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.n1 |
51870o4 |
51870.n |
51870o |
$4$ |
$4$ |
\( 2 \cdot 3 \cdot 5 \cdot 7 \cdot 13 \cdot 19 \) |
\( 2^{3} \cdot 3^{3} \cdot 5^{4} \cdot 7^{8} \cdot 13^{2} \cdot 19 \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$2$ |
4.6.0.1 |
2B |
$2280$ |
$48$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$1474560$ |
$2.295105$ |
$5603281597654963338329641/2498954761485000$ |
$[1, 1, 0, -3700322, 2738185356]$ |
\(y^2+xy=x^3+x^2-3700322x+2738185356\) |
2.3.0.a.1, 4.6.0.c.1, 24.12.0-4.c.1.1, 40.12.0-4.c.1.5, 76.12.0.?, $\ldots$ |
$[]$ |
155610.dj1 |
155610bx4 |
155610.dj |
155610bx |
$4$ |
$4$ |
\( 2 \cdot 3^{2} \cdot 5 \cdot 7 \cdot 13 \cdot 19 \) |
\( 2^{3} \cdot 3^{9} \cdot 5^{4} \cdot 7^{8} \cdot 13^{2} \cdot 19 \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.12.0.7 |
2B |
$2280$ |
$48$ |
$0$ |
$6.376648792$ |
$1$ |
|
$0$ |
$11796480$ |
$2.844410$ |
$5603281597654963338329641/2498954761485000$ |
$[1, -1, 1, -33302903, -73964307513]$ |
\(y^2+xy+y=x^3-x^2-33302903x-73964307513\) |
2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.3, 120.24.0.?, 228.12.0.?, $\ldots$ |
$[(73103/2, 18553851/2)]$ |
259350.gg1 |
259350gg3 |
259350.gg |
259350gg |
$4$ |
$4$ |
\( 2 \cdot 3 \cdot 5^{2} \cdot 7 \cdot 13 \cdot 19 \) |
\( 2^{3} \cdot 3^{3} \cdot 5^{10} \cdot 7^{8} \cdot 13^{2} \cdot 19 \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.12.0.6 |
2B |
$2280$ |
$48$ |
$0$ |
$0.587916145$ |
$1$ |
|
$8$ |
$35389440$ |
$3.099823$ |
$5603281597654963338329641/2498954761485000$ |
$[1, 0, 0, -92508063, 342458185617]$ |
\(y^2+xy=x^3-92508063x+342458185617\) |
2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.5, 120.24.0.?, 380.12.0.?, $\ldots$ |
$[(5568, -873)]$ |
363090.ch1 |
363090ch4 |
363090.ch |
363090ch |
$4$ |
$4$ |
\( 2 \cdot 3 \cdot 5 \cdot 7^{2} \cdot 13 \cdot 19 \) |
\( 2^{3} \cdot 3^{3} \cdot 5^{4} \cdot 7^{14} \cdot 13^{2} \cdot 19 \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
4.6.0.1 |
2B |
$15960$ |
$48$ |
$0$ |
$2.436419228$ |
$4$ |
$2$ |
$6$ |
$70778880$ |
$3.268059$ |
$5603281597654963338329641/2498954761485000$ |
$[1, 0, 1, -181315804, -939741524494]$ |
\(y^2+xy+y=x^3-181315804x-939741524494\) |
2.3.0.a.1, 4.6.0.c.1, 120.12.0.?, 168.12.0.?, 280.12.0.?, $\ldots$ |
$[(-7772, 4373)]$ |
414960.hu1 |
414960hu4 |
414960.hu |
414960hu |
$4$ |
$4$ |
\( 2^{4} \cdot 3 \cdot 5 \cdot 7 \cdot 13 \cdot 19 \) |
\( 2^{15} \cdot 3^{3} \cdot 5^{4} \cdot 7^{8} \cdot 13^{2} \cdot 19 \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
4.6.0.1 |
2B |
$2280$ |
$48$ |
$0$ |
$1$ |
$1$ |
|
$1$ |
$35389440$ |
$2.988251$ |
$5603281597654963338329641/2498954761485000$ |
$[0, 1, 0, -59205160, -175362273100]$ |
\(y^2=x^3+x^2-59205160x-175362273100\) |
2.3.0.a.1, 4.6.0.c.1, 24.12.0-4.c.1.2, 40.12.0-4.c.1.5, 76.12.0.?, $\ldots$ |
$[]$ |