| 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 |
| 1849.a1 |
1849c1 |
1849.a |
1849c |
$1$ |
$1$ |
\( 43^{2} \) |
\( 43^{10} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
$2$ |
2.2.0.1 |
2Cn |
$172$ |
$12$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$9030$ |
$1.825340$ |
$1849$ |
$0.94611$ |
$6.00000$ |
$[1, 1, 1, -71225, 1841958]$ |
\(y^2+xy+y=x^3+x^2-71225x+1841958\) |
2.2.0.a.1, 86.6.0.?, 172.12.0.? |
$[]$ |
| 1849.b1 |
1849a2 |
1849.b |
1849a |
$2$ |
$43$ |
\( 43^{2} \) |
\( - 43^{9} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q(\sqrt{-43})$ |
$-43$ |
$N(\mathrm{U}(1))$ |
|
✓ |
$43$ |
43.1848.57.42 |
43B.1.30 |
|
|
|
$18.29360093$ |
$1$ |
|
$0$ |
$11352$ |
$2.106030$ |
$-884736000$ |
$1.44331$ |
$7.23859$ |
$[0, 0, 1, -1590140, -771794326]$ |
\(y^2+y=x^3-1590140x-771794326\) |
|
$[(66276734/173, 419562388765/173)]$ |
| 1849.b2 |
1849a1 |
1849.b |
1849a |
$2$ |
$43$ |
\( 43^{2} \) |
\( - 43^{3} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q(\sqrt{-43})$ |
$-43$ |
$N(\mathrm{U}(1))$ |
|
✓ |
$43$ |
43.1848.57.21 |
43B.1.13 |
|
|
|
$0.425432579$ |
$1$ |
|
$4$ |
$264$ |
$0.225430$ |
$-884736000$ |
$1.44331$ |
$4.23859$ |
$[0, 0, 1, -860, 9707]$ |
\(y^2+y=x^3-860x+9707\) |
|
$[(17, 0)]$ |
| 1849.c1 |
1849b1 |
1849.c |
1849b |
$1$ |
$1$ |
\( 43^{2} \) |
\( 43^{4} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
$2$ |
4.4.0.2 |
2Cn |
$172$ |
$12$ |
$0$ |
$1.945886264$ |
$1$ |
|
$2$ |
$210$ |
$-0.055260$ |
$1849$ |
$0.94611$ |
$3.00000$ |
$[1, 0, 1, -39, -27]$ |
\(y^2+xy+y=x^3-39x-27\) |
2.2.0.a.1, 4.4.0-2.a.1.1, 86.6.0.?, 172.12.0.? |
$[(-3, 9)]$ |
| 1849.d1 |
1849d1 |
1849.d |
1849d |
$1$ |
$1$ |
\( 43^{2} \) |
\( - 43^{7} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$86$ |
$2$ |
$0$ |
$1$ |
$4$ |
$2$ |
$0$ |
$3696$ |
$0.876169$ |
$-4096/43$ |
$0.78068$ |
$4.49814$ |
$[0, -1, 1, -616, -25561]$ |
\(y^2+y=x^3-x^2-616x-25561\) |
86.2.0.? |
$[]$ |
