Elliptic curve isogeny class with LMFDB label 64.a (Cremona label 64a)

• Label: 64.a
• Number of curves: $4$
• Conductor: $64$
• CM: \(\Q(\sqrt{-1}) \)
• Rank: $0$

Elliptic curves in class 64.a

LMFDB label	Cremona label	Weierstrass coefficients	Torsion structure	Modular degree	Optimality	CM discriminant
64.a1	64a2	[0, 0, 0, -44, -112]	[2]	4		-16
64.a2	64a3	[0, 0, 0, -44, 112]	[4]	4		-16
64.a3	64a1	[0, 0, 0, -4, 0]	[2, 2]	2	\(\Gamma_0(N)\)-optimal	-4
64.a4	64a4	[0, 0, 0, 1, 0]	[2]	4		-4

Rank

The elliptic curves in class 64.a have rank \(0\).

Complex multiplication

Each elliptic curve in class 64.a has complex multiplication by an order in the imaginary quadratic field \(\Q(\sqrt{-1}) \).

Modular form 64.2.a.a

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.

\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with LMFDB labels.