| 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 |
Intrinsic torsion order |
Weierstrass coefficients |
Weierstrass equation |
mod-$m$ images |
MW-generators |
Manin constant |
| 370.a1 |
370c3 |
370.a |
370c |
$3$ |
$9$ |
\( 2 \cdot 5 \cdot 37 \) |
\( - 2 \cdot 5 \cdot 37 \) |
$0$ |
$\Z/3\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$3$ |
9.24.0.1 |
3B.1.1 |
$13320$ |
$144$ |
$3$ |
$1$ |
$1$ |
|
$2$ |
$324$ |
$-0.391213$ |
$-16954786009/370$ |
$0.88414$ |
$3.98306$ |
$3$ |
$[1, 0, 1, -54, 146]$ |
\(y^2+xy+y=x^3-54x+146\) |
3.8.0-3.a.1.2, 9.24.0-9.a.1.2, 333.72.0.?, 1480.2.0.?, 4440.16.0.?, $\ldots$ |
$[ ]$ |
$3$ |
| 370.a2 |
370c1 |
370.a |
370c |
$3$ |
$9$ |
\( 2 \cdot 5 \cdot 37 \) |
\( - 2^{3} \cdot 5^{3} \cdot 37^{3} \) |
$0$ |
$\Z/3\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$3$ |
3.24.0.1 |
3Cs.1.1 |
$13320$ |
$144$ |
$3$ |
$1$ |
$1$ |
|
$2$ |
$108$ |
$0.158093$ |
$-702595369/50653000$ |
$0.95453$ |
$4.26198$ |
$1$ |
$[1, 0, 1, -19, 342]$ |
\(y^2+xy+y=x^3-19x+342\) |
3.24.0-3.a.1.1, 333.72.0.?, 1480.2.0.?, 4440.48.1.?, 13320.144.3.? |
$[ ]$ |
$1$ |
| 370.a3 |
370c2 |
370.a |
370c |
$3$ |
$9$ |
\( 2 \cdot 5 \cdot 37 \) |
\( - 2^{9} \cdot 5^{9} \cdot 37 \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$3$ |
9.24.0.3 |
3B.1.2 |
$13320$ |
$144$ |
$3$ |
$1$ |
$1$ |
|
$0$ |
$324$ |
$0.707399$ |
$510273943271/37000000000$ |
$0.99687$ |
$5.37429$ |
$1$ |
$[1, 0, 1, 166, -9204]$ |
\(y^2+xy+y=x^3+166x-9204\) |
3.8.0-3.a.1.1, 9.24.0-9.a.1.1, 333.72.0.?, 1480.2.0.?, 4440.16.0.?, $\ldots$ |
$[ ]$ |
$1$ |
| 370.b1 |
370a3 |
370.b |
370a |
$4$ |
$4$ |
\( 2 \cdot 5 \cdot 37 \) |
\( 2 \cdot 5^{4} \cdot 37 \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$2$ |
8.12.0.7 |
2B |
$1480$ |
$48$ |
$0$ |
$2.419964833$ |
$1$ |
|
$2$ |
$64$ |
$0.076511$ |
$6825481747209/46250$ |
$0.96373$ |
$4.99732$ |
$2$ |
$[1, -1, 0, -395, -2925]$ |
\(y^2+xy=x^3-x^2-395x-2925\) |
2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.3, 40.24.0-40.y.1.6, 148.12.0.?, $\ldots$ |
$[(45, 240)]$ |
$1$ |
| 370.b2 |
370a2 |
370.b |
370a |
$4$ |
$4$ |
\( 2 \cdot 5 \cdot 37 \) |
\( 2^{2} \cdot 5^{2} \cdot 37^{2} \) |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$2$ |
8.12.0.1 |
2Cs |
$1480$ |
$48$ |
$0$ |
$1.209982416$ |
$1$ |
|
$8$ |
$32$ |
$-0.270063$ |
$1767172329/136900$ |
$0.99471$ |
$3.60068$ |
$1$ |
$[1, -1, 0, -25, -39]$ |
\(y^2+xy=x^3-x^2-25x-39\) |
2.6.0.a.1, 8.12.0-2.a.1.1, 20.12.0-2.a.1.1, 40.24.0-40.b.1.3, 148.12.0.?, $\ldots$ |
$[(-3, 3)]$ |
$1$ |
| 370.b3 |
370a1 |
370.b |
370a |
$4$ |
$4$ |
\( 2 \cdot 5 \cdot 37 \) |
\( 2^{4} \cdot 5 \cdot 37 \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$2$ |
8.12.0.12 |
2B |
$1480$ |
$48$ |
$0$ |
$0.604991208$ |
$1$ |
|
$7$ |
$16$ |
$-0.616636$ |
$15438249/2960$ |
$0.81779$ |
$2.79908$ |
$2$ |
$[1, -1, 0, -5, 5]$ |
\(y^2+xy=x^3-x^2-5x+5\) |
2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.2, 20.12.0-4.c.1.2, 40.24.0-40.y.1.9, $\ldots$ |
$[(1, 0)]$ |
$1$ |
| 370.b4 |
370a4 |
370.b |
370a |
$4$ |
$4$ |
\( 2 \cdot 5 \cdot 37 \) |
\( - 2 \cdot 5 \cdot 37^{4} \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$2$ |
8.12.0.8 |
2B |
$1480$ |
$48$ |
$0$ |
$2.419964833$ |
$1$ |
|
$2$ |
$64$ |
$0.076511$ |
$1689410871/18741610$ |
$1.06786$ |
$4.08343$ |
$2$ |
$[1, -1, 0, 25, -209]$ |
\(y^2+xy=x^3-x^2+25x-209\) |
2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.4, 20.12.0-4.c.1.1, 40.24.0-40.s.1.4, $\ldots$ |
$[(7, 13)]$ |
$1$ |
| 370.c1 |
370b1 |
370.c |
370b |
$1$ |
$1$ |
\( 2 \cdot 5 \cdot 37 \) |
\( - 2^{11} \cdot 5 \cdot 37 \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
|
$1480$ |
$2$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$44$ |
$-0.244730$ |
$214921799/378880$ |
$0.86906$ |
$3.36548$ |
$1$ |
$[1, 1, 0, 13, -19]$ |
\(y^2+xy=x^3+x^2+13x-19\) |
1480.2.0.? |
$[ ]$ |
$1$ |
| 370.d1 |
370d3 |
370.d |
370d |
$4$ |
$6$ |
\( 2 \cdot 5 \cdot 37 \) |
\( 2^{4} \cdot 5 \cdot 37^{3} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$2, 3$ |
8.12.0.21, 3.8.0.2 |
2B, 3B.1.2 |
$4440$ |
$384$ |
$9$ |
$1$ |
$1$ |
|
$1$ |
$288$ |
$0.643508$ |
$16232905099479601/4052240$ |
$0.97924$ |
$6.31196$ |
$2$ |
$[1, 0, 0, -5275, -147903]$ |
\(y^2+xy=x^3-5275x-147903\) |
2.3.0.a.1, 3.8.0-3.a.1.1, 4.6.0.b.1, 6.24.0-6.a.1.2, 8.12.0-4.b.1.3, $\ldots$ |
$[ ]$ |
$1$ |
| 370.d2 |
370d4 |
370.d |
370d |
$4$ |
$6$ |
\( 2 \cdot 5 \cdot 37 \) |
\( - 2^{2} \cdot 5^{2} \cdot 37^{6} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$2, 3$ |
4.12.0.12, 3.8.0.2 |
2B, 3B.1.2 |
$4440$ |
$384$ |
$9$ |
$1$ |
$1$ |
|
$0$ |
$576$ |
$0.990082$ |
$-16048965315233521/256572640900$ |
$0.97955$ |
$6.31464$ |
$1$ |
$[1, 0, 0, -5255, -149075]$ |
\(y^2+xy=x^3-5255x-149075\) |
2.3.0.a.1, 3.8.0-3.a.1.1, 4.12.0-4.a.1.1, 6.24.0-6.a.1.2, 12.96.0-12.b.2.7, $\ldots$ |
$[ ]$ |
$1$ |
| 370.d3 |
370d1 |
370.d |
370d |
$4$ |
$6$ |
\( 2 \cdot 5 \cdot 37 \) |
\( 2^{12} \cdot 5^{3} \cdot 37 \) |
$0$ |
$\Z/6\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$2, 3$ |
8.12.0.21, 3.8.0.1 |
2B, 3B.1.1 |
$4440$ |
$384$ |
$9$ |
$1$ |
$1$ |
|
$5$ |
$96$ |
$0.094202$ |
$46694890801/18944000$ |
$0.91392$ |
$4.15437$ |
$2$ |
$[1, 0, 0, -75, -143]$ |
\(y^2+xy=x^3-75x-143\) |
2.3.0.a.1, 3.8.0-3.a.1.2, 4.6.0.b.1, 6.24.0-6.a.1.4, 8.12.0-4.b.1.3, $\ldots$ |
$[ ]$ |
$1$ |
| 370.d4 |
370d2 |
370.d |
370d |
$4$ |
$6$ |
\( 2 \cdot 5 \cdot 37 \) |
\( - 2^{6} \cdot 5^{6} \cdot 37^{2} \) |
$0$ |
$\Z/6\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$2, 3$ |
4.12.0.12, 3.8.0.1 |
2B, 3B.1.1 |
$4440$ |
$384$ |
$9$ |
$1$ |
$1$ |
|
$4$ |
$192$ |
$0.440775$ |
$1625964918479/1369000000$ |
$0.94818$ |
$4.75473$ |
$1$ |
$[1, 0, 0, 245, -975]$ |
\(y^2+xy=x^3+245x-975\) |
2.3.0.a.1, 3.8.0-3.a.1.2, 4.12.0-4.a.1.1, 6.24.0-6.a.1.4, 12.96.0-12.b.1.3, $\ldots$ |
$[ ]$ |
$1$ |
