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 |
Weierstrass coefficients |
Weierstrass equation |
mod-$m$ images |
MW-generators |
12882.a1 |
12882b1 |
12882.a |
12882b |
$1$ |
$1$ |
\( 2 \cdot 3 \cdot 19 \cdot 113 \) |
\( 2 \cdot 3 \cdot 19 \cdot 113 \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
|
$51528$ |
$2$ |
$0$ |
$0.872280018$ |
$1$ |
|
$4$ |
$992$ |
$-0.514425$ |
$30664297/12882$ |
$[1, 1, 0, -6, -6]$ |
\(y^2+xy=x^3+x^2-6x-6\) |
51528.2.0.? |
$[(-1, 1)]$ |
12882.b1 |
12882d1 |
12882.b |
12882d |
$2$ |
$2$ |
\( 2 \cdot 3 \cdot 19 \cdot 113 \) |
\( 2^{6} \cdot 3 \cdot 19 \cdot 113 \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$2$ |
8.6.0.4 |
2B |
$51528$ |
$12$ |
$0$ |
$1.371532365$ |
$1$ |
|
$5$ |
$2496$ |
$-0.026100$ |
$251598106297/412224$ |
$[1, 1, 0, -131, 525]$ |
\(y^2+xy=x^3+x^2-131x+525\) |
2.3.0.a.1, 8.6.0.d.1, 12882.6.0.?, 51528.12.0.? |
$[(7, 0)]$ |
12882.b2 |
12882d2 |
12882.b |
12882d |
$2$ |
$2$ |
\( 2 \cdot 3 \cdot 19 \cdot 113 \) |
\( - 2^{3} \cdot 3^{2} \cdot 19^{2} \cdot 113^{2} \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$2$ |
8.6.0.5 |
2B |
$51528$ |
$12$ |
$0$ |
$0.685766182$ |
$1$ |
|
$6$ |
$4992$ |
$0.320474$ |
$-84778086457/331891848$ |
$[1, 1, 0, -91, 901]$ |
\(y^2+xy=x^3+x^2-91x+901\) |
2.3.0.a.1, 8.6.0.a.1, 25764.6.0.?, 51528.12.0.? |
$[(1, 28)]$ |
12882.c1 |
12882a1 |
12882.c |
12882a |
$1$ |
$1$ |
\( 2 \cdot 3 \cdot 19 \cdot 113 \) |
\( - 2^{7} \cdot 3^{3} \cdot 19 \cdot 113 \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
|
$51528$ |
$2$ |
$0$ |
$2.985689601$ |
$1$ |
|
$2$ |
$6384$ |
$0.088006$ |
$-193602111625/7420032$ |
$[1, 1, 0, -120, -576]$ |
\(y^2+xy=x^3+x^2-120x-576\) |
51528.2.0.? |
$[(13, 10)]$ |
12882.d1 |
12882c1 |
12882.d |
12882c |
$1$ |
$1$ |
\( 2 \cdot 3 \cdot 19 \cdot 113 \) |
\( - 2^{25} \cdot 3 \cdot 19^{5} \cdot 113 \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
|
$51528$ |
$2$ |
$0$ |
$6.308843499$ |
$1$ |
|
$0$ |
$162000$ |
$1.979385$ |
$-3111302831921821954873/28165508381540352$ |
$[1, 1, 0, -304139, -65188803]$ |
\(y^2+xy=x^3+x^2-304139x-65188803\) |
51528.2.0.? |
$[(13701/4, 1087005/4)]$ |
12882.e1 |
12882e1 |
12882.e |
12882e |
$2$ |
$2$ |
\( 2 \cdot 3 \cdot 19 \cdot 113 \) |
\( 2^{10} \cdot 3^{13} \cdot 19 \cdot 113^{4} \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$2$ |
8.6.0.4 |
2B |
$456$ |
$12$ |
$0$ |
$8.882293768$ |
$1$ |
|
$1$ |
$632320$ |
$2.288509$ |
$13403946614821979039929/5057590268826067968$ |
$[1, 1, 0, -494883, -79253235]$ |
\(y^2+xy=x^3+x^2-494883x-79253235\) |
2.3.0.a.1, 8.6.0.d.1, 114.6.0.?, 456.12.0.? |
$[(-193505/18, -9514385/18)]$ |
12882.e2 |
12882e2 |
12882.e |
12882e |
$2$ |
$2$ |
\( 2 \cdot 3 \cdot 19 \cdot 113 \) |
\( - 2^{5} \cdot 3^{26} \cdot 19^{2} \cdot 113^{2} \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$2$ |
8.6.0.5 |
2B |
$456$ |
$12$ |
$0$ |
$17.76458753$ |
$1$ |
|
$0$ |
$1264640$ |
$2.635082$ |
$410363075617640914325831/374944243169850027552$ |
$[1, 1, 0, 1548157, -563453715]$ |
\(y^2+xy=x^3+x^2+1548157x-563453715\) |
2.3.0.a.1, 8.6.0.a.1, 228.6.0.?, 456.12.0.? |
$[(142549591/630, 1518017170321/630)]$ |
12882.f1 |
12882i2 |
12882.f |
12882i |
$2$ |
$3$ |
\( 2 \cdot 3 \cdot 19 \cdot 113 \) |
\( 2^{45} \cdot 3^{3} \cdot 19^{3} \cdot 113 \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$3$ |
3.8.0.2 |
3B.1.2 |
$51528$ |
$16$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$609120$ |
$2.701450$ |
$1788952473315990499029625/736296634487918297088$ |
$[1, 0, 1, -2529056, -832121746]$ |
\(y^2+xy+y=x^3-2529056x-832121746\) |
3.8.0-3.a.1.1, 51528.16.0.? |
$[]$ |
12882.f2 |
12882i1 |
12882.f |
12882i |
$2$ |
$3$ |
\( 2 \cdot 3 \cdot 19 \cdot 113 \) |
\( 2^{15} \cdot 3^{9} \cdot 19 \cdot 113^{3} \) |
$0$ |
$\Z/3\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$3$ |
3.8.0.1 |
3B.1.1 |
$51528$ |
$16$ |
$0$ |
$1$ |
$1$ |
|
$2$ |
$203040$ |
$2.152145$ |
$177744208950637895247625/17681950027579392$ |
$[1, 0, 1, -1171361, 487820180]$ |
\(y^2+xy+y=x^3-1171361x+487820180\) |
3.8.0-3.a.1.2, 51528.16.0.? |
$[]$ |
12882.g1 |
12882h1 |
12882.g |
12882h |
$2$ |
$2$ |
\( 2 \cdot 3 \cdot 19 \cdot 113 \) |
\( 2^{18} \cdot 3^{3} \cdot 19^{3} \cdot 113 \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$2$ |
8.6.0.4 |
2B |
$51528$ |
$12$ |
$0$ |
$16.81161723$ |
$1$ |
|
$1$ |
$108864$ |
$1.767267$ |
$9153747013124116391113/5485837418496$ |
$[1, 0, 1, -435805, -110771464]$ |
\(y^2+xy+y=x^3-435805x-110771464\) |
2.3.0.a.1, 8.6.0.d.1, 12882.6.0.?, 51528.12.0.? |
$[(38460340/91, 234218339237/91)]$ |
12882.g2 |
12882h2 |
12882.g |
12882h |
$2$ |
$2$ |
\( 2 \cdot 3 \cdot 19 \cdot 113 \) |
\( - 2^{9} \cdot 3^{6} \cdot 19^{6} \cdot 113^{2} \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$2$ |
8.6.0.5 |
2B |
$51528$ |
$12$ |
$0$ |
$8.405808618$ |
$1$ |
|
$0$ |
$217728$ |
$2.113842$ |
$-8993380100968273380553/224220843480310272$ |
$[1, 0, 1, -433245, -112136456]$ |
\(y^2+xy+y=x^3-433245x-112136456\) |
2.3.0.a.1, 8.6.0.a.1, 25764.6.0.?, 51528.12.0.? |
$[(906704/7, 859650840/7)]$ |
12882.h1 |
12882g2 |
12882.h |
12882g |
$2$ |
$2$ |
\( 2 \cdot 3 \cdot 19 \cdot 113 \) |
\( 2^{3} \cdot 3^{6} \cdot 19^{6} \cdot 113 \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$2$ |
2.3.0.1 |
2B |
$51528$ |
$12$ |
$0$ |
$3.206978247$ |
$1$ |
|
$4$ |
$41472$ |
$1.285213$ |
$72312097990757113/31003988313096$ |
$[1, 0, 1, -8680, -159154]$ |
\(y^2+xy+y=x^3-8680x-159154\) |
2.3.0.a.1, 228.6.0.?, 904.6.0.?, 51528.12.0.? |
$[(-80, 197)]$ |
12882.h2 |
12882g1 |
12882.h |
12882g |
$2$ |
$2$ |
\( 2 \cdot 3 \cdot 19 \cdot 113 \) |
\( 2^{6} \cdot 3^{3} \cdot 19^{3} \cdot 113^{2} \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$2$ |
2.3.0.1 |
2B |
$51528$ |
$12$ |
$0$ |
$1.603489123$ |
$1$ |
|
$7$ |
$20736$ |
$0.938640$ |
$7958910549046393/151342682688$ |
$[1, 0, 1, -4160, 101198]$ |
\(y^2+xy+y=x^3-4160x+101198\) |
2.3.0.a.1, 114.6.0.?, 904.6.0.?, 51528.12.0.? |
$[(33, -5)]$ |
12882.i1 |
12882f1 |
12882.i |
12882f |
$1$ |
$1$ |
\( 2 \cdot 3 \cdot 19 \cdot 113 \) |
\( - 2^{12} \cdot 3 \cdot 19^{2} \cdot 113 \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
|
$678$ |
$2$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$6336$ |
$0.348290$ |
$-30664297/501264384$ |
$[1, 0, 1, -7, -1078]$ |
\(y^2+xy+y=x^3-7x-1078\) |
678.2.0.? |
$[]$ |
12882.j1 |
12882j1 |
12882.j |
12882j |
$1$ |
$1$ |
\( 2 \cdot 3 \cdot 19 \cdot 113 \) |
\( 2^{3} \cdot 3^{7} \cdot 19 \cdot 113 \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
|
$51528$ |
$2$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$4704$ |
$0.303982$ |
$8136367582897/37563912$ |
$[1, 1, 1, -419, -3463]$ |
\(y^2+xy+y=x^3+x^2-419x-3463\) |
51528.2.0.? |
$[]$ |
12882.k1 |
12882n1 |
12882.k |
12882n |
$1$ |
$1$ |
\( 2 \cdot 3 \cdot 19 \cdot 113 \) |
\( - 2^{13} \cdot 3^{7} \cdot 19^{3} \cdot 113 \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
|
$51528$ |
$2$ |
$0$ |
$0.061566823$ |
$1$ |
|
$14$ |
$48048$ |
$1.208658$ |
$13576487274110879/13886025965568$ |
$[1, 0, 0, 4970, -117724]$ |
\(y^2+xy=x^3+4970x-117724\) |
51528.2.0.? |
$[(140, 1754)]$ |
12882.l1 |
12882k1 |
12882.l |
12882k |
$1$ |
$1$ |
\( 2 \cdot 3 \cdot 19 \cdot 113 \) |
\( 2^{11} \cdot 3^{3} \cdot 19 \cdot 113 \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
|
$51528$ |
$2$ |
$0$ |
$0.150130726$ |
$1$ |
|
$8$ |
$11616$ |
$0.260647$ |
$496981290961/118720512$ |
$[1, 0, 0, -165, -639]$ |
\(y^2+xy=x^3-165x-639\) |
51528.2.0.? |
$[(-6, 15)]$ |
12882.m1 |
12882m1 |
12882.m |
12882m |
$1$ |
$1$ |
\( 2 \cdot 3 \cdot 19 \cdot 113 \) |
\( - 2 \cdot 3^{2} \cdot 19 \cdot 113 \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
|
$17176$ |
$2$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$1520$ |
$-0.439036$ |
$2924207/38646$ |
$[1, 0, 0, 3, -9]$ |
\(y^2+xy=x^3+3x-9\) |
17176.2.0.? |
$[]$ |
12882.n1 |
12882l1 |
12882.n |
12882l |
$1$ |
$1$ |
\( 2 \cdot 3 \cdot 19 \cdot 113 \) |
\( 2^{21} \cdot 3^{3} \cdot 19^{9} \cdot 113 \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
|
$51528$ |
$2$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$816480$ |
$2.784176$ |
$4387362075365553105987313/2064688435007280119808$ |
$[1, 0, 0, -3410567, -1048093047]$ |
\(y^2+xy=x^3-3410567x-1048093047\) |
51528.2.0.? |
$[]$ |