Elliptic curve isogeny class with LMFDB label 6400.x (Cremona label 6400f)

• Label: 6400.x
• Number of curves: $2$
• Conductor: $6400$
• CM: $\Q(\sqrt{-2})$
• Rank: $1$

Elliptic curves in class 6400.x

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality	CM discriminant
6400.x1	6400f2	$[0, -1, 0, -333, -1963]$	$8000$	$512000000$	$[2]$	$2304$	$0.40075$		$-8$
6400.x2	6400f1	$[0, -1, 0, -83, 287]$	$8000$	$8000000$	$[2]$	$1152$	$0.054173$	$\Gamma_0(N)$-optimal	$-8$

Rank

The elliptic curves in class 6400.x have rank $1$.

Complex multiplication

Each elliptic curve in class 6400.x has complex multiplication by an order in the imaginary quadratic field $\Q(\sqrt{-2})$.

Modular form 6400.2.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.

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

Isogeny graph

The vertices are labelled with LMFDB labels.