Elliptic curve isogeny class with Cremona label 19600cb (LMFDB label 19600.bw)

• Label: 19600cb
• Number of curves: $4$
• Conductor: $19600$
• CM: \(\Q(\sqrt{-7}) \)
• Rank: $1$

Elliptic curves in class 19600cb

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality	CM discriminant
19600.bw4	19600cb1	\([0, 0, 0, -875, 12250]\)	\(-3375\)	\(-21952000000\)	\([2]\)	\(9216\)	\(0.69873\)	\(\Gamma_0(N)\)-optimal	\(-7\)
19600.bw3	19600cb2	\([0, 0, 0, -14875, 698250]\)	\(16581375\)	\(21952000000\)	\([2]\)	\(18432\)	\(1.0453\)		\(-28\)
19600.bw2	19600cb3	\([0, 0, 0, -42875, -4201750]\)	\(-3375\)	\(-2582630848000000\)	\([2]\)	\(64512\)	\(1.6717\)		\(-7\)
19600.bw1	19600cb4	\([0, 0, 0, -728875, -239499750]\)	\(16581375\)	\(2582630848000000\)	\([2]\)	\(129024\)	\(2.0183\)		\(-28\)

Rank

The elliptic curves in class 19600cb have rank \(1\).

Complex multiplication

Each elliptic curve in class 19600cb has complex multiplication by an order in the imaginary quadratic field \(\Q(\sqrt{-7}) \).

Modular form 19600.2.a.cb

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.

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

Isogeny graph

The vertices are labelled with Cremona labels.