Elliptic curve isogeny class with LMFDB label 2304.a (Cremona label 2304p)

• Label: 2304.a
• Number of curves: $2$
• Conductor: $2304$
• CM: \(\Q(\sqrt{-1}) \)
• Rank: $1$

Elliptic curves in class 2304.a

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality	CM discriminant
2304.a1	2304p2	\([0, 0, 0, -72, 0]\)	\(1728\)	\(23887872\)	\([2]\)	\(512\)	\(0.10521\)		\(-4\)
2304.a2	2304p1	\([0, 0, 0, 18, 0]\)	\(1728\)	\(-373248\)	\([2]\)	\(256\)	\(-0.24137\)	\(\Gamma_0(N)\)-optimal	\(-4\)

Rank

The elliptic curves in class 2304.a have rank \(1\).

Complex multiplication

Each elliptic curve in class 2304.a has complex multiplication by an order in the imaginary quadratic field \(\Q(\sqrt{-1}) \).

Modular form 2304.2.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.

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

Isogeny graph

The vertices are labelled with LMFDB labels.