| 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 |
| 2005.a1 |
2005b1 |
2005.a |
2005b |
$2$ |
$2$ |
\( 5 \cdot 401 \) |
\( 5^{2} \cdot 401 \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$2$ |
2.3.0.1 |
2B |
$8020$ |
$12$ |
$0$ |
$1.052561425$ |
$1$ |
|
$5$ |
$96$ |
$-0.527206$ |
$33076161/10025$ |
$0.87540$ |
$2.27718$ |
$[1, -1, 1, -7, 6]$ |
\(y^2+xy+y=x^3-x^2-7x+6\) |
2.3.0.a.1, 20.6.0.b.1, 802.6.0.?, 8020.12.0.? |
$[(0, 2)]$ |
| 2005.a2 |
2005b2 |
2005.a |
2005b |
$2$ |
$2$ |
\( 5 \cdot 401 \) |
\( - 5 \cdot 401^{2} \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$2$ |
2.3.0.1 |
2B |
$8020$ |
$12$ |
$0$ |
$2.105122850$ |
$1$ |
|
$2$ |
$192$ |
$-0.180633$ |
$679151439/804005$ |
$0.85075$ |
$2.68051$ |
$[1, -1, 1, 18, 26]$ |
\(y^2+xy+y=x^3-x^2+18x+26\) |
2.3.0.a.1, 20.6.0.a.1, 1604.6.0.?, 8020.12.0.? |
$[(5, 12)]$ |
| 2005.b1 |
2005a3 |
2005.b |
2005a |
$4$ |
$4$ |
\( 5 \cdot 401 \) |
\( 5^{2} \cdot 401 \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$2$ |
8.24.0.57 |
2B |
$32080$ |
$192$ |
$3$ |
$12.98462096$ |
$1$ |
|
$0$ |
$1792$ |
$0.992018$ |
$16903379714178579201/10025$ |
$1.05475$ |
$5.82293$ |
$[1, -1, 1, -53467, -4745166]$ |
\(y^2+xy+y=x^3-x^2-53467x-4745166\) |
2.3.0.a.1, 4.12.0-4.c.1.2, 8.24.0-8.o.1.3, 80.48.0.?, 802.6.0.?, $\ldots$ |
$[(716197/44, 418555099/44)]$ |
| 2005.b2 |
2005a2 |
2005.b |
2005a |
$4$ |
$4$ |
\( 5 \cdot 401 \) |
\( 5^{4} \cdot 401^{2} \) |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$2$ |
4.24.0.7 |
2Cs |
$16040$ |
$192$ |
$3$ |
$6.492310483$ |
$1$ |
|
$2$ |
$896$ |
$0.645444$ |
$4126874048961201/100500625$ |
$0.96441$ |
$4.72898$ |
$[1, -1, 1, -3342, -73516]$ |
\(y^2+xy+y=x^3-x^2-3342x-73516\) |
2.6.0.a.1, 4.24.0-4.a.1.1, 40.48.0-40.j.1.1, 1604.48.0.?, 3208.96.0.?, $\ldots$ |
$[(1677/4, 50899/4)]$ |
| 2005.b3 |
2005a4 |
2005.b |
2005a |
$4$ |
$4$ |
\( 5 \cdot 401 \) |
\( - 5^{2} \cdot 401^{4} \) |
$1$ |
$\Z/4\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$2$ |
4.24.0.11 |
2B |
$32080$ |
$192$ |
$3$ |
$12.98462096$ |
$1$ |
|
$2$ |
$1792$ |
$0.992018$ |
$-3680868702543201/646424040025$ |
$0.93742$ |
$4.74879$ |
$[1, -1, 1, -3217, -79366]$ |
\(y^2+xy+y=x^3-x^2-3217x-79366\) |
2.3.0.a.1, 4.24.0-4.d.1.1, 40.48.0-40.z.1.3, 3208.48.0.?, 6416.96.0.?, $\ldots$ |
$[(738277/84, 472091159/84)]$ |
| 2005.b4 |
2005a1 |
2005.b |
2005a |
$4$ |
$4$ |
\( 5 \cdot 401 \) |
\( 5^{8} \cdot 401 \) |
$1$ |
$\Z/4\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$2$ |
8.24.0.47 |
2B |
$32080$ |
$192$ |
$3$ |
$3.246155241$ |
$1$ |
|
$5$ |
$448$ |
$0.298871$ |
$1125188511201/156640625$ |
$0.87372$ |
$3.64955$ |
$[1, -1, 1, -217, -1016]$ |
\(y^2+xy+y=x^3-x^2-217x-1016\) |
2.3.0.a.1, 4.12.0-4.c.1.1, 8.24.0-8.o.1.1, 80.48.0.?, 802.6.0.?, $\ldots$ |
$[(97, 891)]$ |
