| 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 |
| 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 |
✓ |
✓ |
$1$ |
\( 2^{2} \) |
\(1.000000\) |
\(9.467159\) |
\(0.262977\) |
$[92,4981,43947,-12000]$ |
$[92,-2968,47600,-1107456,-96000]$ |
$[-\frac{25745372}{375},\frac{9027914}{375},-\frac{62951}{15}]$ |
$y^2 + (x + 1)y = 4x^5 + 5x^4 + 3x^3 + 2x^2$ |
| 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 |
✓ |
✓ |
$1$ |
\( 2^{2} \) |
\(1.000000\) |
\(11.976027\) |
\(0.332667\) |
$[134,-464,-15328,-176]$ |
$[268,4230,61444,-356477,-45056]$ |
$[-\frac{1350125107}{44},-\frac{636113745}{352},-\frac{68955529}{704}]$ |
$y^2 + y = 4x^5 + 4x^4 - x^3 - 2x^2$ |
| 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.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 |
✓ |
✓ |
$1$ |
\( 2^{2} \) |
\(1.000000\) |
\(11.270100\) |
\(0.313058\) |
$[116,445,16259,1568]$ |
$[116,264,-1280,-54544,12544]$ |
$[\frac{82044596}{49},\frac{1609674}{49},-\frac{67280}{49}]$ |
$y^2 + (x^3 + x)y = -1$ |
| 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 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(1.000000\) |
\(22.166697\) |
\(0.307871\) |
$[688,9592,2944404,55488]$ |
$[344,3332,-80164,-9669660,13872]$ |
$[\frac{301073291264}{867},\frac{498667904}{51},-\frac{592892944}{867}]$ |
$y^2 + (x^3 + x^2)y = -2x^4 + 6x^2 - 8x + 3$ |
| 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 |
✓ |
✓ |
$1$ |
\( 2^{2} \) |
\(1.000000\) |
\(13.174483\) |
\(0.365958\) |
$[92,-554591,-3126961,1480192]$ |
$[23,23130,-104176,-134348237,11564]$ |
$[\frac{6436343}{11564},\frac{140711355}{5782},-\frac{13777276}{2891}]$ |
$y^2 + (x^2 + x)y = x^5 + x^4 + 3x^3 - 4x^2 - 4x + 3$ |
| 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 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(1.000000\) |
\(22.653846\) |
\(0.314637\) |
$[32,-368,-11044,-6848]$ |
$[16,72,964,2560,-1712]$ |
$[-\frac{65536}{107},-\frac{18432}{107},-\frac{15424}{107}]$ |
$y^2 + (x^3 + x)y = -x^4 - x^3 + x$ |
| 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 |
✓ |
✓ |
$1$ |
\( 2^{2} \) |
\(1.000000\) |
\(14.356290\) |
\(0.398786\) |
$[148,-48575,-4076175,-8112000]$ |
$[37,2081,35929,-750297,-63375]$ |
$[-\frac{69343957}{63375},-\frac{105408893}{63375},-\frac{49186801}{63375}]$ |
$y^2 + (x^3 + 1)y = -x^5 + x^3 + 2x^2 + x - 1$ |
| 1122.b.2244.1 |
1122.b |
\( 2 \cdot 3 \cdot 11 \cdot 17 \) |
\( 2^{2} \cdot 3 \cdot 11 \cdot 17 \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/6\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,3$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$4$ |
$2$ |
2.180.3, 3.80.1 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(1.000000\) |
\(30.724131\) |
\(0.426724\) |
$[1828,153793,73850145,287232]$ |
$[457,2294,8704,-321177,2244]$ |
$[\frac{19933382494057}{2244},\frac{109474259971}{1122},\frac{26732672}{33}]$ |
$y^2 + (x^2 + x)y = x^5 + 7x^4 + 5x^3 - x^2 - x$ |
| 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 |
✓ |
✓ |
$1$ |
\( 2^{2} \) |
\(1.000000\) |
\(13.019302\) |
\(0.361647\) |
$[160,4720,130020,-65856]$ |
$[80,-520,4220,16800,-16464]$ |
$[-\frac{204800000}{1029},\frac{16640000}{1029},-\frac{1688000}{1029}]$ |
$y^2 + (x + 1)y = -2x^5 + x^2$ |
| 1272.a.122112.1 |
1272.a |
\( 2^{3} \cdot 3 \cdot 53 \) |
\( - 2^{8} \cdot 3^{2} \cdot 53 \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/6\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,3$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$5$ |
$3$ |
2.120.3, 3.80.1 |
✓ |
✓ |
$1$ |
\( 2^{2} \) |
\(1.000000\) |
\(14.397916\) |
\(0.399942\) |
$[124,-5027,-35457,15264]$ |
$[124,3992,-79504,-6448640,122112]$ |
$[\frac{114516604}{477},\frac{29731418}{477},-\frac{4775209}{477}]$ |
$y^2 + (x^2 + 1)y = 3x^5 + 4x^4 + 2x^3 - x^2 - x$ |
| 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 |
✓ |
✓ |
$1$ |
\( 3 \) |
\(1.000000\) |
\(23.235042\) |
\(0.484063\) |
$[78,216,4806,81]$ |
$[156,438,-428,-64653,20736]$ |
$[4455516,\frac{160381}{2},-\frac{18083}{36}]$ |
$y^2 = x^5 - x^4 - 3x^3 + 4x^2 - x$ |
| 1312.b.83968.1 |
1312.b |
\( 2^{5} \cdot 41 \) |
\( 2^{11} \cdot 41 \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/6\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,3$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$4$ |
$2$ |
2.180.3, 3.80.1 |
✓ |
✓ |
$1$ |
\( 2^{2} \) |
\(1.000000\) |
\(14.584701\) |
\(0.405131\) |
$[1556,36553,20209667,10496]$ |
$[1556,76512,1289104,-962060080,83968]$ |
$[\frac{8907339520949}{82},\frac{140743510779}{41},\frac{12191781649}{328}]$ |
$y^2 + xy = 8x^5 - 21x^4 + 15x^3 - x^2 - x$ |
| 1338.b.72252.1 |
1338.b |
\( 2 \cdot 3 \cdot 223 \) |
\( 2^{2} \cdot 3^{4} \cdot 223 \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/6\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,3$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$5$ |
$3$ |
2.120.3, 3.80.1 |
✓ |
✓ |
$1$ |
\( 2^{2} \) |
\(1.000000\) |
\(17.653207\) |
\(0.490367\) |
$[9956,4983313,12890442777,9248256]$ |
$[2489,50492,218356,-501488495,72252]$ |
$[\frac{95526635745351449}{72252},\frac{194642319821287}{18063},\frac{338185460269}{18063}]$ |
$y^2 + (x^2 + x)y = x^5 + 7x^4 + 4x^3 - 12x^2 - 6x + 5$ |
| 1350.c.656100.1 |
1350.c |
\( 2 \cdot 3^{3} \cdot 5^{2} \) |
\( 2^{2} \cdot 3^{8} \cdot 5^{2} \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/6\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$4$ |
$2$ |
2.360.1, 3.720.4 |
✓ |
✓ |
$1$ |
\( 2^{2} \cdot 3 \) |
\(1.000000\) |
\(6.178250\) |
\(0.514854\) |
$[364,3529,393211,345600]$ |
$[273,1782,0,-793881,656100]$ |
$[\frac{6240321451}{2700},\frac{8289281}{150},0]$ |
$y^2 + (x^2 + x)y = x^5 + x^4 + 4x^3 + x^2 + x$ |
| 1416.a.8496.1 |
1416.a |
\( 2^{3} \cdot 3 \cdot 59 \) |
\( - 2^{4} \cdot 3^{2} \cdot 59 \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/6\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,3$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$5$ |
$3$ |
2.120.3, 3.80.1 |
✓ |
✓ |
$1$ |
\( 2^{2} \) |
\(1.000000\) |
\(14.958620\) |
\(0.415517\) |
$[256,-2144,-178692,-33984]$ |
$[128,1040,12004,113728,-8496]$ |
$[-\frac{2147483648}{531},-\frac{136314880}{531},-\frac{12292096}{531}]$ |
$y^2 + (x^3 + x)y = x^5 - x^3 - 1$ |
| 1440.a.116640.1 |
1440.a |
\( 2^{5} \cdot 3^{2} \cdot 5 \) |
\( - 2^{5} \cdot 3^{6} \cdot 5 \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/6\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$2$ |
$0$ |
2.90.6, 3.720.4 |
✓ |
✓ |
$1$ |
\( 2^{2} \cdot 3 \) |
\(1.000000\) |
\(5.650548\) |
\(0.470879\) |
$[35416,45688,537039964,466560]$ |
$[17708,13057938,12831384960,14177105014959,116640]$ |
$[\frac{54412363190235229024}{3645},\frac{251762275020280012}{405},\frac{310461362928064}{9}]$ |
$y^2 + (x^3 + x)y = 5x^4 + 39x^2 + 90$ |
| 1488.a.71424.1 |
1488.a |
\( 2^{4} \cdot 3 \cdot 31 \) |
\( - 2^{8} \cdot 3^{2} \cdot 31 \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/6\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,3$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$3$ |
$3$ |
2.120.3, 3.80.1 |
✓ |
✓ |
$1$ |
\( 2 \cdot 3 \) |
\(1.000000\) |
\(11.909626\) |
\(0.496234\) |
$[34,-104,-438,279]$ |
$[68,470,-1396,-78957,71424]$ |
$[\frac{5679428}{279},\frac{1154555}{558},-\frac{100861}{1116}]$ |
$y^2 = x^5 - x^3 - x^2 - x$ |
| 1536.a.12288.1 |
1536.a |
\( 2^{9} \cdot 3 \) |
\( 2^{12} \cdot 3 \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/6\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,3$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$4$ |
$2$ |
2.180.3, 3.80.1 |
✓ |
✓ |
$1$ |
\( 2 \cdot 3 \) |
\(1.000000\) |
\(12.002671\) |
\(0.500111\) |
$[38,112,1704,48]$ |
$[76,-58,-4796,-91965,12288]$ |
$[\frac{2476099}{12},-\frac{198911}{96},-\frac{432839}{192}]$ |
$y^2 = x^5 - 3x^4 + 5x^3 - 4x^2 + 2x$ |
| 1600.b.409600.1 |
1600.b |
\( 2^{6} \cdot 5^{2} \) |
\( 2^{14} \cdot 5^{2} \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/6\Z$ |
\(\mathrm{M}_2(\Q)\) |
\(\Q \times \Q\) |
✓ |
$J(E_1)$ |
|
|
|
$C_2^2$ |
$D_4$ |
$4$ |
$2$ |
2.360.1, 3.8640.8 |
✓ |
✓ |
$1$ |
\( 2 \cdot 3 \) |
\(1.000000\) |
\(12.846191\) |
\(0.535258\) |
$[248,181,14873,50]$ |
$[992,39072,1945600,100853504,409600]$ |
$[\frac{58632501248}{25},\frac{2327987904}{25},4674304]$ |
$y^2 = x^6 - 4x^4 + 4x^2 - 1$ |
| 1650.a.371250.1 |
1650.a |
\( 2 \cdot 3 \cdot 5^{2} \cdot 11 \) |
\( 2 \cdot 3^{3} \cdot 5^{4} \cdot 11 \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/6\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$2$ |
$2$ |
2.180.3, 3.720.4 |
✓ |
✓ |
$1$ |
\( 2 \cdot 3 \) |
\(1.000000\) |
\(13.792193\) |
\(0.574675\) |
$[30180,172689,1721884569,47520000]$ |
$[7545,2364764,985411548,460705338491,371250]$ |
$[\frac{1448946796623435}{22},\frac{150474103581314}{55},\frac{3777545308302}{25}]$ |
$y^2 + (x^2 + x)y = x^5 - 11x^4 + 30x^3 - 11x^2 + x$ |
| 1680.c.241920.1 |
1680.c |
\( 2^{4} \cdot 3 \cdot 5 \cdot 7 \) |
\( 2^{8} \cdot 3^{3} \cdot 5 \cdot 7 \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/6\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$2$ |
$2$ |
2.180.3, 3.720.4 |
✓ |
✓ |
$1$ |
\( 2 \cdot 3 \) |
\(1.000000\) |
\(11.725763\) |
\(0.488573\) |
$[182340,50613,3073006935,30240]$ |
$[182340,1385294408,14032351630080,159904599848179184,241920]$ |
$[\frac{5832248478791381977500}{7},\frac{243004434356588125950}{7},1928513067842084400]$ |
$y^2 + (x^2 + 1)y = 135x^6 - 96x^4 + 22x^2 - 2$ |
| 1740.a.104400.1 |
1740.a |
\( 2^{2} \cdot 3 \cdot 5 \cdot 29 \) |
\( - 2^{4} \cdot 3^{2} \cdot 5^{2} \cdot 29 \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/6\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,3$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$5$ |
$3$ |
2.120.3, 3.80.1 |
✓ |
✓ |
$1$ |
\( 2^{4} \) |
\(1.000000\) |
\(5.116047\) |
\(0.568450\) |
$[28100,7231657,99549877317,-13363200]$ |
$[7025,1754957,7872289,-756142810406,-104400]$ |
$[-\frac{684371056797265625}{4176},-\frac{24336911168273125}{4176},-\frac{15540095293225}{4176}]$ |
$y^2 + (x^2 + x)y = 2x^5 - 14x^3 - 5x^2 + 30x$ |
| 1770.a.26550.1 |
1770.a |
\( 2 \cdot 3 \cdot 5 \cdot 59 \) |
\( - 2 \cdot 3^{2} \cdot 5^{2} \cdot 59 \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/6\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,3$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$3$ |
$3$ |
2.120.3, 3.80.1 |
✓ |
✓ |
$1$ |
\( 2^{2} \) |
\(1.000000\) |
\(18.809597\) |
\(0.522489\) |
$[8740,87985,236184393,-3398400]$ |
$[2185,195260,23092156,3082473315,-26550]$ |
$[-\frac{1992127808244625}{1062},-\frac{40737803081950}{531},-\frac{2204942969582}{531}]$ |
$y^2 + (x^2 + x)y = 3x^5 - 7x^3 + 7x + 3$ |
| 1944.a.34992.1 |
1944.a |
\( 2^{3} \cdot 3^{5} \) |
\( - 2^{4} \cdot 3^{7} \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/6\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,3$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$5$ |
$3$ |
2.120.3, 3.1920.4 |
✓ |
✓ |
$1$ |
\( 2 \cdot 3 \) |
\(1.000000\) |
\(11.436286\) |
\(0.476512\) |
$[224,-432,-16812,-576]$ |
$[336,5352,77764,-628800,-34992]$ |
$[-\frac{1101463552}{9},-\frac{156649472}{27},-\frac{60966976}{243}]$ |
$y^2 + xy = 2x^5 + 2x^4 - 3x^2 + x$ |
| 2145.a.70785.1 |
2145.a |
\( 3 \cdot 5 \cdot 11 \cdot 13 \) |
\( 3^{2} \cdot 5 \cdot 11^{2} \cdot 13 \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/6\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,3$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$4$ |
$2$ |
2.180.3, 3.80.1 |
✓ |
✓ |
$1$ |
\( 2^{2} \) |
\(1.000000\) |
\(20.223270\) |
\(0.561757\) |
$[2356,108625,76880361,9060480]$ |
$[589,9929,145729,-3187665,70785]$ |
$[\frac{70888612161949}{70785},\frac{2028856800701}{70785},\frac{50556450409}{70785}]$ |
$y^2 + (x^3 + 1)y = x^5 - x^4 - 5x^3 + 3x^2 + 2x - 1$ |
| 2208.b.847872.1 |
2208.b |
\( 2^{5} \cdot 3 \cdot 23 \) |
\( - 2^{12} \cdot 3^{2} \cdot 23 \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/6\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,3$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$5$ |
$3$ |
2.120.3, 3.80.1 |
✓ |
✓ |
$1$ |
\( 2^{2} \cdot 3 \) |
\(1.000000\) |
\(7.533472\) |
\(0.627789\) |
$[598,-5348,-286836,-3312]$ |
$[1196,73862,1261924,-986583485,-847872]$ |
$[-\frac{103903004413}{36},-\frac{42921688303}{288},-\frac{1226274647}{576}]$ |
$y^2 = 3x^5 - 4x^4 - 3x^3 + x^2 + 4x$ |
| 2618.b.921536.1 |
2618.b |
\( 2 \cdot 7 \cdot 11 \cdot 17 \) |
\( - 2^{6} \cdot 7 \cdot 11^{2} \cdot 17 \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/6\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,3$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$4$ |
$2$ |
2.180.3, 3.80.1 |
✓ |
✓ |
$1$ |
\( 2^{2} \cdot 3 \) |
\(1.000000\) |
\(7.808782\) |
\(0.650732\) |
$[1988,-46607,-32301175,-117956608]$ |
$[497,12234,464704,20321783,-921536]$ |
$[-\frac{4331954671751}{131648},-\frac{107277737763}{65824},-\frac{256218907}{2057}]$ |
$y^2 + (x^2 + x)y = -x^6 + x^3 + x^2 - 3x + 1$ |
| 2788.a.11152.1 |
2788.a |
\( 2^{2} \cdot 17 \cdot 41 \) |
\( 2^{4} \cdot 17 \cdot 41 \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/6\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,3$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$4$ |
$2$ |
2.180.3, 3.80.1 |
✓ |
✓ |
$1$ |
\( 2^{2} \) |
\(1.000000\) |
\(25.523537\) |
\(0.708987\) |
$[3716,738553,703947677,1427456]$ |
$[929,5187,20041,-2071720,11152]$ |
$[\frac{691956144175649}{11152},\frac{4158755516643}{11152},\frac{17296204681}{11152}]$ |
$y^2 + (x^2 + x)y = x^5 + 8x^4 + 16x^3 + 8x^2 - 2x$ |
| 2880.b.43200.1 |
2880.b |
\( 2^{6} \cdot 3^{2} \cdot 5 \) |
\( 2^{6} \cdot 3^{3} \cdot 5^{2} \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/6\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$2$ |
$0$ |
2.180.7, 3.720.4 |
✓ |
✓ |
$1$ |
\( 2 \cdot 3 \) |
\(1.000000\) |
\(15.706158\) |
\(0.654423\) |
$[19036,1343263,8004572494,5400]$ |
$[19036,14203212,13587811200,14231585721564,43200]$ |
$[\frac{39056966269184124784}{675},\frac{510284561561447516}{225},\frac{341930942967008}{3}]$ |
$y^2 + (x^3 + x)y = -7x^4 + 48x^2 - 75$ |
| 2886.a.225108.1 |
2886.a |
\( 2 \cdot 3 \cdot 13 \cdot 37 \) |
\( 2^{2} \cdot 3^{2} \cdot 13^{2} \cdot 37 \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/6\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,3$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$3$ |
$3$ |
2.120.3, 3.80.1 |
✓ |
✓ |
$1$ |
\( 2^{3} \) |
\(1.000000\) |
\(15.248361\) |
\(0.847131\) |
$[15592,65512,335745691,900432]$ |
$[7796,2521482,1083150769,521592979700,225108]$ |
$[\frac{7199447364348095744}{56277},\frac{99561198863910496}{18759},\frac{16457830377096676}{56277}]$ |
$y^2 + xy = 3x^5 - 7x^4 - 9x^3 + 12x^2 + 17x + 5$ |
| 2940.a.164640.1 |
2940.a |
\( 2^{2} \cdot 3 \cdot 5 \cdot 7^{2} \) |
\( 2^{5} \cdot 3 \cdot 5 \cdot 7^{3} \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/6\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2$ |
$C_2$ |
$4$ |
$2$ |
2.180.3, 3.640.2 |
✓ |
✓ |
$1$ |
\( 2^{2} \) |
\(1.000000\) |
\(13.988232\) |
\(0.388562\) |
$[16804,12258145,55198853169,21073920]$ |
$[4201,224594,995716,-11564865480,164640]$ |
$[\frac{1308468909056421001}{164640},\frac{8325804308294497}{82320},\frac{4393198812529}{41160}]$ |
$y^2 + (x^2 + x)y = 14x^5 + 37x^4 + 21x^3 - x^2 - 2x$ |
| 2944.a.23552.1 |
2944.a |
\( 2^{7} \cdot 23 \) |
\( - 2^{10} \cdot 23 \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/6\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,3$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$5$ |
$3$ |
2.120.3, 3.80.1 |
✓ |
✓ |
$1$ |
\( 2 \cdot 3 \) |
\(1.000000\) |
\(15.314939\) |
\(0.638122\) |
$[38,-308,-4456,-92]$ |
$[76,1062,15364,9955,-23552]$ |
$[-\frac{2476099}{23},-\frac{3642129}{184},-\frac{60287}{16}]$ |
$y^2 = x^5 + x^4 - x^3 - 2x^2 + 1$ |
| 3136.b.153664.1 |
3136.b |
\( 2^{6} \cdot 7^{2} \) |
\( 2^{6} \cdot 7^{4} \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/6\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$4$ |
$2$ |
2.360.1, 3.720.4 |
✓ |
✓ |
$1$ |
\( 2^{2} \) |
\(1.000000\) |
\(20.417952\) |
\(0.567165\) |
$[620,11155,1926860,19208]$ |
$[620,8580,119680,146300,153664]$ |
$[\frac{1431457550000}{2401},\frac{31950847500}{2401},\frac{718828000}{2401}]$ |
$y^2 + (x^3 + x)y = -3x^4 + 6x^2 - 1$ |
| 3160.a.505600.1 |
3160.a |
\( 2^{3} \cdot 5 \cdot 79 \) |
\( 2^{8} \cdot 5^{2} \cdot 79 \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/6\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,3$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$5$ |
$3$ |
2.120.3, 3.80.1 |
✓ |
✓ |
$1$ |
\( 2^{2} \) |
\(1.000000\) |
\(17.415488\) |
\(0.483764\) |
$[1060,37717,11059237,63200]$ |
$[1060,21672,330256,-29901056,505600]$ |
$[\frac{209097746500}{79},\frac{4033077930}{79},\frac{57980569}{79}]$ |
$y^2 + (x + 1)y = 4x^5 + x^4 - 7x^3 + x$ |
| 3200.f.819200.1 |
3200.f |
\( 2^{7} \cdot 5^{2} \) |
\( 2^{15} \cdot 5^{2} \) |
$1$ |
$3$ |
$\Z/2\Z\oplus\Z/6\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$6$ |
$0$ |
2.180.7, 3.720.4 |
✓ |
✓ |
$1$ |
\( 2 \cdot 3 \) |
\(0.717386\) |
\(15.397662\) |
\(0.460253\) |
$[520,1141,186367,100]$ |
$[2080,168096,17260544,1911416576,819200]$ |
$[47525504000,1846534560,91157248]$ |
$y^2 = x^6 - 5x^4 + 7x^2 - 2$ |
| 3240.a.58320.1 |
3240.a |
\( 2^{3} \cdot 3^{4} \cdot 5 \) |
\( 2^{4} \cdot 3^{6} \cdot 5 \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/6\Z$ |
\(\mathsf{CM} \times \Q\) |
\(\Q \times \Q\) |
✓ |
$N(\mathrm{U}(1)\times\mathrm{SU}(2))$ |
|
|
|
$C_2$ |
$C_2$ |
$4$ |
$2$ |
2.180.3, 3.640.2 |
✓ |
✓ |
$1$ |
\( 2^{3} \) |
\(1.000000\) |
\(10.347832\) |
\(0.574880\) |
$[64,1440,11244,-960]$ |
$[96,-1776,25916,-166560,-58320]$ |
$[-\frac{2097152}{15},\frac{1212416}{45},-\frac{1658624}{405}]$ |
$y^2 + (x^3 + x)y = x^4 - x^3 + 2x^2 - 3x$ |
| 3336.a.20016.1 |
3336.a |
\( 2^{3} \cdot 3 \cdot 139 \) |
\( - 2^{4} \cdot 3^{2} \cdot 139 \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/6\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,3$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$5$ |
$3$ |
2.120.3, 3.80.1 |
✓ |
✓ |
$1$ |
\( 2^{2} \) |
\(1.000000\) |
\(18.112920\) |
\(0.503137\) |
$[64,-3104,71652,80064]$ |
$[32,560,-12484,-178272,20016]$ |
$[\frac{2097152}{1251},\frac{1146880}{1251},-\frac{798976}{1251}]$ |
$y^2 + (x + 1)y = -2x^5 + 2x^4 - x^2$ |
| 3360.b.241920.1 |
3360.b |
\( 2^{5} \cdot 3 \cdot 5 \cdot 7 \) |
\( - 2^{8} \cdot 3^{3} \cdot 5 \cdot 7 \) |
$0$ |
$3$ |
$\Z/2\Z\oplus\Z/6\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$0$ |
$0$ |
2.90.6, 3.720.4 |
|
|
$2$ |
\( 2^{2} \cdot 3 \) |
\(1.000000\) |
\(3.848391\) |
\(0.641398\) |
$[182340,50613,3073006935,30240]$ |
$[182340,1385294408,14032351630080,159904599848179184,241920]$ |
$[\frac{5832248478791381977500}{7},\frac{243004434356588125950}{7},1928513067842084400]$ |
$y^2 + (x^2 + 1)y = -135x^6 - 96x^4 - 23x^2 - 2$ |
| 3400.b.34000.1 |
3400.b |
\( 2^{3} \cdot 5^{2} \cdot 17 \) |
\( 2^{4} \cdot 5^{3} \cdot 17 \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/6\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,3$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$4$ |
$2$ |
2.180.3, 3.80.1 |
✓ |
✓ |
$1$ |
\( 2^{2} \) |
\(1.000000\) |
\(20.935606\) |
\(0.581545\) |
$[1024,16000,5129500,136000]$ |
$[512,8256,120004,-1679872,34000]$ |
$[\frac{2199023255552}{2125},\frac{69256347648}{2125},\frac{1966145536}{2125}]$ |
$y^2 + (x^3 + x)y = -3x^4 - x^3 + 6x^2 + 5x$ |
| 3402.a.95256.1 |
3402.a |
\( 2 \cdot 3^{5} \cdot 7 \) |
\( 2^{3} \cdot 3^{5} \cdot 7^{2} \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/6\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,3$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$3$ |
$3$ |
2.120.3, 3.80.1 |
✓ |
✓ |
$1$ |
\( 2 \cdot 3 \) |
\(1.000000\) |
\(17.469709\) |
\(0.727905\) |
$[4876,45081,70647363,50176]$ |
$[3657,540330,103891936,21994075263,95256]$ |
$[\frac{2691649634002099}{392},\frac{23303486795035}{84},\frac{19297420638812}{1323}]$ |
$y^2 + (x^2 + x)y = x^5 - 8x^4 + 13x^3 + 6x^2 - x$ |
| 3454.b.110528.1 |
3454.b |
\( 2 \cdot 11 \cdot 157 \) |
\( - 2^{6} \cdot 11 \cdot 157 \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/6\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,3$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$5$ |
$3$ |
2.120.3, 3.80.1 |
✓ |
✓ |
$1$ |
\( 2 \cdot 3 \) |
\(1.000000\) |
\(15.520036\) |
\(0.646668\) |
$[196,-1487,-336023,-14147584]$ |
$[49,162,4096,43615,-110528]$ |
$[-\frac{282475249}{110528},-\frac{9529569}{55264},-\frac{153664}{1727}]$ |
$y^2 + (x^2 + x)y = x^5 - 2x^4 + 2x^2 - x$ |
| 3468.b.353736.1 |
3468.b |
\( 2^{2} \cdot 3 \cdot 17^{2} \) |
\( 2^{3} \cdot 3^{2} \cdot 17^{3} \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/6\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2$ |
$C_2$ |
$4$ |
$2$ |
2.180.3, 3.640.2 |
✓ |
✓ |
$1$ |
\( 2^{3} \) |
\(1.000000\) |
\(12.525210\) |
\(0.695845\) |
$[23620,25616905,160250062485,45278208]$ |
$[5905,385505,1713745,-34623610200,353736]$ |
$[\frac{7179587780780940625}{353736},\frac{79376093464900625}{353736},\frac{59756617248625}{353736}]$ |
$y^2 + (x^2 + x)y = x^5 + 11x^4 + 27x^3 + x^2 - 34x$ |
| 3600.b.43200.1 |
3600.b |
\( 2^{4} \cdot 3^{2} \cdot 5^{2} \) |
\( - 2^{6} \cdot 3^{3} \cdot 5^{2} \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/6\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$2$ |
$0$ |
2.180.7, 3.720.4 |
✓ |
✓ |
$1$ |
\( 2^{2} \cdot 3 \) |
\(1.000000\) |
\(8.345749\) |
\(0.695479\) |
$[4360,4024,5725876,172800]$ |
$[2180,197346,23751936,3208444191,43200]$ |
$[\frac{30772479098000}{27},\frac{425947988390}{9},\frac{7838798656}{3}]$ |
$y^2 + (x^3 + x)y = 2x^4 + 9x^2 + 12$ |
| 3969.d.250047.1 |
3969.d |
\( 3^{4} \cdot 7^{2} \) |
\( - 3^{6} \cdot 7^{3} \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/6\Z$ |
\(\mathrm{M}_2(\Q)\) |
\(\mathsf{RM}\) |
✓ |
$J(E_1)$ |
|
✓ |
|
$C_2$ |
$C_2$ |
$4$ |
$2$ |
2.180.3, 3.1920.1 |
✓ |
✓ |
$1$ |
\( 2^{3} \) |
\(1.000000\) |
\(13.559050\) |
\(0.753281\) |
$[452,-15543,-660459,131712]$ |
$[339,10617,-211009,-46063185,250047]$ |
$[\frac{18424351793}{1029},\frac{5106412483}{3087},-\frac{2694373921}{27783}]$ |
$y^2 + (x^2 + x + 1)y = -3x^5 + 5x^4 - 4x^3 + x$ |
| 4624.c.295936.1 |
4624.c |
\( 2^{4} \cdot 17^{2} \) |
\( 2^{10} \cdot 17^{2} \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/6\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$4$ |
$2$ |
2.360.1, 3.720.4 |
✓ |
✓ |
$1$ |
\( 2^{2} \cdot 3 \) |
\(1.000000\) |
\(12.890243\) |
\(1.074187\) |
$[980,2605,845915,36992]$ |
$[980,38280,1899520,99042800,295936]$ |
$[\frac{882735153125}{289},\frac{70368808125}{578},\frac{1781542000}{289}]$ |
$y^2 + (x^3 + x)y = -3x^4 + 6x^2 - 4$ |
| 4736.d.606208.1 |
4736.d |
\( 2^{7} \cdot 37 \) |
\( 2^{14} \cdot 37 \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/6\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,3$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$5$ |
$3$ |
2.120.3, 3.80.1 |
✓ |
✓ |
$1$ |
\( 2 \cdot 3 \) |
\(1.000000\) |
\(17.901454\) |
\(0.745894\) |
$[259,2608,181648,74]$ |
$[1036,16902,245764,-7766525,606208]$ |
$[\frac{31499023927}{16},\frac{3968310717}{128},\frac{111392533}{256}]$ |
$y^2 = x^5 + 4x^4 - x^3 - 8x^2 + 4$ |
