| 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 |
| 81733.a1 |
81733b1 |
81733.a |
81733b |
$1$ |
$1$ |
\( 37 \cdot 47^{2} \) |
\( 37 \cdot 47^{6} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$74$ |
$2$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$204516$ |
$0.928532$ |
$110592/37$ |
$0.76978$ |
$3.06903$ |
$[0, 0, 1, -2209, -25956]$ |
\(y^2+y=x^3-2209x-25956\) |
74.2.0.? |
$[ ]$ |
| 81733.b1 |
81733a1 |
81733.b |
81733a |
$1$ |
$1$ |
\( 37 \cdot 47^{2} \) |
\( - 37 \cdot 47^{9} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$3478$ |
$2$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$4424832$ |
$2.386196$ |
$-754963064303616/3841451$ |
$0.93866$ |
$5.07095$ |
$[0, 0, 1, -4190473, 3301753090]$ |
\(y^2+y=x^3-4190473x+3301753090\) |
3478.2.0.? |
$[ ]$ |
| 81733.c1 |
81733c3 |
81733.c |
81733c |
$3$ |
$9$ |
\( 37 \cdot 47^{2} \) |
\( 37 \cdot 47^{6} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$3$ |
27.36.0.1 |
3B |
$93906$ |
$1296$ |
$43$ |
$10.21475293$ |
$1$ |
|
$0$ |
$633420$ |
$2.147156$ |
$727057727488000/37$ |
$1.08598$ |
$5.06762$ |
$[0, 1, 1, -4138193, 3238764355]$ |
\(y^2+y=x^3+x^2-4138193x+3238764355\) |
3.4.0.a.1, 9.12.0.a.1, 27.36.0.a.1, 74.2.0.?, 141.8.0.?, $\ldots$ |
$[(22597/6, 6439987/6)]$ |
| 81733.c2 |
81733c2 |
81733.c |
81733c |
$3$ |
$9$ |
\( 37 \cdot 47^{2} \) |
\( 37^{3} \cdot 47^{6} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$3$ |
9.36.0.2 |
3Cs |
$93906$ |
$1296$ |
$43$ |
$3.404917644$ |
$1$ |
|
$2$ |
$211140$ |
$1.597849$ |
$1404928000/50653$ |
$0.97274$ |
$3.90446$ |
$[0, 1, 1, -51543, 4344346]$ |
\(y^2+y=x^3+x^2-51543x+4344346\) |
3.12.0.a.1, 9.36.0.b.1, 74.2.0.?, 141.24.0.?, 222.24.1.?, $\ldots$ |
$[(-170, 2867)]$ |
| 81733.c3 |
81733c1 |
81733.c |
81733c |
$3$ |
$9$ |
\( 37 \cdot 47^{2} \) |
\( 37 \cdot 47^{6} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$3$ |
27.36.0.1 |
3B |
$93906$ |
$1296$ |
$43$ |
$10.21475293$ |
$1$ |
|
$0$ |
$70380$ |
$1.048544$ |
$4096000/37$ |
$0.88268$ |
$3.38836$ |
$[0, 1, 1, -7363, -243747]$ |
\(y^2+y=x^3+x^2-7363x-243747\) |
3.4.0.a.1, 9.12.0.a.1, 27.36.0.a.1, 74.2.0.?, 141.8.0.?, $\ldots$ |
$[(-40761/29, 967483/29)]$ |
