Elliptic curve isogeny class with LMFDB label 14400.n (Cremona label 14400cz)

• Label: 14400.n
• Number of curves: $4$
• Conductor: $14400$
• CM: \(\Q(\sqrt{-3}) \)
• Rank: $0$

Elliptic curves in class 14400.n

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality	CM discriminant
14400.n1	14400cz4	\([0, 0, 0, -13500, 594000]\)	\(54000\)	\(5038848000000\)	\([2]\)	\(27648\)	\(1.2318\)		\(-12\)
14400.n2	14400cz2	\([0, 0, 0, -1500, -22000]\)	\(54000\)	\(6912000000\)	\([2]\)	\(9216\)	\(0.68245\)		\(-12\)
14400.n3	14400cz1	\([0, 0, 0, 0, -1000]\)	\(0\)	\(-432000000\)	\([2]\)	\(4608\)	\(0.33588\)	\(\Gamma_0(N)\)-optimal	\(-3\)
14400.n4	14400cz3	\([0, 0, 0, 0, 27000]\)	\(0\)	\(-314928000000\)	\([2]\)	\(13824\)	\(0.88518\)		\(-3\)

Rank

The elliptic curves in class 14400.n have rank \(0\).

Complex multiplication

Each elliptic curve in class 14400.n has complex multiplication by an order in the imaginary quadratic field \(\Q(\sqrt{-3}) \).

Modular form 14400.2.a.n

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.

\(\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with LMFDB labels.