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 |
890.a1 |
890b2 |
890.a |
890b |
$2$ |
$2$ |
\( 2 \cdot 5 \cdot 89 \) |
\( 2^{2} \cdot 5 \cdot 89^{2} \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$2$ |
2.3.0.1 |
2B |
$1780$ |
$12$ |
$0$ |
$0.851103202$ |
$1$ |
|
$6$ |
$192$ |
$-0.088189$ |
$141339344329/158420$ |
$0.87673$ |
$3.78053$ |
$[1, 0, 1, -109, -444]$ |
\(y^2+xy+y=x^3-109x-444\) |
2.3.0.a.1, 10.6.0.a.1, 356.6.0.?, 1780.12.0.? |
$[(-6, 3)]$ |
890.a2 |
890b1 |
890.a |
890b |
$2$ |
$2$ |
\( 2 \cdot 5 \cdot 89 \) |
\( 2^{4} \cdot 5^{2} \cdot 89 \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$2$ |
2.3.0.1 |
2B |
$1780$ |
$12$ |
$0$ |
$0.425551601$ |
$1$ |
|
$9$ |
$96$ |
$-0.434763$ |
$68417929/35600$ |
$0.82844$ |
$2.65654$ |
$[1, 0, 1, -9, -4]$ |
\(y^2+xy+y=x^3-9x-4\) |
2.3.0.a.1, 20.6.0.c.1, 178.6.0.?, 1780.12.0.? |
$[(-2, 3)]$ |
890.b1 |
890e1 |
890.b |
890e |
$2$ |
$2$ |
\( 2 \cdot 5 \cdot 89 \) |
\( 2^{12} \cdot 5^{4} \cdot 89 \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$2$ |
8.12.0.21 |
2B |
$712$ |
$48$ |
$0$ |
$0.880929457$ |
$1$ |
|
$7$ |
$576$ |
$0.507392$ |
$162780279643801/227840000$ |
$0.93075$ |
$4.81849$ |
$[1, 0, 1, -1138, -14844]$ |
\(y^2+xy+y=x^3-1138x-14844\) |
2.3.0.a.1, 4.6.0.b.1, 8.12.0-4.b.1.3, 178.6.0.?, 356.24.0.?, $\ldots$ |
$[(-20, 7)]$ |
890.b2 |
890e2 |
890.b |
890e |
$2$ |
$2$ |
\( 2 \cdot 5 \cdot 89 \) |
\( - 2^{6} \cdot 5^{8} \cdot 89^{2} \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$2$ |
4.12.0.12 |
2B |
$712$ |
$48$ |
$0$ |
$0.440464728$ |
$1$ |
|
$12$ |
$1152$ |
$0.853965$ |
$-60425492474521/198025000000$ |
$0.95315$ |
$4.95183$ |
$[1, 0, 1, -818, -23292]$ |
\(y^2+xy+y=x^3-818x-23292\) |
2.3.0.a.1, 4.12.0-4.a.1.1, 356.24.0.?, 712.48.0.? |
$[(69, 465)]$ |
890.c1 |
890a2 |
890.c |
890a |
$2$ |
$2$ |
\( 2 \cdot 5 \cdot 89 \) |
\( 2 \cdot 5 \cdot 89^{2} \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$2$ |
2.3.0.1 |
2B |
$3560$ |
$12$ |
$0$ |
$1.025400975$ |
$1$ |
|
$4$ |
$128$ |
$-0.206056$ |
$18588565449/79210$ |
$0.96908$ |
$3.48182$ |
$[1, -1, 0, -55, 171]$ |
\(y^2+xy=x^3-x^2-55x+171\) |
2.3.0.a.1, 40.6.0.b.1, 356.6.0.?, 3560.12.0.? |
$[(5, -1)]$ |
890.c2 |
890a1 |
890.c |
890a |
$2$ |
$2$ |
\( 2 \cdot 5 \cdot 89 \) |
\( 2^{2} \cdot 5^{2} \cdot 89 \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$2$ |
2.3.0.1 |
2B |
$3560$ |
$12$ |
$0$ |
$0.512700487$ |
$1$ |
|
$7$ |
$64$ |
$-0.552629$ |
$15438249/8900$ |
$1.07701$ |
$2.43732$ |
$[1, -1, 0, -5, 1]$ |
\(y^2+xy=x^3-x^2-5x+1\) |
2.3.0.a.1, 40.6.0.c.1, 178.6.0.?, 3560.12.0.? |
$[(0, 1)]$ |
890.d1 |
890d1 |
890.d |
890d |
$1$ |
$1$ |
\( 2 \cdot 5 \cdot 89 \) |
\( - 2^{3} \cdot 5 \cdot 89 \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
|
$3560$ |
$2$ |
$0$ |
$0.449162415$ |
$1$ |
|
$4$ |
$72$ |
$-0.518641$ |
$-217081801/3560$ |
$0.80433$ |
$2.83067$ |
$[1, 0, 1, -13, 16]$ |
\(y^2+xy+y=x^3-13x+16\) |
3560.2.0.? |
$[(2, -1)]$ |
890.e1 |
890c2 |
890.e |
890c |
$2$ |
$2$ |
\( 2 \cdot 5 \cdot 89 \) |
\( 2 \cdot 5^{4} \cdot 89^{2} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$2$ |
8.6.0.6 |
2B |
$712$ |
$12$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$896$ |
$0.706430$ |
$32795348404864969/9901250$ |
$0.96080$ |
$5.59974$ |
$[1, 1, 0, -6668, 206822]$ |
\(y^2+xy=x^3+x^2-6668x+206822\) |
2.3.0.a.1, 8.6.0.b.1, 356.6.0.?, 712.12.0.? |
$[]$ |
890.e2 |
890c1 |
890.e |
890c |
$2$ |
$2$ |
\( 2 \cdot 5 \cdot 89 \) |
\( 2^{2} \cdot 5^{8} \cdot 89 \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$2$ |
8.6.0.1 |
2B |
$712$ |
$12$ |
$0$ |
$1$ |
$1$ |
|
$1$ |
$448$ |
$0.359857$ |
$8107275964969/139062500$ |
$0.91053$ |
$4.37679$ |
$[1, 1, 0, -418, 3072]$ |
\(y^2+xy=x^3+x^2-418x+3072\) |
2.3.0.a.1, 8.6.0.c.1, 178.6.0.?, 712.12.0.? |
$[]$ |
890.f1 |
890f1 |
890.f |
890f |
$1$ |
$1$ |
\( 2 \cdot 5 \cdot 89 \) |
\( - 2^{13} \cdot 5 \cdot 89 \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
|
$3560$ |
$2$ |
$0$ |
$0.090346383$ |
$1$ |
|
$10$ |
$312$ |
$-0.060440$ |
$206425071/3645440$ |
$1.00372$ |
$3.31758$ |
$[1, -1, 1, 12, 87]$ |
\(y^2+xy+y=x^3-x^2+12x+87\) |
3560.2.0.? |
$[(5, 13)]$ |
890.g1 |
890g2 |
890.g |
890g |
$2$ |
$5$ |
\( 2 \cdot 5 \cdot 89 \) |
\( - 2 \cdot 5 \cdot 89^{5} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$5$ |
5.24.0.3 |
5B.1.2 |
$3560$ |
$48$ |
$1$ |
$7.965230967$ |
$1$ |
|
$0$ |
$1000$ |
$0.817688$ |
$-938917686360961/55840594490$ |
$0.94287$ |
$5.09092$ |
$[1, 1, 1, -2040, -38093]$ |
\(y^2+xy+y=x^3+x^2-2040x-38093\) |
5.24.0-5.a.2.2, 3560.48.1.? |
$[(1915/6, 12823/6)]$ |
890.g2 |
890g1 |
890.g |
890g |
$2$ |
$5$ |
\( 2 \cdot 5 \cdot 89 \) |
\( - 2^{5} \cdot 5^{5} \cdot 89 \) |
$1$ |
$\Z/5\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$5$ |
5.24.0.1 |
5B.1.1 |
$3560$ |
$48$ |
$1$ |
$1.593046193$ |
$1$ |
|
$12$ |
$200$ |
$0.012969$ |
$109902239/8900000$ |
$0.90965$ |
$3.45286$ |
$[1, 1, 1, 10, 147]$ |
\(y^2+xy+y=x^3+x^2+10x+147\) |
5.24.0-5.a.1.2, 3560.48.1.? |
$[(-5, 3)]$ |
890.h1 |
890h3 |
890.h |
890h |
$4$ |
$4$ |
\( 2 \cdot 5 \cdot 89 \) |
\( 2^{2} \cdot 5^{8} \cdot 89 \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$2$ |
8.24.0.57 |
2B |
$7120$ |
$192$ |
$3$ |
$1$ |
$1$ |
|
$0$ |
$640$ |
$0.566391$ |
$772635063744081/139062500$ |
$1.00068$ |
$5.04781$ |
$[1, -1, 1, -1912, -31689]$ |
\(y^2+xy+y=x^3-x^2-1912x-31689\) |
2.3.0.a.1, 4.12.0-4.c.1.2, 8.24.0-8.o.1.3, 80.48.0.?, 178.6.0.?, $\ldots$ |
$[]$ |
890.h2 |
890h2 |
890.h |
890h |
$4$ |
$4$ |
\( 2 \cdot 5 \cdot 89 \) |
\( 2^{4} \cdot 5^{4} \cdot 89^{2} \) |
$0$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$2$ |
4.24.0.7 |
2Cs |
$3560$ |
$192$ |
$3$ |
$1$ |
$1$ |
|
$2$ |
$320$ |
$0.219818$ |
$252555814161/79210000$ |
$1.04647$ |
$3.86601$ |
$[1, -1, 1, -132, -361]$ |
\(y^2+xy+y=x^3-x^2-132x-361\) |
2.6.0.a.1, 4.24.0-4.a.1.1, 40.48.0-40.k.1.2, 356.48.0.?, 712.96.0.?, $\ldots$ |
$[]$ |
890.h3 |
890h1 |
890.h |
890h |
$4$ |
$4$ |
\( 2 \cdot 5 \cdot 89 \) |
\( 2^{8} \cdot 5^{2} \cdot 89 \) |
$0$ |
$\Z/4\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$2$ |
8.24.0.47 |
2B |
$7120$ |
$192$ |
$3$ |
$1$ |
$1$ |
|
$3$ |
$160$ |
$-0.126756$ |
$15271450641/569600$ |
$0.87612$ |
$3.45288$ |
$[1, -1, 1, -52, 151]$ |
\(y^2+xy+y=x^3-x^2-52x+151\) |
2.3.0.a.1, 4.12.0-4.c.1.1, 8.24.0-8.o.1.1, 80.48.0.?, 178.6.0.?, $\ldots$ |
$[]$ |
890.h4 |
890h4 |
890.h |
890h |
$4$ |
$4$ |
\( 2 \cdot 5 \cdot 89 \) |
\( - 2^{2} \cdot 5^{2} \cdot 89^{4} \) |
$0$ |
$\Z/4\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$2$ |
4.24.0.11 |
2B |
$7120$ |
$192$ |
$3$ |
$1$ |
$4$ |
$2$ |
$2$ |
$640$ |
$0.566391$ |
$5525519137839/6274224100$ |
$0.95675$ |
$4.32034$ |
$[1, -1, 1, 368, -2761]$ |
\(y^2+xy+y=x^3-x^2+368x-2761\) |
2.3.0.a.1, 4.24.0-4.d.1.1, 20.48.0-20.d.1.2, 712.48.0.?, 1424.96.0.?, $\ldots$ |
$[]$ |