Label |
Cremona label |
Class |
Cremona class |
Class size |
Class degree |
Conductor |
Discriminant |
Rank |
Torsion |
$\textrm{End}^0(E_{\overline\Q})$ |
CM |
Sato-Tate |
Semistable |
Potentially good |
Nonmax $\ell$ |
$\ell$-adic images |
mod-$\ell$ images |
Adelic level |
Adelic index |
Adelic genus |
Regulator |
$Ш_{\textrm{an}}$ |
Ш primes |
Integral points |
Modular degree |
Faltings height |
j-invariant |
Weierstrass coefficients |
Weierstrass equation |
mod-$m$ images |
MW-generators |
51870.y6 |
51870bd2 |
51870.y |
51870bd |
$8$ |
$12$ |
\( 2 \cdot 3 \cdot 5 \cdot 7 \cdot 13 \cdot 19 \) |
\( 2^{2} \cdot 3^{6} \cdot 5^{2} \cdot 7^{6} \cdot 13^{6} \cdot 19^{2} \) |
$1$ |
$\Z/2\Z\oplus\Z/6\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$2, 3$ |
2.6.0.1, 3.8.0.1 |
2Cs, 3B.1.1 |
$207480$ |
$384$ |
$5$ |
$2.503003782$ |
$1$ |
|
$24$ |
$1327104$ |
$2.376385$ |
$35872512095393194378249/14944558319037792900$ |
$[1, 0, 1, -687089, -116077264]$ |
\(y^2+xy+y=x^3-687089x-116077264\) |
2.6.0.a.1, 3.8.0-3.a.1.2, 6.48.0-6.a.1.1, 52.12.0-2.a.1.1, 120.96.0.?, $\ldots$ |
$[(-684, 6172)]$ |
155610.fe6 |
155610j2 |
155610.fe |
155610j |
$8$ |
$12$ |
\( 2 \cdot 3^{2} \cdot 5 \cdot 7 \cdot 13 \cdot 19 \) |
\( 2^{2} \cdot 3^{12} \cdot 5^{2} \cdot 7^{6} \cdot 13^{6} \cdot 19^{2} \) |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2, 3$ |
2.6.0.1, 3.8.0.2 |
2Cs, 3B.1.2 |
$207480$ |
$384$ |
$5$ |
$1.718533484$ |
$1$ |
|
$6$ |
$10616832$ |
$2.925690$ |
$35872512095393194378249/14944558319037792900$ |
$[1, -1, 1, -6183797, 3134086121]$ |
\(y^2+xy+y=x^3-x^2-6183797x+3134086121\) |
2.6.0.a.1, 3.8.0-3.a.1.1, 6.48.0-6.a.1.2, 40.12.0-2.a.1.1, 120.96.0.?, $\ldots$ |
$[(2611, 67854)]$ |
259350.ek6 |
259350ek2 |
259350.ek |
259350ek |
$8$ |
$12$ |
\( 2 \cdot 3 \cdot 5^{2} \cdot 7 \cdot 13 \cdot 19 \) |
\( 2^{2} \cdot 3^{6} \cdot 5^{8} \cdot 7^{6} \cdot 13^{6} \cdot 19^{2} \) |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2, 3$ |
2.6.0.1, 3.4.0.1 |
2Cs, 3B |
$207480$ |
$384$ |
$5$ |
$17.73612014$ |
$1$ |
|
$2$ |
$31850496$ |
$3.181103$ |
$35872512095393194378249/14944558319037792900$ |
$[1, 1, 1, -17177213, -14509657969]$ |
\(y^2+xy+y=x^3+x^2-17177213x-14509657969\) |
2.6.0.a.1, 3.4.0.a.1, 6.24.0.a.1, 15.8.0-3.a.1.2, 24.48.0-6.a.1.2, $\ldots$ |
$[(-115907125/299, 2014673534138/299)]$ |
363090.bn6 |
363090bn2 |
363090.bn |
363090bn |
$8$ |
$12$ |
\( 2 \cdot 3 \cdot 5 \cdot 7^{2} \cdot 13 \cdot 19 \) |
\( 2^{2} \cdot 3^{6} \cdot 5^{2} \cdot 7^{12} \cdot 13^{6} \cdot 19^{2} \) |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2, 3$ |
2.6.0.1, 3.4.0.1 |
2Cs, 3B |
$207480$ |
$384$ |
$5$ |
$9.167718509$ |
$1$ |
|
$2$ |
$63700992$ |
$3.349339$ |
$35872512095393194378249/14944558319037792900$ |
$[1, 1, 0, -33667337, 39780834129]$ |
\(y^2+xy=x^3+x^2-33667337x+39780834129\) |
2.6.0.a.1, 3.4.0.a.1, 6.24.0.a.1, 21.8.0-3.a.1.1, 42.48.0-6.a.1.1, $\ldots$ |
$[(-13264/7, 75875519/7)]$ |
414960.p6 |
414960p2 |
414960.p |
414960p |
$8$ |
$12$ |
\( 2^{4} \cdot 3 \cdot 5 \cdot 7 \cdot 13 \cdot 19 \) |
\( 2^{14} \cdot 3^{6} \cdot 5^{2} \cdot 7^{6} \cdot 13^{6} \cdot 19^{2} \) |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2, 3$ |
2.6.0.1, 3.4.0.1 |
2Cs, 3B |
$207480$ |
$384$ |
$5$ |
$2.246046388$ |
$1$ |
|
$9$ |
$31850496$ |
$3.069530$ |
$35872512095393194378249/14944558319037792900$ |
$[0, -1, 0, -10993416, 7428944880]$ |
\(y^2=x^3-x^2-10993416x+7428944880\) |
2.6.0.a.1, 3.4.0.a.1, 6.24.0.a.1, 12.48.0-6.a.1.2, 52.12.0-2.a.1.1, $\ldots$ |
$[(7364, 570752)]$ |