Elliptic curve isogeny class with LMFDB label 7744.v (Cremona label 7744t)

• Label: 7744.v
• Number of curves: $4$
• Conductor: $7744$
• CM: \(\Q(\sqrt{-1}) \)
• Rank: $1$

Elliptic curves in class 7744.v

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality	CM discriminant
7744.v1	7744t3	\([0, 0, 0, -5324, -149072]\)	\(287496\)	\(58050510848\)	\([2]\)	\(5760\)	\(0.92814\)		\(-16\)
7744.v2	7744t4	\([0, 0, 0, -5324, 149072]\)	\(287496\)	\(58050510848\)	\([2]\)	\(5760\)	\(0.92814\)		\(-16\)
7744.v3	7744t2	\([0, 0, 0, -484, 0]\)	\(1728\)	\(7256313856\)	\([2, 2]\)	\(2880\)	\(0.58156\)		\(-4\)
7744.v4	7744t1	\([0, 0, 0, 121, 0]\)	\(1728\)	\(-113379904\)	\([2]\)	\(1440\)	\(0.23499\)	\(\Gamma_0(N)\)-optimal	\(-4\)

Rank

The elliptic curves in class 7744.v have rank \(1\).

Complex multiplication

Each elliptic curve in class 7744.v has complex multiplication by an order in the imaginary quadratic field \(\Q(\sqrt{-1}) \).

Modular form 7744.2.a.v

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.