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 |
425.a1 |
425d1 |
425.a |
425d |
$2$ |
$2$ |
\( 5^{2} \cdot 17 \) |
\( 5^{8} \cdot 17 \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
4.6.0.3 |
2B |
$680$ |
$48$ |
$0$ |
$1.629233938$ |
$1$ |
|
$7$ |
$96$ |
$0.147032$ |
$68417929/425$ |
$0.84846$ |
$4.57656$ |
$[1, 0, 0, -213, -1208]$ |
\(y^2+xy=x^3-213x-1208\) |
2.3.0.a.1, 4.6.0.b.1, 34.6.0.a.1, 40.12.0-4.b.1.2, 68.12.0.e.1, $\ldots$ |
$[(-9, 5)]$ |
425.a2 |
425d2 |
425.a |
425d |
$2$ |
$2$ |
\( 5^{2} \cdot 17 \) |
\( - 5^{10} \cdot 17^{2} \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
4.6.0.5 |
2B |
$680$ |
$48$ |
$0$ |
$0.814616969$ |
$1$ |
|
$8$ |
$192$ |
$0.493605$ |
$-4826809/180625$ |
$1.05314$ |
$4.82988$ |
$[1, 0, 0, -88, -2583]$ |
\(y^2+xy=x^3-88x-2583\) |
2.3.0.a.1, 4.6.0.a.1, 40.12.0-4.a.1.1, 68.12.0.d.1, 136.24.0.?, $\ldots$ |
$[(37, 194)]$ |
425.b1 |
425c1 |
425.b |
425c |
$1$ |
$1$ |
\( 5^{2} \cdot 17 \) |
\( - 5^{2} \cdot 17 \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$68$ |
$2$ |
$0$ |
$0.274350700$ |
$1$ |
|
$4$ |
$12$ |
$-0.764193$ |
$-121945/17$ |
$0.76627$ |
$2.50261$ |
$[1, 0, 0, -3, 2]$ |
\(y^2+xy=x^3-3x+2\) |
68.2.0.a.1 |
$[(1, 0)]$ |
425.c1 |
425b1 |
425.c |
425b |
$1$ |
$1$ |
\( 5^{2} \cdot 17 \) |
\( - 5^{8} \cdot 17 \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$68$ |
$2$ |
$0$ |
$0.282380024$ |
$1$ |
|
$4$ |
$60$ |
$0.040527$ |
$-121945/17$ |
$0.76627$ |
$4.09820$ |
$[1, 1, 0, -75, 250]$ |
\(y^2+xy=x^3+x^2-75x+250\) |
68.2.0.a.1 |
$[(10, 20)]$ |
425.d1 |
425a3 |
425.d |
425a |
$4$ |
$4$ |
\( 5^{2} \cdot 17 \) |
\( 5^{6} \cdot 17 \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
32.48.0.12 |
2B |
$5440$ |
$1536$ |
$53$ |
$6.003812221$ |
$1$ |
|
$0$ |
$128$ |
$0.428083$ |
$82483294977/17$ |
$1.03131$ |
$5.74884$ |
$[1, -1, 0, -2267, -40984]$ |
\(y^2+xy=x^3-x^2-2267x-40984\) |
2.3.0.a.1, 4.6.0.c.1, 8.12.0.o.1, 16.24.0.j.1, 20.12.0-4.c.1.1, $\ldots$ |
$[(1589/4, 50597/4)]$ |
425.d2 |
425a2 |
425.d |
425a |
$4$ |
$4$ |
\( 5^{2} \cdot 17 \) |
\( 5^{6} \cdot 17^{2} \) |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
16.48.0.20 |
2Cs |
$2720$ |
$1536$ |
$53$ |
$3.001906110$ |
$1$ |
|
$4$ |
$64$ |
$0.081509$ |
$20346417/289$ |
$1.02963$ |
$4.37618$ |
$[1, -1, 0, -142, -609]$ |
\(y^2+xy=x^3-x^2-142x-609\) |
2.6.0.a.1, 4.12.0.a.1, 8.24.0.f.1, 16.48.0.c.2, 20.24.0-4.a.1.1, $\ldots$ |
$[(94, 853)]$ |
425.d3 |
425a4 |
425.d |
425a |
$4$ |
$4$ |
\( 5^{2} \cdot 17 \) |
\( - 5^{6} \cdot 17^{4} \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
16.48.0.76 |
2B |
$5440$ |
$1536$ |
$53$ |
$1.500953055$ |
$1$ |
|
$4$ |
$128$ |
$0.428083$ |
$-35937/83521$ |
$1.18071$ |
$4.69994$ |
$[1, -1, 0, -17, -1734]$ |
\(y^2+xy=x^3-x^2-17x-1734\) |
2.3.0.a.1, 4.12.0.d.1, 8.24.0.t.1, 16.48.0.m.2, 20.24.0-4.d.1.1, $\ldots$ |
$[(14, 18)]$ |
425.d4 |
425a1 |
425.d |
425a |
$4$ |
$4$ |
\( 5^{2} \cdot 17 \) |
\( 5^{6} \cdot 17 \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
32.48.0.12 |
2B |
$5440$ |
$1536$ |
$53$ |
$1.500953055$ |
$1$ |
|
$3$ |
$32$ |
$-0.265064$ |
$35937/17$ |
$1.02432$ |
$3.32879$ |
$[1, -1, 0, -17, 16]$ |
\(y^2+xy=x^3-x^2-17x+16\) |
2.3.0.a.1, 4.6.0.c.1, 8.12.0.o.1, 16.24.0.j.1, 20.12.0-4.c.1.2, $\ldots$ |
$[(0, 4)]$ |