| 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 |
| 663.a1 |
663b5 |
663.a |
663b |
$6$ |
$8$ |
\( 3 \cdot 13 \cdot 17 \) |
\( 3^{16} \cdot 13 \cdot 17^{2} \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$2$ |
16.48.0.47 |
2B |
$3536$ |
$192$ |
$1$ |
$2.975812071$ |
$1$ |
|
$0$ |
$1024$ |
$1.155155$ |
$908031902324522977/161726530797$ |
$0.99284$ |
$6.36470$ |
$[1, 1, 1, -20174, -1111138]$ |
\(y^2+xy+y=x^3+x^2-20174x-1111138\) |
2.3.0.a.1, 4.12.0-4.c.1.2, 8.24.0-8.n.1.6, 16.48.0-16.f.2.11, 26.6.0.b.1, $\ldots$ |
$[(-329/2, 427/2)]$ |
| 663.a2 |
663b3 |
663.a |
663b |
$6$ |
$8$ |
\( 3 \cdot 13 \cdot 17 \) |
\( 3^{8} \cdot 13^{2} \cdot 17^{4} \) |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$2$ |
8.48.0.33 |
2Cs |
$1768$ |
$192$ |
$1$ |
$1.487906035$ |
$1$ |
|
$6$ |
$512$ |
$0.808582$ |
$296380748763217/92608836489$ |
$0.96390$ |
$5.12911$ |
$[1, 1, 1, -1389, -14094]$ |
\(y^2+xy+y=x^3+x^2-1389x-14094\) |
2.6.0.a.1, 4.24.0-4.b.1.1, 8.48.0-8.d.2.2, 52.48.0-52.c.1.2, 104.96.0.?, $\ldots$ |
$[(-27, 81)]$ |
| 663.a3 |
663b2 |
663.a |
663b |
$6$ |
$8$ |
\( 3 \cdot 13 \cdot 17 \) |
\( 3^{4} \cdot 13^{4} \cdot 17^{2} \) |
$1$ |
$\Z/2\Z\oplus\Z/4\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$2$ |
8.48.0.27 |
2Cs |
$1768$ |
$192$ |
$1$ |
$2.975812071$ |
$1$ |
|
$10$ |
$256$ |
$0.462009$ |
$17806161424897/668584449$ |
$0.93643$ |
$4.69626$ |
$[1, 1, 1, -544, 4496]$ |
\(y^2+xy+y=x^3+x^2-544x+4496\) |
2.6.0.a.1, 4.24.0-4.b.1.3, 8.48.0-8.d.1.10, 68.48.0-68.c.1.1, 104.96.0.?, $\ldots$ |
$[(79, 640)]$ |
| 663.a4 |
663b1 |
663.a |
663b |
$6$ |
$8$ |
\( 3 \cdot 13 \cdot 17 \) |
\( 3^{2} \cdot 13^{2} \cdot 17 \) |
$1$ |
$\Z/4\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$2$ |
16.48.0.31 |
2B |
$3536$ |
$192$ |
$1$ |
$1.487906035$ |
$1$ |
|
$7$ |
$128$ |
$0.115435$ |
$17319700013617/25857$ |
$0.93528$ |
$4.69200$ |
$[1, 1, 1, -539, 4592]$ |
\(y^2+xy+y=x^3+x^2-539x+4592\) |
2.3.0.a.1, 4.12.0-4.c.1.1, 8.24.0-8.n.1.2, 16.48.0-16.f.1.4, 34.6.0.a.1, $\ldots$ |
$[(9, 19)]$ |
| 663.a5 |
663b4 |
663.a |
663b |
$6$ |
$8$ |
\( 3 \cdot 13 \cdot 17 \) |
\( - 3^{2} \cdot 13^{8} \cdot 17 \) |
$1$ |
$\Z/4\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$2$ |
8.48.0.162 |
2B |
$3536$ |
$192$ |
$1$ |
$1.487906035$ |
$1$ |
|
$8$ |
$512$ |
$0.808582$ |
$1193377118543/124806800313$ |
$1.00139$ |
$5.07932$ |
$[1, 1, 1, 221, 17042]$ |
\(y^2+xy+y=x^3+x^2+221x+17042\) |
2.3.0.a.1, 4.12.0-4.c.1.1, 8.48.0-8.ba.1.2, 68.24.0-68.h.1.2, 136.96.0.?, $\ldots$ |
$[(6, 133)]$ |
| 663.a6 |
663b6 |
663.a |
663b |
$6$ |
$8$ |
\( 3 \cdot 13 \cdot 17 \) |
\( - 3^{4} \cdot 13 \cdot 17^{8} \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$2$ |
8.48.0.178 |
2B |
$3536$ |
$192$ |
$1$ |
$0.743953017$ |
$1$ |
|
$4$ |
$1024$ |
$1.155155$ |
$6439735268725823/7345472585373$ |
$0.98854$ |
$5.60297$ |
$[1, 1, 1, 3876, -89910]$ |
\(y^2+xy+y=x^3+x^2+3876x-89910\) |
2.3.0.a.1, 4.12.0-4.c.1.2, 8.48.0-8.ba.2.6, 52.24.0-52.h.1.1, 104.96.0.?, $\ldots$ |
$[(25, 140)]$ |
| 663.b1 |
663c2 |
663.b |
663c |
$2$ |
$2$ |
\( 3 \cdot 13 \cdot 17 \) |
\( 3^{8} \cdot 13 \cdot 17^{2} \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$2$ |
2.3.0.1 |
2B |
$884$ |
$12$ |
$0$ |
$0.204192024$ |
$1$ |
|
$10$ |
$128$ |
$0.129896$ |
$104154702625/24649677$ |
$0.90385$ |
$3.90488$ |
$[1, 0, 0, -98, 279]$ |
\(y^2+xy=x^3-98x+279\) |
2.3.0.a.1, 26.6.0.b.1, 68.6.0.c.1, 884.12.0.? |
$[(1, 13)]$ |
| 663.b2 |
663c1 |
663.b |
663c |
$2$ |
$2$ |
\( 3 \cdot 13 \cdot 17 \) |
\( 3^{4} \cdot 13^{2} \cdot 17 \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$2$ |
2.3.0.1 |
2B |
$884$ |
$12$ |
$0$ |
$0.408384049$ |
$1$ |
|
$9$ |
$64$ |
$-0.216677$ |
$3981876625/232713$ |
$0.86491$ |
$3.40246$ |
$[1, 0, 0, -33, -72]$ |
\(y^2+xy=x^3-33x-72\) |
2.3.0.a.1, 34.6.0.a.1, 52.6.0.c.1, 884.12.0.? |
$[(-3, 3)]$ |
| 663.c1 |
663a2 |
663.c |
663a |
$2$ |
$2$ |
\( 3 \cdot 13 \cdot 17 \) |
\( 3^{12} \cdot 13 \cdot 17^{2} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$2$ |
2.3.0.1 |
2B |
$884$ |
$12$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$576$ |
$0.476744$ |
$3885442650361/1996623837$ |
$0.95822$ |
$4.46195$ |
$[1, 1, 0, -327, -900]$ |
\(y^2+xy=x^3+x^2-327x-900\) |
2.3.0.a.1, 26.6.0.b.1, 68.6.0.c.1, 884.12.0.? |
$[ ]$ |
| 663.c2 |
663a1 |
663.c |
663a |
$2$ |
$2$ |
\( 3 \cdot 13 \cdot 17 \) |
\( 3^{6} \cdot 13^{2} \cdot 17 \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$2$ |
2.3.0.1 |
2B |
$884$ |
$12$ |
$0$ |
$1$ |
$1$ |
|
$1$ |
$288$ |
$0.130171$ |
$2000852317801/2094417$ |
$0.91984$ |
$4.35979$ |
$[1, 1, 0, -262, -1745]$ |
\(y^2+xy=x^3+x^2-262x-1745\) |
2.3.0.a.1, 34.6.0.a.1, 52.6.0.c.1, 884.12.0.? |
$[ ]$ |
