Elliptic curve isogeny class with LMFDB label 53361.bq (Cremona label 53361bd)

• Label: 53361.bq
• Number of curves: $4$
• Conductor: $53361$
• CM: \(\Q(\sqrt{-7}) \)
• Rank: $0$

Elliptic curves in class 53361.bq

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality	CM discriminant
53361.bq1	53361bd4	\([1, -1, 0, -1984362, 1076358905]\)	\(16581375\)	\(52115390874114183\)	\([2]\)	\(573440\)	\(2.2686\)		\(-28\)
53361.bq2	53361bd3	\([1, -1, 0, -116727, 18903968]\)	\(-3375\)	\(-52115390874114183\)	\([2]\)	\(286720\)	\(1.9221\)		\(-7\)
53361.bq3	53361bd2	\([1, -1, 0, -40497, -3126502]\)	\(16581375\)	\(442973513367\)	\([2]\)	\(81920\)	\(1.2957\)		\(-28\)
53361.bq4	53361bd1	\([1, -1, 0, -2382, -54433]\)	\(-3375\)	\(-442973513367\)	\([2]\)	\(40960\)	\(0.94912\)	\(\Gamma_0(N)\)-optimal	\(-7\)

Rank

The elliptic curves in class 53361.bq have rank \(0\).

Complex multiplication

Each elliptic curve in class 53361.bq has complex multiplication by an order in the imaginary quadratic field \(\Q(\sqrt{-7}) \).

Modular form 53361.2.a.bq

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.

\(\left(\begin{array}{rrrr} 1 & 2 & 7 & 14 \\ 2 & 1 & 14 & 7 \\ 7 & 14 & 1 & 2 \\ 14 & 7 & 2 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with LMFDB labels.