| 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 |
$abc$ quality |
Szpiro ratio |
Weierstrass coefficients |
Weierstrass equation |
mod-$m$ images |
MW-generators |
| 51870.j3 |
51870j3 |
51870.j |
51870j |
$4$ |
$4$ |
\( 2 \cdot 3 \cdot 5 \cdot 7 \cdot 13 \cdot 19 \) |
\( - 2^{4} \cdot 3^{2} \cdot 5^{2} \cdot 7^{12} \cdot 13 \cdot 19^{4} \) |
$0$ |
$\Z/4\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$2$ |
4.12.0.7 |
2B |
$13832$ |
$48$ |
$0$ |
$1$ |
$1$ |
|
$2$ |
$2359296$ |
$2.510372$ |
$-28346090452899214800169/84418326220247182800$ |
$0.97571$ |
$4.92927$ |
$[1, 1, 0, -635218, -483364028]$ |
\(y^2+xy=x^3+x^2-635218x-483364028\) |
2.3.0.a.1, 4.12.0-4.c.1.1, 52.24.0-52.h.1.2, 1064.24.0.?, 13832.48.0.? |
$[]$ |
| 155610.eu3 |
155610a4 |
155610.eu |
155610a |
$4$ |
$4$ |
\( 2 \cdot 3^{2} \cdot 5 \cdot 7 \cdot 13 \cdot 19 \) |
\( - 2^{4} \cdot 3^{8} \cdot 5^{2} \cdot 7^{12} \cdot 13 \cdot 19^{4} \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
4.6.0.1 |
2B |
$41496$ |
$48$ |
$0$ |
$0.640513338$ |
$1$ |
|
$10$ |
$18874368$ |
$3.059677$ |
$-28346090452899214800169/84418326220247182800$ |
$0.97571$ |
$5.02767$ |
$[1, -1, 1, -5716967, 13045111791]$ |
\(y^2+xy+y=x^3-x^2-5716967x+13045111791\) |
2.3.0.a.1, 4.6.0.c.1, 12.12.0-4.c.1.2, 52.12.0.h.1, 156.24.0.?, $\ldots$ |
$[(1281, 87804)]$ |
| 259350.fy3 |
259350fy3 |
259350.fy |
259350fy |
$4$ |
$4$ |
\( 2 \cdot 3 \cdot 5^{2} \cdot 7 \cdot 13 \cdot 19 \) |
\( - 2^{4} \cdot 3^{2} \cdot 5^{8} \cdot 7^{12} \cdot 13 \cdot 19^{4} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
4.6.0.1 |
2B |
$69160$ |
$48$ |
$0$ |
$1$ |
$4$ |
$2$ |
$0$ |
$56623104$ |
$3.315090$ |
$-28346090452899214800169/84418326220247182800$ |
$0.97571$ |
$5.06751$ |
$[1, 0, 0, -15880463, -60388742583]$ |
\(y^2+xy=x^3-15880463x-60388742583\) |
2.3.0.a.1, 4.6.0.c.1, 20.12.0-4.c.1.2, 52.12.0.h.1, 260.24.0.?, $\ldots$ |
$[]$ |
| 363090.dy3 |
363090dy4 |
363090.dy |
363090dy |
$4$ |
$4$ |
\( 2 \cdot 3 \cdot 5 \cdot 7^{2} \cdot 13 \cdot 19 \) |
\( - 2^{4} \cdot 3^{2} \cdot 5^{2} \cdot 7^{18} \cdot 13 \cdot 19^{4} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
4.6.0.1 |
2B |
$13832$ |
$48$ |
$0$ |
$1$ |
$4$ |
$2$ |
$0$ |
$113246208$ |
$3.483326$ |
$-28346090452899214800169/84418326220247182800$ |
$0.97571$ |
$5.09202$ |
$[1, 0, 1, -31125708, 165700484506]$ |
\(y^2+xy+y=x^3-31125708x+165700484506\) |
2.3.0.a.1, 4.6.0.c.1, 28.12.0-4.c.1.2, 52.12.0.h.1, 152.12.0.?, $\ldots$ |
$[]$ |
| 414960.ei3 |
414960ei4 |
414960.ei |
414960ei |
$4$ |
$4$ |
\( 2^{4} \cdot 3 \cdot 5 \cdot 7 \cdot 13 \cdot 19 \) |
\( - 2^{16} \cdot 3^{2} \cdot 5^{2} \cdot 7^{12} \cdot 13 \cdot 19^{4} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
4.12.0.8 |
2B |
$13832$ |
$48$ |
$0$ |
$1$ |
$4$ |
$2$ |
$1$ |
$56623104$ |
$3.203518$ |
$-28346090452899214800169/84418326220247182800$ |
$0.97571$ |
$4.77989$ |
$[0, 1, 0, -10163496, 30914970804]$ |
\(y^2=x^3+x^2-10163496x+30914970804\) |
2.3.0.a.1, 4.12.0-4.c.1.2, 52.24.0-52.h.1.1, 1064.24.0.?, 13832.48.0.? |
$[]$ |
