Elliptic curve isogeny class with LMFDB label 14400.b (Cremona label 14400dm)

• Label: 14400.b
• Number of curves: $2$
• Conductor: $14400$
• CM: \(\Q(\sqrt{-3}) \)
• Rank: $1$

Elliptic curves in class 14400.b

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality	CM discriminant
14400.b1	14400dm1	\([0, 0, 0, 0, -1250]\)	\(0\)	\(-675000000\)	\([]\)	\(5760\)	\(0.37307\)	\(\Gamma_0(N)\)-optimal	\(-3\)
14400.b2	14400dm2	\([0, 0, 0, 0, 33750]\)	\(0\)	\(-492075000000\)	\([]\)	\(17280\)	\(0.92237\)		\(-3\)

Rank

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

Complex multiplication

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

Modular form 14400.2.a.b

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.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with LMFDB labels.