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.