Elliptic curve isogeny class with Cremona label 389376c (LMFDB label 389376.c)

• Label: 389376c
• Number of curves: $2$
• Conductor: $389376$
• CM: \(\Q(\sqrt{-1}) \)
• Rank: $0$

Elliptic curves in class 389376c

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality	CM discriminant
389376.c1	389376c1	\([0, 0, 0, -3042, 0]\)	\(1728\)	\(1801596805632\)	\([2]\)	\(552960\)	\(1.0411\)	\(\Gamma_0(N)\)-optimal	\(-4\)
389376.c2	389376c2	\([0, 0, 0, 12168, 0]\)	\(1728\)	\(-115302195560448\)	\([2]\)	\(1105920\)	\(1.3877\)		\(-4\)

Rank

The elliptic curves in class 389376c have rank \(0\).

Complex multiplication

Each elliptic curve in class 389376c has complex multiplication by an order in the imaginary quadratic field \(\Q(\sqrt{-1}) \).

Modular form 389376.2.a.c

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.