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 |
468.a1 |
468b2 |
468.a |
468b |
$2$ |
$2$ |
\( 2^{2} \cdot 3^{2} \cdot 13 \) |
\( 2^{8} \cdot 3^{9} \cdot 13^{2} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.12.0.33 |
2B |
$312$ |
$48$ |
$1$ |
$1$ |
$1$ |
|
$1$ |
$1152$ |
$1.043194$ |
$315978926832/169$ |
$[0, 0, 0, -24327, 1460430]$ |
\(y^2=x^3-24327x+1460430\) |
2.3.0.a.1, 4.6.0.e.1, 8.12.0.u.1, 12.12.0.m.1, 24.24.0.dc.1, $\ldots$ |
$[]$ |
468.a2 |
468b1 |
468.a |
468b |
$2$ |
$2$ |
\( 2^{2} \cdot 3^{2} \cdot 13 \) |
\( - 2^{4} \cdot 3^{9} \cdot 13^{4} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
4.12.0.5 |
2B |
$312$ |
$48$ |
$1$ |
$1$ |
$1$ |
|
$1$ |
$576$ |
$0.696620$ |
$-1213857792/28561$ |
$[0, 0, 0, -1512, 23085]$ |
\(y^2=x^3-1512x+23085\) |
2.3.0.a.1, 4.12.0.e.1, 6.6.0.a.1, 12.24.0.k.1, 104.24.0.?, $\ldots$ |
$[]$ |
468.b1 |
468c1 |
468.b |
468c |
$2$ |
$2$ |
\( 2^{2} \cdot 3^{2} \cdot 13 \) |
\( 2^{4} \cdot 3^{6} \cdot 13 \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
4.6.0.3 |
2B |
$312$ |
$48$ |
$0$ |
$0.180117663$ |
$1$ |
|
$13$ |
$48$ |
$-0.228567$ |
$442368/13$ |
$[0, 0, 0, -36, 81]$ |
\(y^2=x^3-36x+81\) |
2.3.0.a.1, 4.6.0.b.1, 24.12.0-4.b.1.4, 26.6.0.b.1, 52.24.0.e.1, $\ldots$ |
$[(0, 9)]$ |
468.b2 |
468c2 |
468.b |
468c |
$2$ |
$2$ |
\( 2^{2} \cdot 3^{2} \cdot 13 \) |
\( - 2^{8} \cdot 3^{6} \cdot 13^{2} \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
4.6.0.5 |
2B |
$312$ |
$48$ |
$0$ |
$0.360235326$ |
$1$ |
|
$9$ |
$96$ |
$0.118007$ |
$432/169$ |
$[0, 0, 0, 9, 270]$ |
\(y^2=x^3+9x+270\) |
2.3.0.a.1, 4.6.0.a.1, 24.12.0-4.a.1.1, 52.12.0.d.1, 104.24.0.?, $\ldots$ |
$[(3, 18)]$ |
468.c1 |
468d4 |
468.c |
468d |
$4$ |
$6$ |
\( 2^{2} \cdot 3^{2} \cdot 13 \) |
\( 2^{8} \cdot 3^{7} \cdot 13^{6} \) |
$0$ |
$\Z/6\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2, 3$ |
2.3.0.1, 3.8.0.1 |
2B, 3B.1.1 |
$156$ |
$96$ |
$1$ |
$1$ |
$1$ |
|
$5$ |
$576$ |
$1.128765$ |
$181037698000/14480427$ |
$[0, 0, 0, -6735, 197494]$ |
\(y^2=x^3-6735x+197494\) |
2.3.0.a.1, 3.8.0-3.a.1.2, 6.24.0-6.a.1.4, 12.48.0-12.h.1.7, 52.6.0.c.1, $\ldots$ |
$[]$ |
468.c2 |
468d3 |
468.c |
468d |
$4$ |
$6$ |
\( 2^{2} \cdot 3^{2} \cdot 13 \) |
\( 2^{4} \cdot 3^{8} \cdot 13^{3} \) |
$0$ |
$\Z/6\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2, 3$ |
2.3.0.1, 3.8.0.1 |
2B, 3B.1.1 |
$156$ |
$96$ |
$1$ |
$1$ |
$1$ |
|
$5$ |
$288$ |
$0.782191$ |
$2725888000000/19773$ |
$[0, 0, 0, -6600, 206377]$ |
\(y^2=x^3-6600x+206377\) |
2.3.0.a.1, 3.8.0-3.a.1.2, 6.24.0-6.a.1.4, 12.48.0-12.i.1.8, 26.6.0.b.1, $\ldots$ |
$[]$ |
468.c3 |
468d2 |
468.c |
468d |
$4$ |
$6$ |
\( 2^{2} \cdot 3^{2} \cdot 13 \) |
\( 2^{8} \cdot 3^{9} \cdot 13^{2} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2, 3$ |
2.3.0.1, 3.8.0.2 |
2B, 3B.1.2 |
$156$ |
$96$ |
$1$ |
$1$ |
$1$ |
|
$1$ |
$192$ |
$0.579458$ |
$1409938000/4563$ |
$[0, 0, 0, -1335, -18722]$ |
\(y^2=x^3-1335x-18722\) |
2.3.0.a.1, 3.8.0-3.a.1.1, 6.24.0-6.a.1.2, 12.48.0-12.h.1.5, 52.6.0.c.1, $\ldots$ |
$[]$ |
468.c4 |
468d1 |
468.c |
468d |
$4$ |
$6$ |
\( 2^{2} \cdot 3^{2} \cdot 13 \) |
\( 2^{4} \cdot 3^{12} \cdot 13 \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2, 3$ |
2.3.0.1, 3.8.0.2 |
2B, 3B.1.2 |
$156$ |
$96$ |
$1$ |
$1$ |
$1$ |
|
$1$ |
$96$ |
$0.232885$ |
$16384000/9477$ |
$[0, 0, 0, -120, -11]$ |
\(y^2=x^3-120x-11\) |
2.3.0.a.1, 3.8.0-3.a.1.1, 6.24.0-6.a.1.2, 12.48.0-12.i.1.6, 26.6.0.b.1, $\ldots$ |
$[]$ |
468.d1 |
468e2 |
468.d |
468e |
$2$ |
$2$ |
\( 2^{2} \cdot 3^{2} \cdot 13 \) |
\( 2^{8} \cdot 3^{7} \cdot 13^{2} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
2.3.0.1 |
2B |
$156$ |
$12$ |
$0$ |
$1$ |
$1$ |
|
$1$ |
$192$ |
$0.256780$ |
$3631696/507$ |
$[0, 0, 0, -183, 830]$ |
\(y^2=x^3-183x+830\) |
2.3.0.a.1, 12.6.0.a.1, 52.6.0.c.1, 156.12.0.? |
$[]$ |
468.d2 |
468e1 |
468.d |
468e |
$2$ |
$2$ |
\( 2^{2} \cdot 3^{2} \cdot 13 \) |
\( 2^{4} \cdot 3^{8} \cdot 13 \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
2.3.0.1 |
2B |
$156$ |
$12$ |
$0$ |
$1$ |
$1$ |
|
$1$ |
$96$ |
$-0.089794$ |
$1048576/117$ |
$[0, 0, 0, -48, -115]$ |
\(y^2=x^3-48x-115\) |
2.3.0.a.1, 12.6.0.b.1, 26.6.0.b.1, 156.12.0.? |
$[]$ |
468.e1 |
468a2 |
468.e |
468a |
$2$ |
$2$ |
\( 2^{2} \cdot 3^{2} \cdot 13 \) |
\( 2^{8} \cdot 3^{3} \cdot 13^{2} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.12.0.33 |
2B |
$312$ |
$48$ |
$1$ |
$1$ |
$1$ |
|
$1$ |
$384$ |
$0.493887$ |
$315978926832/169$ |
$[0, 0, 0, -2703, -54090]$ |
\(y^2=x^3-2703x-54090\) |
2.3.0.a.1, 4.6.0.e.1, 8.12.0.u.1, 12.12.0.m.1, 24.24.0.dc.1, $\ldots$ |
$[]$ |
468.e2 |
468a1 |
468.e |
468a |
$2$ |
$2$ |
\( 2^{2} \cdot 3^{2} \cdot 13 \) |
\( - 2^{4} \cdot 3^{3} \cdot 13^{4} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
4.12.0.5 |
2B |
$312$ |
$48$ |
$1$ |
$1$ |
$1$ |
|
$1$ |
$192$ |
$0.147314$ |
$-1213857792/28561$ |
$[0, 0, 0, -168, -855]$ |
\(y^2=x^3-168x-855\) |
2.3.0.a.1, 4.12.0.e.1, 6.6.0.a.1, 12.24.0.k.1, 104.24.0.?, $\ldots$ |
$[]$ |