Elliptic curve isogeny class with Cremona label 288a (LMFDB label 288.a)

• Label: 288a
• Number of curves: $2$
• Conductor: $288$
• CM: \(\Q(\sqrt{-1}) \)
• Rank: $1$

Elliptic curves in class 288a

LMFDB label	Cremona label	Weierstrass coefficients	Torsion structure	Modular degree	Optimality	CM discriminant
288.a2	288a1	[0, 0, 0, 3, 0]	[2]	16	\(\Gamma_0(N)\)-optimal	-4
288.a1	288a2	[0, 0, 0, -12, 0]	[2]	32		-4

Rank

The elliptic curves in class 288a have rank \(1\).

Complex multiplication

Each elliptic curve in class 288a has complex multiplication by an order in the imaginary quadratic field \(\Q(\sqrt{-1}) \).

Modular form 288.2.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 Cremona numbering.

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

Isogeny graph

The vertices are labelled with Cremona labels.