Elliptic curve isogeny class with LMFDB label 14400.cx (Cremona label 14400dn)

• Label: 14400.cx
• Number of curves: $4$
• Conductor: $14400$
• CM: \(\Q(\sqrt{-1}) \)
• Rank: $1$

Elliptic curves in class 14400.cx

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality	CM discriminant
14400.cx1	14400dn3	\([0, 0, 0, -9900, -378000]\)	\(287496\)	\(373248000000\)	\([2]\)	\(16384\)	\(1.0832\)		\(-16\)
14400.cx2	14400dn4	\([0, 0, 0, -9900, 378000]\)	\(287496\)	\(373248000000\)	\([2]\)	\(16384\)	\(1.0832\)		\(-16\)
14400.cx3	14400dn2	\([0, 0, 0, -900, 0]\)	\(1728\)	\(46656000000\)	\([2, 2]\)	\(8192\)	\(0.73664\)		\(-4\)
14400.cx4	14400dn1	\([0, 0, 0, 225, 0]\)	\(1728\)	\(-729000000\)	\([2]\)	\(4096\)	\(0.39007\)	\(\Gamma_0(N)\)-optimal	\(-4\)

Rank

The elliptic curves in class 14400.cx have rank \(1\).

Complex multiplication

Each elliptic curve in class 14400.cx has complex multiplication by an order in the imaginary quadratic field \(\Q(\sqrt{-1}) \).

Modular form 14400.2.a.cx

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.