| 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 |
| 65520.b.131040.1 |
65520.b |
\( 2^{4} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 13 \) |
\( - 2^{5} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 13 \) |
$1$ |
$6$ |
$\Z/2\Z\oplus\Z/2\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$0$ |
$0$ |
2.90.6, 3.90.1 |
|
|
$8$ |
\( 2 \) |
\(0.532647\) |
\(3.186150\) |
\(1.697092\) |
$[3148328,708952,743814934788,524160]$ |
$[1574164,103249560962,9029520569946240,888368594905774644479,131040]$ |
$[302064649214662608101539958432/4095,12586012647194024913614166004/4095,170750018582492394877376]$ |
$y^2 + (x^3 + x)y = -10x^6 - 82x^4 - 227x^2 - 210$ |
| 114240.d.114240.1 |
114240.d |
\( 2^{6} \cdot 3 \cdot 5 \cdot 7 \cdot 17 \) |
\( 2^{6} \cdot 3 \cdot 5 \cdot 7 \cdot 17 \) |
$0$ |
$6$ |
$\Z/2\Z\oplus\Z/2\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$0$ |
$0$ |
2.180.7, 3.90.1 |
✓ |
✓ |
$256$ |
\( 1 \) |
\(1.000000\) |
\(0.165182\) |
\(2.642912\) |
$[1256652,52204481283,17891676439496172,14280]$ |
$[1256652,30995939524,838652756430720,23286599174677950716,114240]$ |
$[16322019979578992366124730896/595,320367650677941067851565476/595,11592952003636922822112]$ |
$y^2 + (x^2 + 1)y = 51x^6 - 315x^4 + 103x^2 - 9$ |
| 270720.b.270720.1 |
270720.b |
\( 2^{7} \cdot 3^{2} \cdot 5 \cdot 47 \) |
\( - 2^{7} \cdot 3^{2} \cdot 5 \cdot 47 \) |
$0$ |
$6$ |
$\Z/2\Z\oplus\Z/2\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$0$ |
$0$ |
2.90.6, 3.90.1 |
|
✓ |
$16$ |
\( 1 \) |
\(1.000000\) |
\(3.383512\) |
\(3.383512\) |
$[3249520,48397,52421227290,33840]$ |
$[3249520,439974144002,79428031708101120,16131432551454029721599,270720]$ |
$[566129906277843097800186880000/423,23588744365074445774311454400/423,3098074718373623337958400]$ |
$y^2 + xy = 3x^6 + 70x^4 + 544x^2 + 1410$ |
| 456960.c.913920.1 |
456960.c |
\( 2^{8} \cdot 3 \cdot 5 \cdot 7 \cdot 17 \) |
\( - 2^{9} \cdot 3 \cdot 5 \cdot 7 \cdot 17 \) |
$1$ |
$6$ |
$\Z/2\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$0$ |
$0$ |
2.45.1, 3.90.1 |
|
✓ |
$16$ |
\( 1 \) |
\(0.519810\) |
\(1.587454\) |
\(3.300700\) |
$[2757032,14577118,13377979235542,114240]$ |
$[2757032,316708008964,48506712556968960,8357648948106035343356,913920]$ |
$[311127982838559560387716745536/1785,12963268178085404526178374196/1785,403438438743571080790912]$ |
$y^2 + xy = -5x^6 - 79x^4 - 413x^2 - 714$ |
| 799680.b.799680.1 |
799680.b |
\( 2^{6} \cdot 3 \cdot 5 \cdot 7^{2} \cdot 17 \) |
\( - 2^{6} \cdot 3 \cdot 5 \cdot 7^{2} \cdot 17 \) |
$1$ |
$6$ |
$\Z/6\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$0$ |
$0$ |
2.45.1, 3.720.4 |
✓ |
✓ |
$16$ |
\( 1 \) |
\(2.306125\) |
\(2.035805\) |
\(2.086587\) |
$[2406604,3575875,2866321300076,99960]$ |
$[2406604,241320233284,32263933356762240,4852764019968313102076,799680]$ |
$[1261372031256529020641523732016/12495,52556648780600635811581759084/12495,233673974755154692792288]$ |
$y^2 + (x^2 + 1)y = 7x^6 + 84x^4 + 336x^2 + 446$ |
