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

• Label: 288.d
• Number of curves: $4$
• Conductor: $288$
• CM: \(\Q(\sqrt{-1}) \)
• Rank: $0$

Elliptic curves in class 288.d

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality	CM discriminant
288.d1	288d2	\([0, 0, 0, -99, -378]\)	\(287496\)	\(373248\)	\([2]\)	\(32\)	\(-0.068080\)		\(-16\)
288.d2	288d3	\([0, 0, 0, -99, 378]\)	\(287496\)	\(373248\)	\([2]\)	\(32\)	\(-0.068080\)		\(-16\)
288.d3	288d1	\([0, 0, 0, -9, 0]\)	\(1728\)	\(46656\)	\([2, 2]\)	\(16\)	\(-0.41465\)	\(\Gamma_0(N)\)-optimal	\(-4\)
288.d4	288d4	\([0, 0, 0, 36, 0]\)	\(1728\)	\(-2985984\)	\([2]\)	\(32\)	\(-0.068080\)		\(-4\)

Rank

The elliptic curves in class 288.d have rank \(0\).

Complex multiplication

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

Modular form 288.2.a.d

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.