^4 + 4x^2 + 2x$ |
| 1192.a.19072.1 |
1192.a |
\( 2^{3} \cdot 149 \) |
\( - 2^{7} \cdot 149 \) |
$0$ |
$1$ |
$\Z/22\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,11$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$6$ |
$2$ |
2.30.3 |
✓ |
✓ |
$1$ |
\( 11 \) |
\(1.000000\) |
\(22.627068\) |
\(0.514252\) |
$[160,3184,271780,76288]$ |
$[80,-264,-17220,-361824,19072]$ |
$[\frac{25600000}{149},-\frac{1056000}{149},-\frac{861000}{149}]$ |
$y^2 + (x^3 + x)y = x^3 - 2x^2 - x + 1$ |
| 1197.a.10773.1 |
1197.a |
\( 3^{2} \cdot 7 \cdot 19 \) |
\( 3^{4} \cdot 7 \cdot 19 \) |
$0$ |
$1$ |
$\Z/10\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,5$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$3$ |
$1$ |
2.60.1 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(1.000000\) |
\(18.778043\) |
\(0.375561\) |
$[520,10900,1557089,-43092]$ |
$[260,1000,-1121,-322865,-10773]$ |
$[-\frac{1188137600000}{10773},-\frac{17576000000}{10773},\frac{3988400}{567}]$ |
$y^2 + (x^3 + x^2)y = -x^3 - x^2 - x + 2$ |
| 1200.a.30000.1 |
1200.a |
\( 2^{4} \cdot 3 \cdot 5^{2} \) |
\( - 2^{4} \cdot 3 \cdot 5^{4} \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/8\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$4$ |
$2$ |
2.180.3, 3.90.1 |
✓ |
✓ |
$1$ |
\( 2^{2} \) |
\(1.000000\) |
\(22.621485\) |
\(0.353461\) |
$[600,18744,4690524,120000]$ |
$[300,626,-198336,-14973169,30000]$ |
$[81000000,563400,-595008]$ |
$y^2 + (x^3 + x)y = -2x^4 + x^2 + 3$ |
| 1216.a.19456.1 |
1216.a |
\( 2^{6} \cdot 19 \) |
\( - 2^{10} \cdot 19 \) |
$0$ |
$1$ |
$\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,3$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$1$ |
$1$ |
2.60.1, 3.80.2 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(1.625809\) |
\(0.406452\) |
$[3996,347595,394636194,-2432]$ |
$[3996,433604,54136720,7079476076,-19456]$ |
$[-\frac{995009990004999}{19},-\frac{108076122094599}{76},-\frac{3376781293545}{76}]$ |
$y^2 + x^2y = 4x^5 + 3x^4 - 11x^3 - 6x^2 + 6x - 1$ |
| 1258.a.21386.1 |
1258.a |
\( 2 \cdot 17 \cdot 37 \) |
\( 2 \cdot 17^{2} \cdot 37 \) |
$0$ |
$1$ |
$\Z/10\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,5$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$3$ |
$1$ |
2.60.1 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(1.000000\) |
\(20.931527\) |
\(0.418631\) |
$[2360,51148,37529695,85544]$ |
$[1180,49492,2427545,103761259,21386]$ |
$[\frac{1143878878400000}{10693},\frac{40658469872000}{10693},\frac{1690056829000}{10693}]$ |
$y^2 + xy = x^5 + 4x^4 - 5x^3 - 4x^2 + 5x - 1$ |
| 1280.a.12800.1 |
1280.a |
\( 2^{8} \cdot 5 \) |
\( - 2^{9} \cdot 5^{2} \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/6\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,3$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$4$ |
$2$ |
2.180.3, 3.80.1 |
✓ |
✓ |
$1$ |
\( 2^{2} \) |
\(1.000000\) |
\(17.070788\) |
\(0.474189\) |
$[22,-170,-1832,-50]$ |
$[44,534,7684,13235,-12800]$ |
$[-\frac{322102}{25},-\frac{355377}{100},-\frac{232441}{200}]$ |
$y^2 + y = 2x^5 + x^4 - x^3 - x^2$ |
| 1296.a.20736.1 |
1296.a |
\( 2^{4} \cdot 3^{4} \) |
\( 2^{8} \cdot 3^{4} \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/6\Z$ |
\(\mathrm{M}_2(\Q)\) |
\(\mathsf{CM}\) |
✓ |
$E_3$ |
|
✓ |
|
$C_6$ |
$D_6$ |
$3$ |
$3$ |
2.240.1, 3.1920.3 |
✓ |
✓ |
$1$ |
\( 3 \) |
\(1.000000\) |
\(23.235042\) |
\(0.484063\) |
$[78,216,4806,81]$ |
$[156,438,-428,-64653,20736]$ |
$[4455516,\frac{160381}{2},-\frac{18083}{36}]$ |
$y^2 = x^5 - x^4 - 3x^3 + 4x^2 - x$ |
