Elliptic Curve Isogeny Class 64.a (Cremona label 64a)

• Label: 64.a
• Number of curves: 4
• Conductor: \(64\)
• CM: -4
• Rank: \(0\)

Elliptic curves in class 64.a

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

Rank

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

Modular form 64.2.1.a

Isogeny matrix

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

Isogeny graph