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 |
54.a1 |
54a2 |
54.a |
54a |
$3$ |
$9$ |
\( 2 \cdot 3^{3} \) |
\( - 2^{9} \cdot 3^{11} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$3$ |
9.72.0.11 |
3B.1.2 |
$72$ |
$144$ |
$3$ |
$1$ |
$1$ |
|
$0$ |
$18$ |
$0.234102$ |
$-1167051/512$ |
$1.04966$ |
$6.67312$ |
$[1, -1, 0, -123, -667]$ |
\(y^2+xy=x^3-x^2-123x-667\) |
3.8.0-3.a.1.1, 9.72.0-9.d.1.1, 24.16.0-24.d.1.7, 72.144.3.? |
$[]$ |
54.a2 |
54a3 |
54.a |
54a |
$3$ |
$9$ |
\( 2 \cdot 3^{3} \) |
\( - 2 \cdot 3^{3} \) |
$0$ |
$\Z/3\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$3$ |
9.72.0.6 |
3B.1.1 |
$72$ |
$144$ |
$3$ |
$1$ |
$1$ |
|
$2$ |
$18$ |
$-0.864511$ |
$-132651/2$ |
$1.09453$ |
$3.78970$ |
$[1, -1, 0, -3, 3]$ |
\(y^2+xy=x^3-x^2-3x+3\) |
3.8.0-3.a.1.2, 9.72.0-9.d.2.1, 24.16.0-24.d.1.8, 72.144.3.? |
$[]$ |
54.a3 |
54a1 |
54.a |
54a |
$3$ |
$9$ |
\( 2 \cdot 3^{3} \) |
\( - 2^{3} \cdot 3^{9} \) |
$0$ |
$\Z/3\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$3$ |
9.72.0.2 |
3Cs.1.1 |
$72$ |
$144$ |
$3$ |
$1$ |
$1$ |
|
$2$ |
$6$ |
$-0.315205$ |
$9261/8$ |
$1.19875$ |
$4.76840$ |
$[1, -1, 0, 12, 8]$ |
\(y^2+xy=x^3-x^2+12x+8\) |
3.24.0-3.a.1.1, 9.72.0-9.a.1.2, 24.48.1-24.ci.1.1, 72.144.3.? |
$[]$ |
54.b1 |
54b2 |
54.b |
54b |
$3$ |
$9$ |
\( 2 \cdot 3^{3} \) |
\( - 2 \cdot 3^{9} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$3$ |
9.72.0.12 |
3B.1.2 |
$72$ |
$144$ |
$3$ |
$1$ |
$1$ |
|
$0$ |
$6$ |
$-0.315205$ |
$-132651/2$ |
$1.09453$ |
$5.44216$ |
$[1, -1, 1, -29, -53]$ |
\(y^2+xy+y=x^3-x^2-29x-53\) |
3.8.0-3.a.1.1, 9.72.0-9.d.2.2, 24.16.0-24.d.1.7, 72.144.3.? |
$[]$ |
54.b2 |
54b3 |
54.b |
54b |
$3$ |
$9$ |
\( 2 \cdot 3^{3} \) |
\( - 2^{9} \cdot 3^{5} \) |
$0$ |
$\Z/9\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$3$ |
9.72.0.5 |
3B.1.1 |
$72$ |
$144$ |
$3$ |
$1$ |
$1$ |
|
$8$ |
$6$ |
$-0.315205$ |
$-1167051/512$ |
$1.04966$ |
$5.02065$ |
$[1, -1, 1, -14, 29]$ |
\(y^2+xy+y=x^3-x^2-14x+29\) |
3.8.0-3.a.1.2, 9.72.0-9.d.1.2, 24.16.0-24.d.1.8, 72.144.3.? |
$[]$ |
54.b3 |
54b1 |
54.b |
54b |
$3$ |
$9$ |
\( 2 \cdot 3^{3} \) |
\( - 2^{3} \cdot 3^{3} \) |
$0$ |
$\Z/3\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$3$ |
9.72.0.1 |
3Cs.1.1 |
$72$ |
$144$ |
$3$ |
$1$ |
$1$ |
|
$2$ |
$2$ |
$-0.864511$ |
$9261/8$ |
$1.19875$ |
$3.11593$ |
$[1, -1, 1, 1, -1]$ |
\(y^2+xy+y=x^3-x^2+x-1\) |
3.24.0-3.a.1.1, 9.72.0-9.a.1.1, 24.48.1-24.ci.1.1, 72.144.3.? |
$[]$ |