| 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 |
| 560.a1 |
560e1 |
560.a |
560e |
$1$ |
$1$ |
\( 2^{4} \cdot 5 \cdot 7 \) |
\( - 2^{8} \cdot 5 \cdot 7^{5} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$70$ |
$2$ |
$0$ |
$0.128582376$ |
$1$ |
|
$8$ |
$240$ |
$0.088933$ |
$14155776/84035$ |
$1.21697$ |
$3.83005$ |
$[0, 0, 0, 32, -212]$ |
\(y^2=x^3+32x-212\) |
70.2.0.a.1 |
$[(6, 14)]$ |
| 560.b1 |
560c3 |
560.b |
560c |
$3$ |
$9$ |
\( 2^{4} \cdot 5 \cdot 7 \) |
\( - 2^{12} \cdot 5^{9} \cdot 7 \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$3$ |
9.12.0.1 |
3B |
$1260$ |
$144$ |
$3$ |
$1$ |
$1$ |
|
$0$ |
$432$ |
$0.820609$ |
$-250523582464/13671875$ |
$1.02112$ |
$5.47646$ |
$[0, -1, 0, -2101, 39485]$ |
\(y^2=x^3-x^2-2101x+39485\) |
3.4.0.a.1, 9.12.0.a.1, 12.8.0-3.a.1.2, 36.24.0-9.a.1.1, 63.36.0.e.2, $\ldots$ |
$[]$ |
| 560.b2 |
560c1 |
560.b |
560c |
$3$ |
$9$ |
\( 2^{4} \cdot 5 \cdot 7 \) |
\( - 2^{12} \cdot 5 \cdot 7 \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$3$ |
9.12.0.1 |
3B |
$1260$ |
$144$ |
$3$ |
$1$ |
$1$ |
|
$0$ |
$48$ |
$-0.278003$ |
$-262144/35$ |
$0.88715$ |
$3.31893$ |
$[0, -1, 0, -21, -35]$ |
\(y^2=x^3-x^2-21x-35\) |
3.4.0.a.1, 9.12.0.a.1, 12.8.0-3.a.1.1, 36.24.0-9.a.1.2, 63.36.0.e.1, $\ldots$ |
$[]$ |
| 560.b3 |
560c2 |
560.b |
560c |
$3$ |
$9$ |
\( 2^{4} \cdot 5 \cdot 7 \) |
\( - 2^{12} \cdot 5^{3} \cdot 7^{3} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$3$ |
3.12.0.1 |
3Cs |
$1260$ |
$144$ |
$3$ |
$1$ |
$1$ |
|
$0$ |
$144$ |
$0.271303$ |
$71991296/42875$ |
$1.06493$ |
$4.17353$ |
$[0, -1, 0, 139, 61]$ |
\(y^2=x^3-x^2+139x+61\) |
3.12.0.a.1, 12.24.0-3.a.1.1, 63.36.0.b.1, 70.2.0.a.1, 210.24.1.?, $\ldots$ |
$[]$ |
| 560.c1 |
560f2 |
560.c |
560f |
$2$ |
$3$ |
\( 2^{4} \cdot 5 \cdot 7 \) |
\( - 2^{8} \cdot 5 \cdot 7^{3} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$3$ |
3.4.0.1 |
3B |
$420$ |
$16$ |
$0$ |
$0.337321606$ |
$1$ |
|
$6$ |
$144$ |
$0.257547$ |
$-225637236736/1715$ |
$1.02937$ |
$5.00754$ |
$[0, -1, 0, -805, 9065]$ |
\(y^2=x^3-x^2-805x+9065\) |
3.4.0.a.1, 12.8.0-3.a.1.2, 70.2.0.a.1, 210.8.0.?, 420.16.0.? |
$[(17, 2)]$ |
| 560.c2 |
560f1 |
560.c |
560f |
$2$ |
$3$ |
\( 2^{4} \cdot 5 \cdot 7 \) |
\( - 2^{8} \cdot 5^{3} \cdot 7 \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$3$ |
3.4.0.1 |
3B |
$420$ |
$16$ |
$0$ |
$0.112440535$ |
$1$ |
|
$8$ |
$48$ |
$-0.291759$ |
$-65536/875$ |
$0.97204$ |
$3.13160$ |
$[0, -1, 0, -5, 25]$ |
\(y^2=x^3-x^2-5x+25\) |
3.4.0.a.1, 12.8.0-3.a.1.1, 70.2.0.a.1, 210.8.0.?, 420.16.0.? |
$[(5, 10)]$ |
| 560.d1 |
560d4 |
560.d |
560d |
$4$ |
$4$ |
\( 2^{4} \cdot 5 \cdot 7 \) |
\( 2^{13} \cdot 5^{2} \cdot 7^{4} \) |
$1$ |
$\Z/4\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.24.0.49 |
2B |
$56$ |
$48$ |
$0$ |
$0.613941328$ |
$1$ |
|
$13$ |
$384$ |
$0.732135$ |
$2121328796049/120050$ |
$1.01959$ |
$5.79981$ |
$[0, 0, 0, -4283, 107882]$ |
\(y^2=x^3-4283x+107882\) |
2.3.0.a.1, 4.12.0-4.c.1.1, 8.24.0-8.k.1.2, 56.48.0-56.v.1.3 |
$[(37, 8)]$ |
| 560.d2 |
560d3 |
560.d |
560d |
$4$ |
$4$ |
\( 2^{4} \cdot 5 \cdot 7 \) |
\( 2^{13} \cdot 5^{8} \cdot 7 \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.24.0.101 |
2B |
$56$ |
$48$ |
$0$ |
$2.455765312$ |
$1$ |
|
$3$ |
$384$ |
$0.732135$ |
$74565301329/5468750$ |
$0.99962$ |
$5.27071$ |
$[0, 0, 0, -1403, -18902]$ |
\(y^2=x^3-1403x-18902\) |
2.3.0.a.1, 4.6.0.c.1, 8.24.0-8.p.1.5, 28.12.0-4.c.1.2, 56.48.0-56.bp.1.7 |
$[(-17, 6)]$ |
| 560.d3 |
560d2 |
560.d |
560d |
$4$ |
$4$ |
\( 2^{4} \cdot 5 \cdot 7 \) |
\( 2^{14} \cdot 5^{4} \cdot 7^{2} \) |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.24.0.2 |
2Cs |
$56$ |
$48$ |
$0$ |
$1.227882656$ |
$1$ |
|
$11$ |
$192$ |
$0.385561$ |
$611960049/122500$ |
$1.02632$ |
$4.51173$ |
$[0, 0, 0, -283, 1482]$ |
\(y^2=x^3-283x+1482\) |
2.6.0.a.1, 4.12.0-2.a.1.1, 8.24.0-8.a.1.1, 28.24.0-28.b.1.2, 56.48.0-56.d.1.1 |
$[(-3, 48)]$ |
| 560.d4 |
560d1 |
560.d |
560d |
$4$ |
$4$ |
\( 2^{4} \cdot 5 \cdot 7 \) |
\( - 2^{16} \cdot 5^{2} \cdot 7 \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.24.0.60 |
2B |
$56$ |
$48$ |
$0$ |
$0.613941328$ |
$1$ |
|
$7$ |
$96$ |
$0.038988$ |
$1367631/2800$ |
$1.00023$ |
$3.69436$ |
$[0, 0, 0, 37, 138]$ |
\(y^2=x^3+37x+138\) |
2.3.0.a.1, 4.12.0-4.c.1.2, 8.24.0-8.p.1.3, 14.6.0.b.1, 28.24.0-28.g.1.1, $\ldots$ |
$[(-1, 10)]$ |
| 560.e1 |
560a1 |
560.e |
560a |
$1$ |
$1$ |
\( 2^{4} \cdot 5 \cdot 7 \) |
\( - 2^{8} \cdot 5 \cdot 7 \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$70$ |
$2$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$32$ |
$-0.561331$ |
$-1024/35$ |
$0.78213$ |
$2.61887$ |
$[0, 1, 0, -1, -5]$ |
\(y^2=x^3+x^2-x-5\) |
70.2.0.a.1 |
$[]$ |
| 560.f1 |
560b1 |
560.f |
560b |
$1$ |
$1$ |
\( 2^{4} \cdot 5 \cdot 7 \) |
\( - 2^{8} \cdot 5^{5} \cdot 7^{3} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$70$ |
$2$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$480$ |
$0.391470$ |
$-30211716096/1071875$ |
$1.00205$ |
$4.69919$ |
$[0, 0, 0, -412, -3316]$ |
\(y^2=x^3-412x-3316\) |
70.2.0.a.1 |
$[]$ |
