| 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 |
Regulator |
$Ш_{\textrm{an}}$ |
Ш primes |
Integral points |
Modular degree |
Faltings height |
j-invariant |
Weierstrass coefficients |
Weierstrass equation |
| 1045.a1 |
1045a2 |
1045.a |
1045a |
$2$ |
$2$ |
\( 5 \cdot 11 \cdot 19 \) |
\( 5 \cdot 11^{2} \cdot 19^{2} \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$2$ |
2.3.0.1 |
2B |
$0.342154040$ |
$1$ |
|
$8$ |
$128$ |
$-0.226044$ |
$3301293169/218405$ |
$[1, 0, 0, -31, 60]$ |
\(y^2+xy=x^3-31x+60\) |
| 1045.a2 |
1045a1 |
1045.a |
1045a |
$2$ |
$2$ |
\( 5 \cdot 11 \cdot 19 \) |
\( 5^{2} \cdot 11 \cdot 19 \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$2$ |
2.3.0.1 |
2B |
$0.684308081$ |
$1$ |
|
$7$ |
$64$ |
$-0.572618$ |
$24137569/5225$ |
$[1, 0, 0, -6, -5]$ |
\(y^2+xy=x^3-6x-5\) |
| 1045.b1 |
1045b3 |
1045.b |
1045b |
$4$ |
$4$ |
\( 5 \cdot 11 \cdot 19 \) |
\( 5^{4} \cdot 11 \cdot 19^{12} \) |
$1$ |
$\Z/4\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$2$ |
4.12.0.7 |
2B |
$6.655271875$ |
$1$ |
|
$2$ |
$17664$ |
$2.408970$ |
$116256292809537371612841/15216540068579856875$ |
$[1, -1, 0, -1016789, -346894930]$ |
\(y^2+xy=x^3-x^2-1016789x-346894930\) |
| 1045.b2 |
1045b2 |
1045.b |
1045b |
$4$ |
$4$ |
\( 5 \cdot 11 \cdot 19 \) |
\( 5^{8} \cdot 11^{2} \cdot 19^{6} \) |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$2$ |
4.12.0.1 |
2Cs |
$3.327635937$ |
$1$ |
|
$4$ |
$8832$ |
$2.062397$ |
$104859453317683374662841/2223652969140625$ |
$[1, -1, 0, -982414, -374539305]$ |
\(y^2+xy=x^3-x^2-982414x-374539305\) |
| 1045.b3 |
1045b1 |
1045.b |
1045b |
$4$ |
$4$ |
\( 5 \cdot 11 \cdot 19 \) |
\( 5^{4} \cdot 11 \cdot 19^{3} \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$2$ |
8.12.0.6 |
2B |
$6.655271875$ |
$1$ |
|
$1$ |
$4416$ |
$1.715824$ |
$104857852278310619039721/47155625$ |
$[1, -1, 0, -982409, -374543312]$ |
\(y^2+xy=x^3-x^2-982409x-374543312\) |
| 1045.b4 |
1045b4 |
1045.b |
1045b |
$4$ |
$4$ |
\( 5 \cdot 11 \cdot 19 \) |
\( - 5^{16} \cdot 11^{4} \cdot 19^{3} \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$2$ |
4.12.0.8 |
2B |
$1.663817968$ |
$1$ |
|
$4$ |
$17664$ |
$2.408970$ |
$-94256762600623910012361/15323275604248046875$ |
$[1, -1, 0, -948119, -401927292]$ |
\(y^2+xy=x^3-x^2-948119x-401927292\) |
