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 |
MW-generators |
864.a1 |
864i1 |
864.a |
864i |
$1$ |
$1$ |
\( 2^{5} \cdot 3^{3} \) |
\( - 2^{12} \cdot 3^{9} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
$3$ |
3.3.0.1 |
3Nn |
$12$ |
$24$ |
$1$ |
$1$ |
$1$ |
|
$0$ |
$288$ |
$0.266701$ |
$-13824$ |
$[0, 0, 0, -216, -1296]$ |
\(y^2=x^3-216x-1296\) |
3.3.0.a.1, 6.6.1.b.1, 12.24.1-12.g.1.1 |
$[]$ |
864.b1 |
864k1 |
864.b |
864k |
$1$ |
$1$ |
\( 2^{5} \cdot 3^{3} \) |
\( - 2^{12} \cdot 3^{5} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
|
|
|
$6$ |
$2$ |
$0$ |
$0.622549773$ |
$1$ |
|
$4$ |
$96$ |
$-0.160228$ |
$1536$ |
$[0, 0, 0, 24, 16]$ |
\(y^2=x^3+24x+16\) |
6.2.0.a.1 |
$[(0, 4)]$ |
864.c1 |
864c1 |
864.c |
864c |
$1$ |
$1$ |
\( 2^{5} \cdot 3^{3} \) |
\( - 2^{12} \cdot 3^{5} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
|
|
|
$6$ |
$2$ |
$0$ |
$0.230591702$ |
$1$ |
|
$6$ |
$96$ |
$-0.160228$ |
$1536$ |
$[0, 0, 0, 24, -16]$ |
\(y^2=x^3+24x-16\) |
6.2.0.a.1 |
$[(4, 12)]$ |
864.d1 |
864l1 |
864.d |
864l |
$1$ |
$1$ |
\( 2^{5} \cdot 3^{3} \) |
\( - 2^{12} \cdot 3^{9} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
$3$ |
3.3.0.1 |
3Nn |
$12$ |
$24$ |
$1$ |
$0.196028067$ |
$1$ |
|
$6$ |
$288$ |
$0.266701$ |
$-13824$ |
$[0, 0, 0, -216, 1296]$ |
\(y^2=x^3-216x+1296\) |
3.3.0.a.1, 6.6.1.b.1, 12.24.1-12.g.1.1 |
$[(0, 36)]$ |
864.e1 |
864a1 |
864.e |
864a |
$1$ |
$1$ |
\( 2^{5} \cdot 3^{3} \) |
\( - 2^{9} \cdot 3^{3} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
$3$ |
9.9.0.1 |
3Nn |
$72$ |
$36$ |
$3$ |
$0.317388851$ |
$1$ |
|
$4$ |
$48$ |
$-0.520776$ |
$-216$ |
$[0, 0, 0, -3, 6]$ |
\(y^2=x^3-3x+6\) |
3.3.0.a.1, 9.9.0.a.1, 12.6.0.d.1, 24.12.1.bi.1, 36.18.0.a.1, $\ldots$ |
$[(1, 2)]$ |
864.f1 |
864d1 |
864.f |
864d |
$1$ |
$1$ |
\( 2^{5} \cdot 3^{3} \) |
\( - 2^{9} \cdot 3^{3} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
$3$ |
9.9.0.1 |
3Nn |
$72$ |
$36$ |
$3$ |
$1$ |
$1$ |
|
$0$ |
$48$ |
$-0.520776$ |
$-216$ |
$[0, 0, 0, -3, -6]$ |
\(y^2=x^3-3x-6\) |
3.3.0.a.1, 9.9.0.a.1, 12.6.0.d.1, 24.12.1.bi.1, 36.18.0.a.1, $\ldots$ |
$[]$ |
864.g1 |
864j1 |
864.g |
864j |
$1$ |
$1$ |
\( 2^{5} \cdot 3^{3} \) |
\( - 2^{9} \cdot 3^{9} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
$3$ |
9.9.0.1 |
3Nn |
$72$ |
$36$ |
$3$ |
$0.405350409$ |
$1$ |
|
$6$ |
$144$ |
$0.028531$ |
$-216$ |
$[0, 0, 0, -27, -162]$ |
\(y^2=x^3-27x-162\) |
3.3.0.a.1, 9.9.0.a.1, 12.6.0.d.1, 24.12.1.bi.1, 36.18.0.a.1, $\ldots$ |
$[(9, 18)]$ |
864.h1 |
864g1 |
864.h |
864g |
$1$ |
$1$ |
\( 2^{5} \cdot 3^{3} \) |
\( - 2^{9} \cdot 3^{9} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
$3$ |
9.9.0.1 |
3Nn |
$72$ |
$36$ |
$3$ |
$1$ |
$1$ |
|
$0$ |
$144$ |
$0.028531$ |
$-216$ |
$[0, 0, 0, -27, 162]$ |
\(y^2=x^3-27x+162\) |
3.3.0.a.1, 9.9.0.a.1, 12.6.0.d.1, 24.12.1.bi.1, 36.18.0.a.1, $\ldots$ |
$[]$ |
864.i1 |
864b1 |
864.i |
864b |
$1$ |
$1$ |
\( 2^{5} \cdot 3^{3} \) |
\( - 2^{12} \cdot 3^{3} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
$3$ |
3.3.0.1 |
3Nn |
$12$ |
$24$ |
$1$ |
$0.360874900$ |
$1$ |
|
$4$ |
$96$ |
$-0.282605$ |
$-13824$ |
$[0, 0, 0, -24, 48]$ |
\(y^2=x^3-24x+48\) |
3.3.0.a.1, 6.6.1.b.1, 12.24.1-12.g.1.1 |
$[(4, 4)]$ |
864.j1 |
864e1 |
864.j |
864e |
$1$ |
$1$ |
\( 2^{5} \cdot 3^{3} \) |
\( - 2^{12} \cdot 3^{11} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
|
|
|
$6$ |
$2$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$288$ |
$0.389079$ |
$1536$ |
$[0, 0, 0, 216, -432]$ |
\(y^2=x^3+216x-432\) |
6.2.0.a.1 |
$[]$ |
864.k1 |
864h1 |
864.k |
864h |
$1$ |
$1$ |
\( 2^{5} \cdot 3^{3} \) |
\( - 2^{12} \cdot 3^{11} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
|
|
|
$6$ |
$2$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$288$ |
$0.389079$ |
$1536$ |
$[0, 0, 0, 216, 432]$ |
\(y^2=x^3+216x+432\) |
6.2.0.a.1 |
$[]$ |
864.l1 |
864f1 |
864.l |
864f |
$1$ |
$1$ |
\( 2^{5} \cdot 3^{3} \) |
\( - 2^{12} \cdot 3^{3} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
$3$ |
3.3.0.1 |
3Nn |
$12$ |
$24$ |
$1$ |
$1$ |
$1$ |
|
$0$ |
$96$ |
$-0.282605$ |
$-13824$ |
$[0, 0, 0, -24, -48]$ |
\(y^2=x^3-24x-48\) |
3.3.0.a.1, 6.6.1.b.1, 12.24.1-12.g.1.1 |
$[]$ |