| 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 |
| 588.a1 |
588a1 |
588.a |
588a |
$1$ |
$1$ |
\( 2^{2} \cdot 3 \cdot 7^{2} \) |
\( - 2^{8} \cdot 3^{5} \cdot 7^{4} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$6$ |
$2$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$180$ |
$0.257725$ |
$401408/243$ |
$1.33755$ |
$4.11364$ |
$[0, -1, 0, 131, -167]$ |
\(y^2=x^3-x^2+131x-167\) |
6.2.0.a.1 |
$[]$ |
| 588.b1 |
588c2 |
588.b |
588c |
$2$ |
$2$ |
\( 2^{2} \cdot 3 \cdot 7^{2} \) |
\( 2^{8} \cdot 3^{2} \cdot 7^{3} \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
2.3.0.1 |
2B |
$84$ |
$12$ |
$0$ |
$0.207775952$ |
$1$ |
|
$11$ |
$96$ |
$-0.125780$ |
$109744/9$ |
$0.87899$ |
$3.60511$ |
$[0, -1, 0, -44, 120]$ |
\(y^2=x^3-x^2-44x+120\) |
2.3.0.a.1, 12.6.0.g.1, 28.6.0.a.1, 84.12.0.? |
$[(2, 6)]$ |
| 588.b2 |
588c1 |
588.b |
588c |
$2$ |
$2$ |
\( 2^{2} \cdot 3 \cdot 7^{2} \) |
\( 2^{4} \cdot 3 \cdot 7^{3} \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
2.3.0.1 |
2B |
$84$ |
$12$ |
$0$ |
$0.415551904$ |
$1$ |
|
$9$ |
$48$ |
$-0.472354$ |
$16384/3$ |
$1.03704$ |
$2.87207$ |
$[0, -1, 0, -9, -6]$ |
\(y^2=x^3-x^2-9x-6\) |
2.3.0.a.1, 12.6.0.g.1, 28.6.0.b.1, 42.6.0.a.1, 84.12.0.? |
$[(5, 7)]$ |
| 588.c1 |
588b4 |
588.c |
588b |
$4$ |
$6$ |
\( 2^{2} \cdot 3 \cdot 7^{2} \) |
\( 2^{8} \cdot 3^{2} \cdot 7^{9} \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2, 3$ |
2.3.0.1, 3.4.0.1 |
2B, 3B |
$84$ |
$96$ |
$1$ |
$0.998952810$ |
$1$ |
|
$5$ |
$1728$ |
$1.387764$ |
$2640279346000/3087$ |
$1.02245$ |
$7.18590$ |
$[0, -1, 0, -89588, 10350936]$ |
\(y^2=x^3-x^2-89588x+10350936\) |
2.3.0.a.1, 3.4.0.a.1, 6.12.0.a.1, 12.48.0-12.j.1.7, 21.8.0-3.a.1.2, $\ldots$ |
$[(257, 2058)]$ |
| 588.c2 |
588b3 |
588.c |
588b |
$4$ |
$6$ |
\( 2^{2} \cdot 3 \cdot 7^{2} \) |
\( - 2^{4} \cdot 3 \cdot 7^{12} \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2, 3$ |
2.3.0.1, 3.4.0.1 |
2B, 3B |
$84$ |
$96$ |
$1$ |
$1.997905620$ |
$1$ |
|
$3$ |
$864$ |
$1.041191$ |
$-10061824000/352947$ |
$1.07286$ |
$5.88686$ |
$[0, -1, 0, -5553, 165894]$ |
\(y^2=x^3-x^2-5553x+165894\) |
2.3.0.a.1, 3.4.0.a.1, 6.24.0.b.1, 12.48.0-6.b.1.5, 21.8.0-3.a.1.2, $\ldots$ |
$[(26, 196)]$ |
| 588.c3 |
588b2 |
588.c |
588b |
$4$ |
$6$ |
\( 2^{2} \cdot 3 \cdot 7^{2} \) |
\( 2^{8} \cdot 3^{6} \cdot 7^{7} \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2, 3$ |
2.3.0.1, 3.4.0.1 |
2B, 3B |
$84$ |
$96$ |
$1$ |
$0.332984270$ |
$1$ |
|
$9$ |
$576$ |
$0.838458$ |
$9826000/5103$ |
$0.97243$ |
$5.22544$ |
$[0, -1, 0, -1388, 6840]$ |
\(y^2=x^3-x^2-1388x+6840\) |
2.3.0.a.1, 3.4.0.a.1, 6.12.0.a.1, 12.48.0-12.j.1.5, 21.8.0-3.a.1.1, $\ldots$ |
$[(-2, 98)]$ |
| 588.c4 |
588b1 |
588.c |
588b |
$4$ |
$6$ |
\( 2^{2} \cdot 3 \cdot 7^{2} \) |
\( - 2^{4} \cdot 3^{3} \cdot 7^{8} \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2, 3$ |
2.3.0.1, 3.4.0.1 |
2B, 3B |
$84$ |
$96$ |
$1$ |
$0.665968540$ |
$1$ |
|
$9$ |
$288$ |
$0.491884$ |
$2048000/1323$ |
$1.10843$ |
$4.54472$ |
$[0, -1, 0, 327, 666]$ |
\(y^2=x^3-x^2+327x+666\) |
2.3.0.a.1, 3.4.0.a.1, 6.24.0.b.1, 12.48.0-6.b.1.2, 21.8.0-3.a.1.1, $\ldots$ |
$[(5, 49)]$ |
| 588.d1 |
588f2 |
588.d |
588f |
$2$ |
$2$ |
\( 2^{2} \cdot 3 \cdot 7^{2} \) |
\( 2^{8} \cdot 3^{2} \cdot 7^{7} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
2.3.0.1 |
2B |
$84$ |
$12$ |
$0$ |
$1$ |
$1$ |
|
$1$ |
$576$ |
$0.648969$ |
$20720464/63$ |
$0.91015$ |
$5.34244$ |
$[0, 1, 0, -1780, 28244]$ |
\(y^2=x^3+x^2-1780x+28244\) |
2.3.0.a.1, 12.6.0.c.1, 28.6.0.a.1, 84.12.0.? |
$[]$ |
| 588.d2 |
588f1 |
588.d |
588f |
$2$ |
$2$ |
\( 2^{2} \cdot 3 \cdot 7^{2} \) |
\( - 2^{4} \cdot 3 \cdot 7^{8} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
2.3.0.1 |
2B |
$84$ |
$12$ |
$0$ |
$1$ |
$1$ |
|
$1$ |
$288$ |
$0.302395$ |
$-16384/147$ |
$1.05520$ |
$4.22720$ |
$[0, 1, 0, -65, 804]$ |
\(y^2=x^3+x^2-65x+804\) |
2.3.0.a.1, 6.6.0.a.1, 28.6.0.b.1, 84.12.0.? |
$[]$ |
| 588.e1 |
588e2 |
588.e |
588e |
$2$ |
$2$ |
\( 2^{2} \cdot 3 \cdot 7^{2} \) |
\( 2^{8} \cdot 3^{2} \cdot 7^{9} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
2.3.0.1 |
2B |
$84$ |
$12$ |
$0$ |
$1$ |
$1$ |
|
$1$ |
$672$ |
$0.847175$ |
$109744/9$ |
$0.87899$ |
$5.43606$ |
$[0, 1, 0, -2172, -36828]$ |
\(y^2=x^3+x^2-2172x-36828\) |
2.3.0.a.1, 12.6.0.g.1, 28.6.0.a.1, 84.12.0.? |
$[]$ |
| 588.e2 |
588e1 |
588.e |
588e |
$2$ |
$2$ |
\( 2^{2} \cdot 3 \cdot 7^{2} \) |
\( 2^{4} \cdot 3 \cdot 7^{9} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
2.3.0.1 |
2B |
$84$ |
$12$ |
$0$ |
$1$ |
$1$ |
|
$1$ |
$336$ |
$0.500601$ |
$16384/3$ |
$1.03704$ |
$4.70301$ |
$[0, 1, 0, -457, 2960]$ |
\(y^2=x^3+x^2-457x+2960\) |
2.3.0.a.1, 12.6.0.g.1, 28.6.0.b.1, 42.6.0.a.1, 84.12.0.? |
$[]$ |
| 588.f1 |
588d1 |
588.f |
588d |
$1$ |
$1$ |
\( 2^{2} \cdot 3 \cdot 7^{2} \) |
\( - 2^{8} \cdot 3^{5} \cdot 7^{10} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$6$ |
$2$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$1260$ |
$1.230680$ |
$401408/243$ |
$1.33755$ |
$5.94459$ |
$[0, 1, 0, 6403, 44463]$ |
\(y^2=x^3+x^2+6403x+44463\) |
6.2.0.a.1 |
$[]$ |
