Elliptic curve isogeny class with Cremona label 576f (LMFDB label 576.i)

• Label: 576f
• Number of curves: $2$
• Conductor: $576$
• CM: \(\Q(\sqrt{-1}) \)
• Rank: $0$

Elliptic curves in class 576f

LMFDB label	Cremona label	Weierstrass coefficients	Torsion structure	Modular degree	Optimality	CM discriminant
576.i1	576f1	[0, 0, 0, -3, 0]	[2]	32	\(\Gamma_0(N)\)-optimal	-4
576.i2	576f2	[0, 0, 0, 12, 0]	[2]	64		-4

Rank

The elliptic curves in class 576f have rank \(0\).

Complex multiplication

Each elliptic curve in class 576f has complex multiplication by an order in the imaginary quadratic field \(\Q(\sqrt{-1}) \).

Modular form 576.2.a.f

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.