| 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 |
| 1586.a1 |
1586a1 |
1586.a |
1586a |
$1$ |
$1$ |
\( 2 \cdot 13 \cdot 61 \) |
\( - 2^{11} \cdot 13 \cdot 61^{2} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
|
$104$ |
$2$ |
$0$ |
$0.613284019$ |
$1$ |
|
$4$ |
$616$ |
$0.235482$ |
$-153388121977/99067904$ |
$0.87461$ |
$3.59695$ |
$[1, 1, 0, -111, 613]$ |
\(y^2+xy=x^3+x^2-111x+613\) |
104.2.0.? |
$[(-3, 32)]$ |
| 1586.b1 |
1586b1 |
1586.b |
1586b |
$1$ |
$1$ |
\( 2 \cdot 13 \cdot 61 \) |
\( - 2 \cdot 13^{3} \cdot 61^{2} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
|
$104$ |
$2$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$984$ |
$0.073211$ |
$26118765063/16350074$ |
$0.91054$ |
$3.25499$ |
$[1, -1, 0, 62, 38]$ |
\(y^2+xy=x^3-x^2+62x+38\) |
104.2.0.? |
$[]$ |
| 1586.c1 |
1586d2 |
1586.c |
1586d |
$2$ |
$5$ |
\( 2 \cdot 13 \cdot 61 \) |
\( - 2^{5} \cdot 13 \cdot 61^{10} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$5$ |
5.24.0.3 |
5B.1.2 |
$520$ |
$48$ |
$1$ |
$1$ |
$1$ |
|
$0$ |
$47000$ |
$2.682072$ |
$-4713056995643685597046321/296750651251759162016$ |
$1.01885$ |
$7.72369$ |
$[1, 1, 1, -3492955, -2647300407]$ |
\(y^2+xy+y=x^3+x^2-3492955x-2647300407\) |
5.24.0-5.a.2.2, 104.2.0.?, 520.48.1.? |
$[]$ |
| 1586.c2 |
1586d1 |
1586.c |
1586d |
$2$ |
$5$ |
\( 2 \cdot 13 \cdot 61 \) |
\( - 2^{25} \cdot 13^{5} \cdot 61^{2} \) |
$0$ |
$\Z/5\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$5$ |
5.24.0.1 |
5B.1.1 |
$520$ |
$48$ |
$1$ |
$1$ |
$1$ |
|
$4$ |
$9400$ |
$1.877352$ |
$453407867428435919/46358174206263296$ |
$1.01999$ |
$6.21854$ |
$[1, 1, 1, 16005, 10336393]$ |
\(y^2+xy+y=x^3+x^2+16005x+10336393\) |
5.24.0-5.a.1.2, 104.2.0.?, 520.48.1.? |
$[]$ |
| 1586.d1 |
1586c1 |
1586.d |
1586c |
$2$ |
$2$ |
\( 2 \cdot 13 \cdot 61 \) |
\( 2^{16} \cdot 13 \cdot 61^{3} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$2$ |
8.12.0.22 |
2B |
$6344$ |
$48$ |
$0$ |
$1$ |
$1$ |
|
$1$ |
$4896$ |
$1.340828$ |
$25585196494633455393/193380548608$ |
$1.02929$ |
$6.06442$ |
$[1, -1, 1, -61389, 5869685]$ |
\(y^2+xy+y=x^3-x^2-61389x+5869685\) |
2.3.0.a.1, 4.6.0.b.1, 8.12.0-4.b.1.2, 1586.6.0.?, 3172.24.0.?, $\ldots$ |
$[]$ |
| 1586.d2 |
1586c2 |
1586.d |
1586c |
$2$ |
$2$ |
\( 2 \cdot 13 \cdot 61 \) |
\( - 2^{8} \cdot 13^{2} \cdot 61^{6} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$2$ |
8.12.0.37 |
2B |
$6344$ |
$48$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$9792$ |
$1.687403$ |
$-24017922952040513313/2228977476354304$ |
$1.04411$ |
$6.07603$ |
$[1, -1, 1, -60109, 6125173]$ |
\(y^2+xy+y=x^3-x^2-60109x+6125173\) |
2.3.0.a.1, 4.6.0.a.1, 8.12.0-4.a.1.1, 3172.12.0.?, 6344.48.0.? |
$[]$ |
