Elliptic curve isogeny class with LMFDB label 5712.x (Cremona label 5712j)

• Label: 5712.x
• Number of curves: $4$
• Conductor: $5712$
• CM: no
• Rank: $0$

Elliptic curves in class 5712.x

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
5712.x1	5712j4	$[0, 1, 0, -2192, 38772]$	$569001644066/122451$	$250779648$	$[2]$	$3072$	$0.60642$
5712.x2	5712j3	$[0, 1, 0, -992, -12012]$	$52767497666/1753941$	$3592071168$	$[2]$	$3072$	$0.60642$
5712.x3	5712j2	$[0, 1, 0, -152, 420]$	$381775972/127449$	$130507776$	$[2, 2]$	$1536$	$0.25985$
5712.x4	5712j1	$[0, 1, 0, 28, 60]$	$9148592/9639$	$-2467584$	$[2]$	$768$	$-0.086725$	$\Gamma_0(N)$-optimal

Rank

The elliptic curves in class 5712.x have rank $0$.

L-function data

Bad L-factors:

Prime	L-Factor
$2$	$1$
$3$	$1 - T$
$7$	$1 + T$
$17$	$1 + T$

Good L-factors:

Prime	L-Factor	Isogeny Class over $\mathbb{F}_p$
$5$	$1 - 2 T + 5 T^{2}$	1.5.ac
$11$	$1 - 4 T + 11 T^{2}$	1.11.ae
$13$	$1 - 2 T + 13 T^{2}$	1.13.ac
$19$	$1 - 4 T + 19 T^{2}$	1.19.ae
$23$	$1 - 4 T + 23 T^{2}$	1.23.ae
$29$	$1 + 2 T + 29 T^{2}$	1.29.c
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 5712.x do not have complex multiplication.

Modular form 5712.2.a.x

Isogeny matrix

The $i,j$ entry is the smallest degree of a cyclic isogeny between the $i$-th and $j$-th curve in the isogeny class, in the LMFDB numbering.

$\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)$

Isogeny graph

The vertices are labelled with LMFDB labels.