| 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 |
| 249.a.6723.1 |
249.a |
\( 3 \cdot 83 \) |
\( - 3^{4} \cdot 83 \) |
$0$ |
$1$ |
$\Z/28\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,7$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$6$ |
$2$ |
2.30.3 |
✓ |
✓ |
$1$ |
\( 2^{2} \) |
\(1.000000\) |
\(25.783703\) |
\(0.131550\) |
$[1932,87897,65765571,860544]$ |
$[483,6058,-161212,-28641190,6723]$ |
$[\frac{324526850403}{83},\frac{25281736298}{249},-\frac{4178776252}{747}]$ |
$y^2 + (x^3 + 1)y = -x^5 + x^3 + x^2 + 3x + 2$ |
| 294.a.8232.1 |
294.a |
\( 2 \cdot 3 \cdot 7^{2} \) |
\( 2^{3} \cdot 3 \cdot 7^{3} \) |
$0$ |
$1$ |
$\Z/12\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$4$ |
$0$ |
2.45.1, 3.2160.20 |
✓ |
✓ |
$1$ |
\( 3 \) |
\(1.000000\) |
\(7.150511\) |
\(0.148969\) |
$[7636,11785,29745701,1053696]$ |
$[1909,151354,15951264,1885732415,8232]$ |
$[\frac{25353016669288549}{8232},\frac{75211396489919}{588},\frac{49431027484}{7}]$ |
$y^2 + (x^3 + 1)y = -2x^4 + 4x^2 - 9x - 14$ |
| 360.a.6480.1 |
360.a |
\( 2^{3} \cdot 3^{2} \cdot 5 \) |
\( 2^{4} \cdot 3^{4} \cdot 5 \) |
$0$ |
$3$ |
$\Z/2\Z\oplus\Z/2\Z\oplus\Z/8\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$6$ |
$4$ |
2.360.2, 3.90.1 |
✓ |
✓ |
$1$ |
\( 2^{3} \) |
\(1.000000\) |
\(24.163379\) |
\(0.188776\) |
$[2360,11992,9047820,25920]$ |
$[1180,56018,3453120,234166319,6480]$ |
$[\frac{28596971960000}{81},\frac{1150492082200}{81},\frac{6677950400}{9}]$ |
$y^2 + (x^3 + x)y = -3x^4 + 7x^2 - 5$ |
| 394.a.3152.1 |
394.a |
\( 2 \cdot 197 \) |
\( 2^{4} \cdot 197 \) |
$0$ |
$1$ |
$\Z/20\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,5$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$6$ |
$2$ |
2.30.3 |
✓ |
✓ |
$1$ |
\( 2^{2} \) |
\(1.000000\) |
\(20.078274\) |
\(0.200783\) |
$[80,-20,649,-12608]$ |
$[40,70,39,-835,-3152]$ |
$[-\frac{6400000}{197},-\frac{280000}{197},-\frac{3900}{197}]$ |
$y^2 + (x + 1)y = -x^5$ |
| 427.a.2989.1 |
427.a |
\( 7 \cdot 61 \) |
\( - 7^{2} \cdot 61 \) |
$0$ |
$1$ |
$\Z/14\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,7$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$4$ |
$2$ |
2.30.3 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(1.000000\) |
\(18.613176\) |
\(0.189930\) |
$[4564,-22439,-35962915,-382592]$ |
$[1141,55180,3641688,277583402,-2989]$ |
$[-\frac{39466820645749}{61},-\frac{1672794336220}{61},-\frac{96756008472}{61}]$ |
$y^2 + (x^3 + 1)y = x^5 - x^4 - 5x^3 + 4x^2 + 4x - 4$ |
| 450.a.2700.1 |
450.a |
\( 2 \cdot 3^{2} \cdot 5^{2} \) |
\( - 2^{2} \cdot 3^{3} \cdot 5^{2} \) |
$0$ |
$1$ |
$\Z/24\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$6$ |
$0$ |
2.180.4, 3.720.4 |
✓ |
✓ |
$1$ |
\( 2 \cdot 3 \) |
\(1.000000\) |
\(18.778996\) |
\(0.195615\) |
$[364,3529,393211,345600]$ |
$[91,198,0,-9801,2700]$ |
$[\frac{6240321451}{2700},\frac{8289281}{150},0]$ |
$y^2 + (x^3 + 1)y = x^5 + 3x^4 + 3x^3 + 3x^2 + x$ |
| 484.a.1936.1 |
484.a |
\( 2^{2} \cdot 11^{2} \) |
\( - 2^{4} \cdot 11^{2} \) |
$0$ |
$0$ |
$\Z/15\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$4$ |
$0$ |
2.60.2, 3.720.4 |
✓ |
✓ |
$1$ |
\( 3 \) |
\(1.000000\) |
\(15.318968\) |
\(0.204253\) |
$[184,37,721,242]$ |
$[184,1386,15040,211591,1936]$ |
$[\frac{13181630464}{121},\frac{49057344}{11},\frac{31824640}{121}]$ |
$y^2 + y = x^6 + 2x^4 + x^2$ |
| 555.a.8325.1 |
555.a |
\( 3 \cdot 5 \cdot 37 \) |
\( 3^{2} \cdot 5^{2} \cdot 37 \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/10\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,5$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$5$ |
$3$ |
2.120.3 |
✓ |
✓ |
$1$ |
\( 2^{2} \) |
\(1.000000\) |
\(25.692472\) |
\(0.256925\) |
$[1264,18124,6869487,33300]$ |
$[632,13622,351361,9125317,8325]$ |
$[\frac{100828984082432}{8325},\frac{3438682756096}{8325},\frac{140342016064}{8325}]$ |
$y^2 + (x + 1)y = 3x^5 - 2x^4 - 4x^3 + x^2 + x$ |
| 578.a.2312.1 |
578.a |
\( 2 \cdot 17^{2} \) |
\( 2^{3} \cdot 17^{2} \) |
$0$ |
$1$ |
$\Z/12\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$4$ |
$2$ |
2.90.3, 3.2160.21 |
✓ |
✓ |
$1$ |
\( 3 \) |
\(1.000000\) |
\(13.910299\) |
\(0.289798\) |
$[228,705,135777,295936]$ |
$[57,106,-992,-16945,2312]$ |
$[\frac{601692057}{2312},\frac{9815229}{1156},-\frac{402876}{289}]$ |
$y^2 + (x^2 + x)y = x^5 - 2x^4 + 2x^3 - 2x^2 + x$ |
| 604.a.9664.1 |
604.a |
\( 2^{2} \cdot 151 \) |
\( 2^{6} \cdot 151 \) |
$0$ |
$0$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,3$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$1$ |
$1$ |
2.6.1, 3.720.5 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(0.291788\) |
\(0.291788\) |
$[49556,-797087975,-23996873337603,1236992]$ |
$[12389,39607304,223396249616,299729401586052,9664]$ |
$[\frac{291864493641401980949}{9664},\frac{9414430497536890397}{1208},\frac{2143030742187944921}{604}]$ |
$y^2 + (x^2 + x + 1)y = 4x^5 + 9x^4 + 48x^3 - 4x^2 - 53x - 21$ |
| 604.a.9664.2 |
604.a |
\( 2^{2} \cdot 151 \) |
\( 2^{6} \cdot 151 \) |
$0$ |
$0$ |
$\Z/27\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,3$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$7$ |
$1$ |
2.6.1, 3.80.1 |
✓ |
✓ |
$1$ |
\( 3^{2} \) |
\(1.000000\) |
\(23.634831\) |
\(0.291788\) |
$[116,6265,95277,1236992]$ |
$[29,-226,836,-6708,9664]$ |
$[\frac{20511149}{9664},-\frac{2755957}{4832},\frac{175769}{2416}]$ |
$y^2 + (x^3 + 1)y = -x^4 + x^3 + x^2 - x$ |
| 644.a.2576.1 |
644.a |
\( 2^{2} \cdot 7 \cdot 23 \) |
\( - 2^{4} \cdot 7 \cdot 23 \) |
$0$ |
$2$ |
$\Z/6\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$0$ |
$0$ |
2.45.1, 3.720.4 |
|
|
$2$ |
\( 1 \) |
\(1.000000\) |
\(3.928431\) |
\(0.218246\) |
$[39036,4124865,50880984159,329728]$ |
$[9759,3796384,1910683600,1058457444236,2576]$ |
$[\frac{88516980336138032799}{2576},\frac{220529201888022246}{161},70640465629725]$ |
$y^2 + (x^2 + x)y = -5x^6 + 11x^5 - 20x^4 + 20x^3 - 20x^2 + 11x - 5$ |
| 676.a.5408.1 |
676.a |
\( 2^{2} \cdot 13^{2} \) |
\( - 2^{5} \cdot 13^{2} \) |
$0$ |
$0$ |
$\Z/21\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$6$ |
$0$ |
2.60.2, 3.2160.21 |
✓ |
✓ |
$1$ |
\( 7 \) |
\(1.000000\) |
\(20.169780\) |
\(0.320155\) |
$[204,3273,161211,692224]$ |
$[51,-28,0,-196,5408]$ |
$[\frac{345025251}{5408},-\frac{928557}{1352},0]$ |
$y^2 + (x^3 + x^2 + x)y = x^3 + 3x^2 + 3x + 1$ |
| 688.a.2752.1 |
688.a |
\( 2^{4} \cdot 43 \) |
\( - 2^{6} \cdot 43 \) |
$0$ |
$1$ |
$\Z/20\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,5$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$6$ |
$2$ |
2.30.3 |
✓ |
✓ |
$1$ |
\( 5 \) |
\(1.000000\) |
\(25.707298\) |
\(0.321341\) |
$[32,112,-680,-344]$ |
$[32,-32,1344,10496,-2752]$ |
$[-\frac{524288}{43},\frac{16384}{43},-\frac{21504}{43}]$ |
$y^2 + y = 2x^5 - 5x^4 + 4x^3 - x$ |
| 708.a.2832.1 |
708.a |
\( 2^{2} \cdot 3 \cdot 59 \) |
\( 2^{4} \cdot 3 \cdot 59 \) |
$0$ |
$1$ |
$\Z/10\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,5$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$3$ |
$1$ |
2.60.1 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(1.000000\) |
\(16.267181\) |
\(0.325344\) |
$[148,2065,76361,362496]$ |
$[37,-29,-59,-756,2832]$ |
$[\frac{69343957}{2832},-\frac{1468937}{2832},-\frac{1369}{48}]$ |
$y^2 + (x^2 + x + 1)y = x^5$ |
| 720.a.6480.1 |
720.a |
\( 2^{4} \cdot 3^{2} \cdot 5 \) |
\( - 2^{4} \cdot 3^{4} \cdot 5 \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/4\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$2$ |
$0$ |
2.180.7, 3.90.1 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(1.000000\) |
\(9.444268\) |
\(0.295133\) |
$[2360,11992,9047820,25920]$ |
$[1180,56018,3453120,234166319,6480]$ |
$[\frac{28596971960000}{81},\frac{1150492082200}{81},\frac{6677950400}{9}]$ |
$y^2 + (x^3 + x)y = 2x^4 + 7x^2 + 5$ |
| 726.a.1452.1 |
726.a |
\( 2 \cdot 3 \cdot 11^{2} \) |
\( - 2^{2} \cdot 3 \cdot 11^{2} \) |
$0$ |
$1$ |
$\Z/10\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2$ |
$C_2$ |
$3$ |
$1$ |
2.60.1, 3.90.1 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(1.000000\) |
\(15.124086\) |
\(0.302482\) |
$[760,-69236,-16142609,-5808]$ |
$[380,17556,702601,-10306189,-1452]$ |
$[-\frac{1980879200000}{363},-\frac{7297976000}{11},-\frac{25363896100}{363}]$ |
$y^2 + (x^2 + 1)y = 2x^5 + 2x^4 + 6x^3 - 2x^2 - x$ |
| 762.a.3048.1 |
762.a |
\( 2 \cdot 3 \cdot 127 \) |
\( - 2^{3} \cdot 3 \cdot 127 \) |
$0$ |
$1$ |
$\Z/12\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,3$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$4$ |
$0$ |
2.15.1, 3.80.1 |
✓ |
✓ |
$1$ |
\( 3 \) |
\(1.000000\) |
\(16.733449\) |
\(0.348614\) |
$[428,3169,355487,390144]$ |
$[107,345,1823,19009,3048]$ |
$[\frac{14025517307}{3048},\frac{140879945}{1016},\frac{20871527}{3048}]$ |
$y^2 + (x^3 + x^2 + x)y = x^2 + x + 1$ |
| 768.a.1536.1 |
768.a |
\( 2^{8} \cdot 3 \) |
\( 2^{9} \cdot 3 \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/6\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,3$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$4$ |
$2$ |
2.180.3, 3.80.1 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(1.000000\) |
\(25.146749\) |
\(0.349260\) |
$[134,82,3600,6]$ |
$[268,2774,35236,437043,1536]$ |
$[\frac{2700250214}{3},\frac{417158281}{12},\frac{39543601}{24}]$ |
$y^2 + y = 2x^5 - x^4 - 3x^3 + x$ |
| 768.a.4608.1 |
768.a |
\( 2^{8} \cdot 3 \) |
\( 2^{9} \cdot 3^{2} \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/6\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,3$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$4$ |
$2$ |
2.180.3, 3.80.1 |
✓ |
✓ |
$1$ |
\( 2^{2} \) |
\(1.000000\) |
\(12.573375\) |
\(0.349260\) |
$[38,22,384,18]$ |
$[76,182,-476,-17325,4608]$ |
$[\frac{4952198}{9},\frac{624169}{36},-\frac{42959}{72}]$ |
$y^2 + (x^3 + x^2 + x + 1)y = -x^3 - x^2 - x - 1$ |
| 784.a.1568.1 |
784.a |
\( 2^{4} \cdot 7^{2} \) |
\( 2^{5} \cdot 7^{2} \) |
$0$ |
$1$ |
$\Z/12\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$4$ |
$2$ |
2.90.3, 3.2160.21 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(1.000000\) |
\(20.793351\) |
\(0.288797\) |
$[792,120,15228,6272]$ |
$[396,6514,144256,3673295,1568]$ |
$[\frac{304316815968}{49},\frac{12641055372}{49},14427072]$ |
$y^2 + (x^3 + x)y = -2x^4 + 3x^2 - 2$ |
| 800.a.1600.1 |
800.a |
\( 2^{5} \cdot 5^{2} \) |
\( 2^{6} \cdot 5^{2} \) |
$0$ |
$1$ |
$\Z/12\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$4$ |
$0$ |
2.90.2, 3.2160.21 |
✓ |
✓ |
$1$ |
\( 3 \) |
\(1.000000\) |
\(16.770151\) |
\(0.349378\) |
$[0,84,936,200]$ |
$[0,-56,832,-784,-1600]$ |
$[0,-\frac{134456}{625},\frac{728}{25}]$ |
$y^2 + (x^3 + x^2 + x + 1)y = -x^4 - x^2$ |
| 800.a.8000.1 |
800.a |
\( 2^{5} \cdot 5^{2} \) |
\( 2^{6} \cdot 5^{3} \) |
$0$ |
$1$ |
$\Z/4\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$0$ |
$0$ |
2.90.4, 3.720.5 |
|
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(5.590050\) |
\(0.349378\) |
$[192,11604,322392,-1000]$ |
$[192,-6200,142400,-2774800,-8000]$ |
$[-\frac{4076863488}{125},\frac{27426816}{5},-\frac{3280896}{5}]$ |
$y^2 + (x^3 + x^2 + x + 1)y = -x^6 + 2x^4 + 4x^3 + 2x^2 - 1$ |
| 807.a.2421.1 |
807.a |
\( 3 \cdot 269 \) |
\( 3^{2} \cdot 269 \) |
$0$ |
$1$ |
$\Z/8\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$4$ |
$2$ |
2.30.3 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(1.000000\) |
\(9.761140\) |
\(0.305036\) |
$[680,640,153059,9684]$ |
$[340,4710,84049,1598140,2421]$ |
$[\frac{4543542400000}{2421},\frac{61707280000}{807},\frac{9716064400}{2421}]$ |
$y^2 + (x^3 + x)y = x^5 - 2x^3 - x^2 + 2x - 1$ |
| 830.a.6640.1 |
830.a |
\( 2 \cdot 5 \cdot 83 \) |
\( - 2^{4} \cdot 5 \cdot 83 \) |
$0$ |
$1$ |
$\Z/16\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$5$ |
$1$ |
2.60.1 |
✓ |
✓ |
$1$ |
\( 2^{2} \) |
\(1.000000\) |
\(23.474917\) |
\(0.366796\) |
$[652,4273,1339719,849920]$ |
$[163,929,-521,-236991,6640]$ |
$[\frac{115063617043}{6640},\frac{4023263963}{6640},-\frac{13842449}{6640}]$ |
$y^2 + (x^3 + 1)y = -x^5 + x^4 - 2x^2 + x + 1$ |
| 834.a.1668.1 |
834.a |
\( 2 \cdot 3 \cdot 139 \) |
\( 2^{2} \cdot 3 \cdot 139 \) |
$0$ |
$1$ |
$\Z/8\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$3$ |
$1$ |
2.60.1 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(1.000000\) |
\(11.763516\) |
\(0.367610\) |
$[372,3345,401289,213504]$ |
$[93,221,-111,-14791,1668]$ |
$[\frac{2318961231}{556},\frac{59254299}{556},-\frac{320013}{556}]$ |
$y^2 + (x^3 + 1)y = -x^2 + x - 1$ |
| 847.b.9317.1 |
847.b |
\( 7 \cdot 11^{2} \) |
\( 7 \cdot 11^{3} \) |
$0$ |
$1$ |
$\Z/10\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2$ |
$C_2$ |
$3$ |
$1$ |
2.60.1, 3.80.4 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(1.000000\) |
\(16.827271\) |
\(0.336545\) |
$[304,5932,452465,-37268]$ |
$[152,-26,-401,-15407,-9317]$ |
$[-\frac{81136812032}{9317},\frac{91307008}{9317},\frac{9264704}{9317}]$ |
$y^2 + (x^2 + 1)y = x^5 + 2x^4 - 3x^3 + 2x^2 - x$ |
| 847.c.9317.1 |
847.c |
\( 7 \cdot 11^{2} \) |
\( 7 \cdot 11^{3} \) |
$0$ |
$1$ |
$\Z/8\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$3$ |
$1$ |
2.60.1 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(1.000000\) |
\(9.983400\) |
\(0.311981\) |
$[424,3520,581427,37268]$ |
$[212,1286,-7999,-837396,9317]$ |
$[\frac{428232184832}{9317},\frac{12253172608}{9317},-\frac{359507056}{9317}]$ |
$y^2 + (x^3 + x^2)y = x^4 + x^3 - x - 2$ |
| 856.a.1712.1 |
856.a |
\( 2^{3} \cdot 107 \) |
\( - 2^{4} \cdot 107 \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/6\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,3$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$5$ |
$3$ |
2.120.3, 3.80.1 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(1.000000\) |
\(22.653846\) |
\(0.314637\) |
$[32,-368,-11044,-6848]$ |
$[16,72,964,2560,-1712]$ |
$[-\frac{65536}{107},-\frac{18432}{107},-\frac{15424}{107}]$ |
$y^2 + (x^3 + x)y = -x^4 - x^3 + x$ |
| 862.a.6896.1 |
862.a |
\( 2 \cdot 431 \) |
\( - 2^{4} \cdot 431 \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/8\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$5$ |
$3$ |
2.120.3 |
✓ |
✓ |
$1$ |
\( 2^{2} \) |
\(1.000000\) |
\(23.926605\) |
\(0.373853\) |
$[932,12385,3688145,-882688]$ |
$[233,1746,11456,-94817,-6896]$ |
$[-\frac{686719856393}{6896},-\frac{11042871201}{3448},-\frac{38870924}{431}]$ |
$y^2 + (x^2 + x)y = 4x^5 + 6x^4 - 3x^2 - x$ |
| 864.a.1728.1 |
864.a |
\( 2^{5} \cdot 3^{3} \) |
\( - 2^{6} \cdot 3^{3} \) |
$0$ |
$1$ |
$\Z/12\Z$ |
\(\mathsf{CM} \times \Q\) |
\(\Q \times \Q\) |
✓ |
$N(\mathrm{U}(1)\times\mathrm{SU}(2))$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$4$ |
$0$ |
2.90.4, 3.720.4 |
✓ |
✓ |
$1$ |
\( 3 \) |
\(1.000000\) |
\(18.142966\) |
\(0.377978\) |
$[96,180,5256,216]$ |
$[96,264,576,-3600,1728]$ |
$[4718592,135168,3072]$ |
$y^2 + (x^3 + x^2 + x + 1)y = x^4 + x^2$ |
| 886.a.3544.1 |
886.a |
\( 2 \cdot 443 \) |
\( 2^{3} \cdot 443 \) |
$0$ |
$0$ |
$\Z/15\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,3,5$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$5$ |
$1$ |
2.6.1, 3.80.1 |
✓ |
✓ |
$1$ |
\( 3 \) |
\(1.000000\) |
\(24.085472\) |
\(0.321140\) |
$[232,1180,93881,-14176]$ |
$[116,364,-481,-47073,-3544]$ |
$[-\frac{2625427072}{443},-\frac{71020768}{443},\frac{809042}{443}]$ |
$y^2 + (x^3 + x)y = -x^4 - x + 1$ |
| 909.a.8181.1 |
909.a |
\( 3^{2} \cdot 101 \) |
\( 3^{4} \cdot 101 \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/8\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$5$ |
$3$ |
2.120.3 |
✓ |
✓ |
$1$ |
\( 2^{2} \) |
\(1.000000\) |
\(21.805548\) |
\(0.340712\) |
$[1384,44560,19431635,32724]$ |
$[692,12526,35569,-33071732,8181]$ |
$[\frac{158683025503232}{8181},\frac{4150789321088}{8181},\frac{17032713616}{8181}]$ |
$y^2 + xy = 3x^5 - 7x^4 + x^3 + 6x^2 - 3x$ |
| 932.a.3728.1 |
932.a |
\( 2^{2} \cdot 233 \) |
\( - 2^{4} \cdot 233 \) |
$1$ |
$1$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$10$ |
$0$ |
2.10.1 |
✓ |
✓ |
$1$ |
\( 3 \) |
\(0.002250\) |
\(25.168364\) |
\(0.169871\) |
$[8,229,527,-466]$ |
$[8,-150,-128,-5881,-3728]$ |
$[-\frac{2048}{233},\frac{4800}{233},\frac{512}{233}]$ |
$y^2 + y = x^6 - 2x^5 + x^4 + x^2 - x$ |
| 936.a.1872.1 |
936.a |
\( 2^{3} \cdot 3^{2} \cdot 13 \) |
\( - 2^{4} \cdot 3^{2} \cdot 13 \) |
$0$ |
$3$ |
$\Z/2\Z\oplus\Z/4\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$0$ |
$0$ |
2.90.6, 3.90.1 |
|
|
$2$ |
\( 2 \) |
\(1.000000\) |
\(7.131061\) |
\(0.445691\) |
$[45352,11224,169415364,7488]$ |
$[22676,21423170,26983749312,38232821637503,1872]$ |
$[\frac{374724646811252438336}{117},\frac{15612163699641478120}{117},7411896491650496]$ |
$y^2 + (x^3 + x)y = -x^6 - 9x^4 - 32x^2 - 39$ |
| 968.a.1936.1 |
968.a |
\( 2^{3} \cdot 11^{2} \) |
\( - 2^{4} \cdot 11^{2} \) |
$1$ |
$1$ |
$\Z/5\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$8$ |
$0$ |
2.60.2, 3.90.1 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(0.080529\) |
\(26.986750\) |
\(0.173857\) |
$[120,357,14937,242]$ |
$[120,362,-1344,-73081,1936]$ |
$[\frac{1555200000}{121},\frac{39096000}{121},-\frac{1209600}{121}]$ |
$y^2 + y = x^6 - x^4$ |
| 970.a.1940.1 |
970.a |
\( 2 \cdot 5 \cdot 97 \) |
\( 2^{2} \cdot 5 \cdot 97 \) |
$0$ |
$1$ |
$\Z/10\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,5$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$4$ |
$2$ |
2.30.3 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(1.000000\) |
\(17.375772\) |
\(0.347515\) |
$[24,684,4887,7760]$ |
$[12,-108,-159,-3393,1940]$ |
$[\frac{62208}{485},-\frac{46656}{485},-\frac{5724}{485}]$ |
$y^2 + (x + 1)y = x^5 + x^4 + x^3 + x^2$ |
| 980.a.7840.1 |
980.a |
\( 2^{2} \cdot 5 \cdot 7^{2} \) |
\( 2^{5} \cdot 5 \cdot 7^{2} \) |
$0$ |
$1$ |
$\Z/12\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$4$ |
$0$ |
2.45.1, 3.720.4 |
✓ |
✓ |
$1$ |
\( 2^{2} \) |
\(1.000000\) |
\(14.031519\) |
\(0.389764\) |
$[276,3945,280149,1003520]$ |
$[69,34,20,56,7840]$ |
$[\frac{1564031349}{7840},\frac{5584653}{3920},\frac{4761}{392}]$ |
$y^2 + (x^2 + x + 1)y = -x^6 + 3x^5 - 3x^4 - x$ |
| 990.a.8910.1 |
990.a |
\( 2 \cdot 3^{2} \cdot 5 \cdot 11 \) |
\( 2 \cdot 3^{4} \cdot 5 \cdot 11 \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/4\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$2$ |
$2$ |
2.180.3, 3.90.1 |
✓ |
✓ |
$1$ |
\( 2^{2} \) |
\(1.000000\) |
\(6.174937\) |
\(0.385934\) |
$[3268,252577,318023313,1140480]$ |
$[817,17288,-766260,-231227341,8910]$ |
$[\frac{364007458703857}{8910},\frac{4713906106372}{4455},-57404054]$ |
$y^2 + (x^2 + x)y = 3x^5 + 4x^4 + 7x^3 + 4x^2 + 3x$ |
| 1012.a.4048.1 |
1012.a |
\( 2^{2} \cdot 11 \cdot 23 \) |
\( 2^{4} \cdot 11 \cdot 23 \) |
$0$ |
$0$ |
$\Z/15\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,3,5$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$5$ |
$1$ |
2.6.1, 3.80.1 |
✓ |
✓ |
$1$ |
\( 5 \) |
\(1.000000\) |
\(18.518969\) |
\(0.411533\) |
$[140,2425,78163,-518144]$ |
$[35,-50,-4,-660,-4048]$ |
$[-\frac{52521875}{4048},\frac{1071875}{2024},\frac{1225}{1012}]$ |
$y^2 + (x^3 + 1)y = x^4 + x^3 + x^2 + x$ |
| 1038.a.1038.2 |
1038.a |
\( 2 \cdot 3 \cdot 173 \) |
\( - 2 \cdot 3 \cdot 173 \) |
$0$ |
$1$ |
$\Z/6\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,3$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$2$ |
$0$ |
2.15.1, 3.80.1 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(15.397347\) |
\(0.427704\) |
$[844,4129,1133983,132864]$ |
$[211,1683,16079,140045,1038]$ |
$[\frac{418227202051}{1038},\frac{5269995291}{346},\frac{715853159}{1038}]$ |
$y^2 + (x^3 + 1)y = x^4 + 2x^2 + x + 1$ |
| 1038.a.1038.1 |
1038.a |
\( 2 \cdot 3 \cdot 173 \) |
\( 2 \cdot 3 \cdot 173 \) |
$0$ |
$1$ |
$\Z/6\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,3$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$1$ |
$1$ |
2.60.1, 3.80.1 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(15.397347\) |
\(0.427704\) |
$[109988,334849,12332566337,132864]$ |
$[27497,31489590,48060441688,82480921681709,1038]$ |
$[\frac{15719059879327073637257}{1038},\frac{109111794064913809345}{173},\frac{18168889743107727596}{519}]$ |
$y^2 + (x^2 + x)y = x^5 - 12x^4 + 26x^3 + 46x^2 + 21x + 3$ |
| 1042.a.1042.1 |
1042.a |
\( 2 \cdot 521 \) |
\( 2 \cdot 521 \) |
$0$ |
$0$ |
$\Z/9\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,3$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$3$ |
$1$ |
2.6.1, 3.80.1 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(30.423017\) |
\(0.375593\) |
$[480,3912,728889,-4168]$ |
$[240,1748,-5521,-1095136,-1042]$ |
$[-\frac{398131200000}{521},-\frac{12082176000}{521},\frac{159004800}{521}]$ |
$y^2 + (x^3 + x)y = -x^4 - x^3 - x^2 + 2x + 2$ |
| 1047.a.3141.1 |
1047.a |
\( 3 \cdot 349 \) |
\( 3^{2} \cdot 349 \) |
$0$ |
$1$ |
$\Z/10\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,5$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$4$ |
$2$ |
2.30.3 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(1.000000\) |
\(17.821680\) |
\(0.356434\) |
$[8,604,1017,-12564]$ |
$[4,-100,-1,-2501,-3141]$ |
$[-\frac{1024}{3141},\frac{6400}{3141},\frac{16}{3141}]$ |
$y^2 + (x^3 + x)y = x$ |
| 1051.a.1051.1 |
1051.a |
\( 1051 \) |
\( -1051 \) |
$1$ |
$1$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$7$ |
$1$ |
2.6.1 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.007925\) |
\(23.437821\) |
\(0.185743\) |
$[96,-144,144,4204]$ |
$[48,120,-80,-4560,1051]$ |
$[\frac{254803968}{1051},\frac{13271040}{1051},-\frac{184320}{1051}]$ |
$y^2 + y = x^5 - x^4 + x^2 - x$ |
| 1051.b.1051.1 |
1051.b |
\( 1051 \) |
\( -1051 \) |
$0$ |
$1$ |
$\Z/8\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$4$ |
$2$ |
2.30.3 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(23.331720\) |
\(0.364558\) |
$[64,-200,185,4204]$ |
$[32,76,-241,-3372,1051]$ |
$[\frac{33554432}{1051},\frac{2490368}{1051},-\frac{246784}{1051}]$ |
$y^2 + (x + 1)y = -x^5 - x^4$ |
| 1051.b.1051.2 |
1051.b |
\( 1051 \) |
\( -1051 \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$3$ |
$3$ |
2.120.3 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(5.832930\) |
\(0.364558\) |
$[6176,-50240,-103225225,-4204]$ |
$[3088,405696,72449921,14784027908,-1051]$ |
$[-\frac{280793117300359168}{1051},-\frac{11946277554880512}{1051},-\frac{690863899476224}{1051}]$ |
$y^2 + xy = x^5 + 8x^4 + 16x^3 + x$ |
| 1055.a.1055.1 |
1055.a |
\( 5 \cdot 211 \) |
\( - 5 \cdot 211 \) |
$0$ |
$1$ |
$\Z/6\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,3$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$3$ |
$1$ |
2.60.1, 3.80.1 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(15.577626\) |
\(0.432712\) |
$[500,-3023,-525127,-135040]$ |
$[125,777,7441,81599,-1055]$ |
$[-\frac{6103515625}{211},-\frac{303515625}{211},-\frac{23253125}{211}]$ |
$y^2 + (x^3 + 1)y = -x^4 + x^2 - x - 1$ |
| 1062.a.6372.1 |
1062.a |
\( 2 \cdot 3^{2} \cdot 59 \) |
\( 2^{2} \cdot 3^{3} \cdot 59 \) |
$1$ |
$2$ |
$\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$11$ |
$1$ |
2.60.1 |
✓ |
✓ |
$1$ |
\( 2^{2} \) |
\(0.008698\) |
\(21.575863\) |
\(0.187677\) |
$[300,2601,306603,-815616]$ |
$[75,126,-1024,-23169,-6372]$ |
$[-\frac{87890625}{236},-\frac{984375}{118},\frac{160000}{177}]$ |
$y^2 + (x^3 + 1)y = x^5 - x^4 + x^2 - x$ |
| 1069.a.1069.1 |
1069.a |
\( 1069 \) |
\( 1069 \) |
$0$ |
$0$ |
$\Z/7\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,7$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$3$ |
$1$ |
2.6.1 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(14.937046\) |
\(0.304838\) |
$[244,3193,263789,136832]$ |
$[61,22,-884,-13602,1069]$ |
$[\frac{844596301}{1069},\frac{4993582}{1069},-\frac{3289364}{1069}]$ |
$y^2 + (x^2 + x + 1)y = x^5 + x^3$ |
