| 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 |
✓ |
✓ |
$1$ |
\( 2^{2} \) |
\(1.000000\) |
\(9.467159\) |
\(0.262977\) |
$[92,4981,43947,-12000]$ |
$[92,-2968,47600,-1107456,-96000]$ |
$[-\frac{25745372}{375},\frac{9027914}{375},-\frac{62951}{15}]$ |
$y^2 + (x + 1)y = 4x^5 + 5x^4 + 3x^3 + 2x^2$ |
| 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 |
✓ |
✓ |
$1$ |
\( 2^{2} \) |
\(1.000000\) |
\(11.270100\) |
\(0.313058\) |
$[116,445,16259,1568]$ |
$[116,264,-1280,-54544,12544]$ |
$[\frac{82044596}{49},\frac{1609674}{49},-\frac{67280}{49}]$ |
$y^2 + (x^3 + x)y = -1$ |
| 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 |
✓ |
✓ |
$1$ |
\( 2^{2} \) |
\(1.000000\) |
\(13.019302\) |
\(0.361647\) |
$[160,4720,130020,-65856]$ |
$[80,-520,4220,16800,-16464]$ |
$[-\frac{204800000}{1029},\frac{16640000}{1029},-\frac{1688000}{1029}]$ |
$y^2 + (x + 1)y = -2x^5 + x^2$ |
| 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 |
✓ |
✓ |
$1$ |
\( 3 \) |
\(1.000000\) |
\(23.235042\) |
\(0.484063\) |
$[78,216,4806,81]$ |
$[156,438,-428,-64653,20736]$ |
$[4455516,\frac{160381}{2},-\frac{18083}{36}]$ |
$y^2 = x^5 - x^4 - 3x^3 + 4x^2 - x$ |
| 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 |
✓ |
✓ |
$1$ |
\( 2^{2} \cdot 3 \) |
\(1.000000\) |
\(6.178250\) |
\(0.514854\) |
$[364,3529,393211,345600]$ |
$[273,1782,0,-793881,656100]$ |
$[\frac{6240321451}{2700},\frac{8289281}{150},0]$ |
$y^2 + (x^2 + x)y = x^5 + x^4 + 4x^3 + x^2 + x$ |
| 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 |
✓ |
✓ |
$1$ |
\( 2^{2} \cdot 3 \) |
\(1.000000\) |
\(5.650548\) |
\(0.470879\) |
$[35416,45688,537039964,466560]$ |
$[17708,13057938,12831384960,14177105014959,116640]$ |
$[\frac{54412363190235229024}{3645},\frac{251762275020280012}{405},\frac{310461362928064}{9}]$ |
$y^2 + (x^3 + x)y = 5x^4 + 39x^2 + 90$ |
| 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 |
✓ |
✓ |
$1$ |
\( 2 \cdot 3 \) |
\(1.000000\) |
\(11.725763\) |
\(0.488573\) |
$[182340,50613,3073006935,30240]$ |
$[182340,1385294408,14032351630080,159904599848179184,241920]$ |
$[\frac{5832248478791381977500}{7},\frac{243004434356588125950}{7},1928513067842084400]$ |
$y^2 + (x^2 + 1)y = 135x^6 - 96x^4 + 22x^2 - 2$ |
| 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 |
✓ |
✓ |
$1$ |
\( 2 \cdot 3 \) |
\(1.000000\) |
\(15.706158\) |
\(0.654423\) |
$[19036,1343263,8004572494,5400]$ |
$[19036,14203212,13587811200,14231585721564,43200]$ |
$[\frac{39056966269184124784}{675},\frac{510284561561447516}{225},\frac{341930942967008}{3}]$ |
$y^2 + (x^3 + x)y = -7x^4 + 48x^2 - 75$ |
| 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 |
✓ |
✓ |
$1$ |
\( 2^{2} \) |
\(1.000000\) |
\(13.988232\) |
\(0.388562\) |
$[16804,12258145,55198853169,21073920]$ |
$[4201,224594,995716,-11564865480,164640]$ |
$[\frac{1308468909056421001}{164640},\frac{8325804308294497}{82320},\frac{4393198812529}{41160}]$ |
$y^2 + (x^2 + x)y = 14x^5 + 37x^4 + 21x^3 - x^2 - 2x$ |
| 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 |
✓ |
✓ |
$1$ |
\( 2^{2} \) |
\(1.000000\) |
\(20.417952\) |
\(0.567165\) |
$[620,11155,1926860,19208]$ |
$[620,8580,119680,146300,153664]$ |
$[\frac{1431457550000}{2401},\frac{31950847500}{2401},\frac{718828000}{2401}]$ |
$y^2 + (x^3 + x)y = -3x^4 + 6x^2 - 1$ |
| 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 |
✓ |
✓ |
$1$ |
\( 2^{3} \) |
\(1.000000\) |
\(10.347832\) |
\(0.574880\) |
$[64,1440,11244,-960]$ |
$[96,-1776,25916,-166560,-58320]$ |
$[-\frac{2097152}{15},\frac{1212416}{45},-\frac{1658624}{405}]$ |
$y^2 + (x^3 + x)y = x^4 - x^3 + 2x^2 - 3x$ |
| 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 |
|
|
$2$ |
\( 2^{2} \cdot 3 \) |
\(1.000000\) |
\(3.848391\) |
\(0.641398\) |
$[182340,50613,3073006935,30240]$ |
$[182340,1385294408,14032351630080,159904599848179184,241920]$ |
$[\frac{5832248478791381977500}{7},\frac{243004434356588125950}{7},1928513067842084400]$ |
$y^2 + (x^2 + 1)y = -135x^6 - 96x^4 - 23x^2 - 2$ |
| 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 |
✓ |
✓ |
$1$ |
\( 2^{2} \cdot 3 \) |
\(1.000000\) |
\(12.890243\) |
\(1.074187\) |
$[980,2605,845915,36992]$ |
$[980,38280,1899520,99042800,295936]$ |
$[\frac{882735153125}{289},\frac{70368808125}{578},\frac{1781542000}{289}]$ |
$y^2 + (x^3 + x)y = -3x^4 + 6x^2 - 4$ |
| 14520.b.319440.1 |
14520.b |
\( 2^{3} \cdot 3 \cdot 5 \cdot 11^{2} \) |
\( 2^{4} \cdot 3 \cdot 5 \cdot 11^{3} \) |
$1$ |
$3$ |
$\Z/2\Z\oplus\Z/6\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2$ |
$C_2$ |
$4$ |
$2$ |
2.180.3, 3.640.2 |
✓ |
✓ |
$1$ |
\( 2^{2} \) |
\(2.194071\) |
\(14.924182\) |
\(0.909576\) |
$[3008,181120,174766332,1277760]$ |
$[1504,64064,1068004,-624479520,319440]$ |
$[\frac{480971340120064}{19965},\frac{1238354231296}{1815},\frac{150990133504}{19965}]$ |
$y^2 + xy = 2x^5 - 14x^4 + 30x^3 - 21x^2 + 3$ |
