Elliptic curve isogeny class with LMFDB label 215296.v (Cremona label 215296w)

• Label: 215296.v
• Number of curves: $2$
• Conductor: $215296$
• CM: \(\Q(\sqrt{-2}) \)
• Rank: $1$

Elliptic curves in class 215296.v

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality	CM discriminant
215296.v1	215296w2	\([0, -1, 0, -11213, -400939]\)	\(8000\)	\(19491170582528\)	\([2]\)	\(403200\)	\(1.2797\)		\(-8\)
215296.v2	215296w1	\([0, -1, 0, -2803, 51519]\)	\(8000\)	\(304549540352\)	\([2]\)	\(201600\)	\(0.93310\)	\(\Gamma_0(N)\)-optimal	\(-8\)

Rank

The elliptic curves in class 215296.v have rank \(1\).

Complex multiplication

Each elliptic curve in class 215296.v has complex multiplication by an order in the imaginary quadratic field \(\Q(\sqrt{-2}) \).

Modular form 215296.2.a.v

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.