| 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 |
| 384.a1 |
384g1 |
384.a |
384g |
$2$ |
$2$ |
\( 2^{7} \cdot 3 \) |
\( 2^{8} \cdot 3^{3} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.6.0.4 |
2B |
$24$ |
$12$ |
$0$ |
$1$ |
$1$ |
|
$1$ |
$48$ |
$-0.360101$ |
$19056256/27$ |
$[0, -1, 0, -35, -69]$ |
\(y^2=x^3-x^2-35x-69\) |
2.3.0.a.1, 8.6.0.d.1, 12.6.0.a.1, 24.12.0.w.1 |
| 384.a2 |
384g2 |
384.a |
384g |
$2$ |
$2$ |
\( 2^{7} \cdot 3 \) |
\( - 2^{13} \cdot 3^{6} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.6.0.5 |
2B |
$24$ |
$12$ |
$0$ |
$1$ |
$1$ |
|
$1$ |
$96$ |
$-0.013528$ |
$-219488/729$ |
$[0, -1, 0, -25, -119]$ |
\(y^2=x^3-x^2-25x-119\) |
2.3.0.a.1, 8.6.0.a.1, 12.6.0.b.1, 24.12.0.c.1 |
| 384.b1 |
384d1 |
384.b |
384d |
$2$ |
$2$ |
\( 2^{7} \cdot 3 \) |
\( 2^{8} \cdot 3 \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.6.0.4 |
2B |
$24$ |
$12$ |
$0$ |
$0.639465641$ |
$1$ |
|
$5$ |
$16$ |
$-0.728445$ |
$16000/3$ |
$[0, -1, 0, -3, 3]$ |
\(y^2=x^3-x^2-3x+3\) |
2.3.0.a.1, 8.6.0.d.1, 12.6.0.a.1, 24.12.0.w.1 |
| 384.b2 |
384d2 |
384.b |
384d |
$2$ |
$2$ |
\( 2^{7} \cdot 3 \) |
\( - 2^{13} \cdot 3^{2} \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.6.0.5 |
2B |
$24$ |
$12$ |
$0$ |
$0.319732820$ |
$1$ |
|
$11$ |
$32$ |
$-0.381871$ |
$4000/9$ |
$[0, -1, 0, 7, 9]$ |
\(y^2=x^3-x^2+7x+9\) |
2.3.0.a.1, 8.6.0.a.1, 12.6.0.b.1, 24.12.0.c.1 |
| 384.c1 |
384b2 |
384.c |
384b |
$2$ |
$2$ |
\( 2^{7} \cdot 3 \) |
\( 2^{14} \cdot 3 \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.6.0.4 |
2B |
$24$ |
$12$ |
$0$ |
$1$ |
$1$ |
|
$1$ |
$32$ |
$-0.381871$ |
$16000/3$ |
$[0, -1, 0, -13, -11]$ |
\(y^2=x^3-x^2-13x-11\) |
2.3.0.a.1, 8.6.0.d.1, 12.6.0.a.1, 24.12.0.w.1 |
| 384.c2 |
384b1 |
384.c |
384b |
$2$ |
$2$ |
\( 2^{7} \cdot 3 \) |
\( - 2^{7} \cdot 3^{2} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.6.0.5 |
2B |
$24$ |
$12$ |
$0$ |
$1$ |
$1$ |
|
$1$ |
$16$ |
$-0.728445$ |
$4000/9$ |
$[0, -1, 0, 2, -2]$ |
\(y^2=x^3-x^2+2x-2\) |
2.3.0.a.1, 8.6.0.a.1, 12.6.0.b.1, 24.12.0.c.1 |
| 384.d1 |
384f2 |
384.d |
384f |
$2$ |
$2$ |
\( 2^{7} \cdot 3 \) |
\( 2^{14} \cdot 3^{3} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.6.0.4 |
2B |
$24$ |
$12$ |
$0$ |
$1$ |
$1$ |
|
$1$ |
$96$ |
$-0.013528$ |
$19056256/27$ |
$[0, -1, 0, -141, 693]$ |
\(y^2=x^3-x^2-141x+693\) |
2.3.0.a.1, 8.6.0.d.1, 12.6.0.a.1, 24.12.0.w.1 |
| 384.d2 |
384f1 |
384.d |
384f |
$2$ |
$2$ |
\( 2^{7} \cdot 3 \) |
\( - 2^{7} \cdot 3^{6} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.6.0.5 |
2B |
$24$ |
$12$ |
$0$ |
$1$ |
$1$ |
|
$1$ |
$48$ |
$-0.360101$ |
$-219488/729$ |
$[0, -1, 0, -6, 18]$ |
\(y^2=x^3-x^2-6x+18\) |
2.3.0.a.1, 8.6.0.a.1, 12.6.0.b.1, 24.12.0.c.1 |
| 384.e1 |
384h1 |
384.e |
384h |
$2$ |
$2$ |
\( 2^{7} \cdot 3 \) |
\( 2^{8} \cdot 3^{3} \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.6.0.4 |
2B |
$24$ |
$12$ |
$0$ |
$0.271689568$ |
$1$ |
|
$9$ |
$48$ |
$-0.360101$ |
$19056256/27$ |
$[0, 1, 0, -35, 69]$ |
\(y^2=x^3+x^2-35x+69\) |
2.3.0.a.1, 8.6.0.d.1, 12.6.0.a.1, 24.12.0.w.1 |
| 384.e2 |
384h2 |
384.e |
384h |
$2$ |
$2$ |
\( 2^{7} \cdot 3 \) |
\( - 2^{13} \cdot 3^{6} \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.6.0.5 |
2B |
$24$ |
$12$ |
$0$ |
$0.135844784$ |
$1$ |
|
$17$ |
$96$ |
$-0.013528$ |
$-219488/729$ |
$[0, 1, 0, -25, 119]$ |
\(y^2=x^3+x^2-25x+119\) |
2.3.0.a.1, 8.6.0.a.1, 12.6.0.b.1, 24.12.0.c.1 |
| 384.f1 |
384c2 |
384.f |
384c |
$2$ |
$2$ |
\( 2^{7} \cdot 3 \) |
\( 2^{14} \cdot 3 \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.6.0.4 |
2B |
$24$ |
$12$ |
$0$ |
$1$ |
$1$ |
|
$1$ |
$32$ |
$-0.381871$ |
$16000/3$ |
$[0, 1, 0, -13, 11]$ |
\(y^2=x^3+x^2-13x+11\) |
2.3.0.a.1, 8.6.0.d.1, 12.6.0.a.1, 24.12.0.w.1 |
| 384.f2 |
384c1 |
384.f |
384c |
$2$ |
$2$ |
\( 2^{7} \cdot 3 \) |
\( - 2^{7} \cdot 3^{2} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.6.0.5 |
2B |
$24$ |
$12$ |
$0$ |
$1$ |
$1$ |
|
$1$ |
$16$ |
$-0.728445$ |
$4000/9$ |
$[0, 1, 0, 2, 2]$ |
\(y^2=x^3+x^2+2x+2\) |
2.3.0.a.1, 8.6.0.a.1, 12.6.0.b.1, 24.12.0.c.1 |
| 384.g1 |
384a1 |
384.g |
384a |
$2$ |
$2$ |
\( 2^{7} \cdot 3 \) |
\( 2^{8} \cdot 3 \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.6.0.4 |
2B |
$24$ |
$12$ |
$0$ |
$1$ |
$1$ |
|
$1$ |
$16$ |
$-0.728445$ |
$16000/3$ |
$[0, 1, 0, -3, -3]$ |
\(y^2=x^3+x^2-3x-3\) |
2.3.0.a.1, 8.6.0.d.1, 12.6.0.a.1, 24.12.0.w.1 |
| 384.g2 |
384a2 |
384.g |
384a |
$2$ |
$2$ |
\( 2^{7} \cdot 3 \) |
\( - 2^{13} \cdot 3^{2} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.6.0.5 |
2B |
$24$ |
$12$ |
$0$ |
$1$ |
$1$ |
|
$1$ |
$32$ |
$-0.381871$ |
$4000/9$ |
$[0, 1, 0, 7, -9]$ |
\(y^2=x^3+x^2+7x-9\) |
2.3.0.a.1, 8.6.0.a.1, 12.6.0.b.1, 24.12.0.c.1 |
| 384.h1 |
384e2 |
384.h |
384e |
$2$ |
$2$ |
\( 2^{7} \cdot 3 \) |
\( 2^{14} \cdot 3^{3} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.6.0.4 |
2B |
$24$ |
$12$ |
$0$ |
$1$ |
$1$ |
|
$1$ |
$96$ |
$-0.013528$ |
$19056256/27$ |
$[0, 1, 0, -141, -693]$ |
\(y^2=x^3+x^2-141x-693\) |
2.3.0.a.1, 8.6.0.d.1, 12.6.0.a.1, 24.12.0.w.1 |
| 384.h2 |
384e1 |
384.h |
384e |
$2$ |
$2$ |
\( 2^{7} \cdot 3 \) |
\( - 2^{7} \cdot 3^{6} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.6.0.5 |
2B |
$24$ |
$12$ |
$0$ |
$1$ |
$1$ |
|
$1$ |
$48$ |
$-0.360101$ |
$-219488/729$ |
$[0, 1, 0, -6, -18]$ |
\(y^2=x^3+x^2-6x-18\) |
2.3.0.a.1, 8.6.0.a.1, 12.6.0.b.1, 24.12.0.c.1 |
