| 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 |
| 21.a1 |
21a5 |
21.a |
21a |
$6$ |
$8$ |
\( 3 \cdot 7 \) |
\( 3 \cdot 7^{2} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$2$ |
16.48.0.48 |
2B |
$336$ |
$192$ |
$1$ |
$1$ |
$1$ |
|
$0$ |
$4$ |
$0.074205$ |
$53297461115137/147$ |
$[1, 0, 0, -784, -8515]$ |
\(y^2+xy=x^3-784x-8515\) |
2.3.0.a.1, 4.12.0-4.c.1.2, 8.24.0-8.n.1.6, 12.24.0-12.h.1.1, 16.48.0-16.e.2.5, $\ldots$ |
| 21.a2 |
21a2 |
21.a |
21a |
$6$ |
$8$ |
\( 3 \cdot 7 \) |
\( 3^{2} \cdot 7^{4} \) |
$0$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$2$ |
8.48.0.34 |
2Cs |
$168$ |
$192$ |
$1$ |
$1$ |
$1$ |
|
$2$ |
$2$ |
$-0.272368$ |
$13027640977/21609$ |
$[1, 0, 0, -49, -136]$ |
\(y^2+xy=x^3-49x-136\) |
2.6.0.a.1, 4.24.0-4.b.1.1, 8.48.0-8.e.1.1, 12.48.0-12.c.1.3, 24.96.0-24.j.2.5, $\ldots$ |
| 21.a3 |
21a3 |
21.a |
21a |
$6$ |
$8$ |
\( 3 \cdot 7 \) |
\( 3^{8} \cdot 7 \) |
$0$ |
$\Z/8\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$2$ |
8.48.0.159 |
2B |
$336$ |
$192$ |
$1$ |
$1$ |
$1$ |
|
$6$ |
$2$ |
$-0.272368$ |
$6570725617/45927$ |
$[1, 0, 0, -39, 90]$ |
\(y^2+xy=x^3-39x+90\) |
2.3.0.a.1, 4.12.0-4.c.1.1, 8.48.0-8.bb.1.1, 28.24.0-28.h.1.2, 48.96.0-48.bf.1.3, $\ldots$ |
| 21.a4 |
21a6 |
21.a |
21a |
$6$ |
$8$ |
\( 3 \cdot 7 \) |
\( - 3 \cdot 7^{8} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$2$ |
8.48.0.177 |
2B |
$336$ |
$192$ |
$1$ |
$1$ |
$1$ |
|
$0$ |
$4$ |
$0.074205$ |
$-4354703137/17294403$ |
$[1, 0, 0, -34, -217]$ |
\(y^2+xy=x^3-34x-217\) |
2.3.0.a.1, 4.12.0-4.c.1.2, 6.6.0.a.1, 8.48.0-8.bb.2.3, 12.24.0-12.g.1.1, $\ldots$ |
| 21.a5 |
21a1 |
21.a |
21a |
$6$ |
$8$ |
\( 3 \cdot 7 \) |
\( 3^{4} \cdot 7^{2} \) |
$0$ |
$\Z/2\Z\oplus\Z/4\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$2$ |
8.48.0.24 |
2Cs |
$168$ |
$192$ |
$1$ |
$1$ |
$1$ |
|
$6$ |
$1$ |
$-0.618942$ |
$7189057/3969$ |
$[1, 0, 0, -4, -1]$ |
\(y^2+xy=x^3-4x-1\) |
2.6.0.a.1, 4.24.0-4.b.1.3, 8.48.0-8.e.2.2, 24.96.0-24.w.2.6, 28.48.0-28.c.1.1, $\ldots$ |
| 21.a6 |
21a4 |
21.a |
21a |
$6$ |
$8$ |
\( 3 \cdot 7 \) |
\( - 3^{2} \cdot 7 \) |
$0$ |
$\Z/4\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$2$ |
16.48.0.27 |
2B |
$336$ |
$192$ |
$1$ |
$1$ |
$1$ |
|
$3$ |
$2$ |
$-0.965515$ |
$103823/63$ |
$[1, 0, 0, 1, 0]$ |
\(y^2+xy=x^3+x\) |
2.3.0.a.1, 4.12.0-4.c.1.1, 8.24.0-8.n.1.2, 14.6.0.b.1, 16.48.0-16.e.1.2, $\ldots$ |
