Elliptic curve isogeny class with Cremona label 43264t (LMFDB label 43264.z)

• Label: 43264t
• Number of curves: $2$
• Conductor: $43264$
• CM: \(\Q(\sqrt{-2}) \)
• Rank: $0$

Elliptic curves in class 43264t

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality	CM discriminant
43264.z2	43264t1	\([0, -1, 0, -563, -4369]\)	\(8000\)	\(2471326208\)	\([2]\)	\(18816\)	\(0.53193\)	\(\Gamma_0(N)\)-optimal	\(-8\)
43264.z1	43264t2	\([0, -1, 0, -2253, 37205]\)	\(8000\)	\(158164877312\)	\([2]\)	\(37632\)	\(0.87850\)		\(-8\)

Rank

The elliptic curves in class 43264t have rank \(0\).

Complex multiplication

Each elliptic curve in class 43264t has complex multiplication by an order in the imaginary quadratic field \(\Q(\sqrt{-2}) \).

Modular form 43264.2.a.t

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.