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.d1 |
51870a4 |
51870.d |
51870a |
$4$ |
$4$ |
\( 2 \cdot 3 \cdot 5 \cdot 7 \cdot 13 \cdot 19 \) |
\( 2^{3} \cdot 3 \cdot 5 \cdot 7^{4} \cdot 13^{2} \cdot 19^{4} \) |
$2$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$2$ |
4.6.0.1 |
2B |
$15960$ |
$48$ |
$0$ |
$4.175801038$ |
$1$ |
|
$10$ |
$245760$ |
$1.533329$ |
$141369383441705190409/6345626621880$ |
$[1, 1, 0, -108528, 13715688]$ |
\(y^2+xy=x^3+x^2-108528x+13715688\) |
2.3.0.a.1, 4.6.0.c.1, 12.12.0-4.c.1.1, 40.12.0-4.c.1.2, 120.24.0.?, $\ldots$ |
$[(203, 217), (463, 7705)]$ |
155610.ek1 |
155610x4 |
155610.ek |
155610x |
$4$ |
$4$ |
\( 2 \cdot 3^{2} \cdot 5 \cdot 7 \cdot 13 \cdot 19 \) |
\( 2^{3} \cdot 3^{7} \cdot 5 \cdot 7^{4} \cdot 13^{2} \cdot 19^{4} \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
4.12.0.8 |
2B |
$15960$ |
$48$ |
$0$ |
$1.758825274$ |
$4$ |
$2$ |
$6$ |
$1966080$ |
$2.082638$ |
$141369383441705190409/6345626621880$ |
$[1, -1, 1, -976757, -371300331]$ |
\(y^2+xy+y=x^3-x^2-976757x-371300331\) |
2.3.0.a.1, 4.12.0-4.c.1.2, 120.24.0.?, 3192.24.0.?, 5320.24.0.?, $\ldots$ |
$[(-571, 402)]$ |
259350.gs1 |
259350gs3 |
259350.gs |
259350gs |
$4$ |
$4$ |
\( 2 \cdot 3 \cdot 5^{2} \cdot 7 \cdot 13 \cdot 19 \) |
\( 2^{3} \cdot 3 \cdot 5^{7} \cdot 7^{4} \cdot 13^{2} \cdot 19^{4} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.12.0.8 |
2B |
$15960$ |
$48$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$5898240$ |
$2.338047$ |
$141369383441705190409/6345626621880$ |
$[1, 0, 0, -2713213, 1719887417]$ |
\(y^2+xy=x^3-2713213x+1719887417\) |
2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.4, 60.12.0-4.c.1.1, 120.24.0.?, $\ldots$ |
$[]$ |
363090.dt1 |
363090dt4 |
363090.dt |
363090dt |
$4$ |
$4$ |
\( 2 \cdot 3 \cdot 5 \cdot 7^{2} \cdot 13 \cdot 19 \) |
\( 2^{3} \cdot 3 \cdot 5 \cdot 7^{10} \cdot 13^{2} \cdot 19^{4} \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
4.6.0.1 |
2B |
$15960$ |
$48$ |
$0$ |
$10.07369535$ |
$1$ |
|
$0$ |
$11796480$ |
$2.506287$ |
$141369383441705190409/6345626621880$ |
$[1, 0, 1, -5317898, -4720434652]$ |
\(y^2+xy+y=x^3-5317898x-4720434652\) |
2.3.0.a.1, 4.6.0.c.1, 84.12.0.?, 120.12.0.?, 152.12.0.?, $\ldots$ |
$[(1113907/6, 1168936817/6)]$ |
414960.fn1 |
414960fn4 |
414960.fn |
414960fn |
$4$ |
$4$ |
\( 2^{4} \cdot 3 \cdot 5 \cdot 7 \cdot 13 \cdot 19 \) |
\( 2^{15} \cdot 3 \cdot 5 \cdot 7^{4} \cdot 13^{2} \cdot 19^{4} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
4.6.0.1 |
2B |
$15960$ |
$48$ |
$0$ |
$1$ |
$1$ |
|
$1$ |
$5898240$ |
$2.226479$ |
$141369383441705190409/6345626621880$ |
$[0, 1, 0, -1736456, -881276940]$ |
\(y^2=x^3+x^2-1736456x-881276940\) |
2.3.0.a.1, 4.6.0.c.1, 12.12.0-4.c.1.2, 40.12.0-4.c.1.1, 120.24.0.?, $\ldots$ |
$[]$ |