Elliptic curve isogeny class with Cremona label 12544d (LMFDB label 12544.n)

• Label: 12544d
• Number of curves: $2$
• Conductor: $12544$
• CM: $\Q(\sqrt{-2})$
• Rank: $0$

Elliptic curves in class 12544d

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality	CM discriminant
12544.n2	12544d1	$[0, -1, 0, -163, -657]$	$8000$	$60236288$	$[2]$	$3072$	$0.22241$	$\Gamma_0(N)$-optimal	$-8$
12544.n1	12544d2	$[0, -1, 0, -653, 5909]$	$8000$	$3855122432$	$[2]$	$6144$	$0.56898$		$-8$

Rank

The elliptic curves in class 12544d have rank $0$.

Complex multiplication

Each elliptic curve in class 12544d has complex multiplication by an order in the imaginary quadratic field $\Q(\sqrt{-2})$.

Modular form 12544.2.a.d

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 Cremona numbering.

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

Isogeny graph

The vertices are labelled with Cremona labels.