Elliptic curve isogeny class with LMFDB label 1600.n (Cremona label 1600o)

• Label: 1600.n
• Number of curves: $4$
• Conductor: $1600$
• CM: \(\Q(\sqrt{-1}) \)
• Rank: $0$

Elliptic curves in class 1600.n

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality	CM discriminant
1600.n1	1600o3	\([0, 0, 0, -1100, -14000]\)	\(287496\)	\(512000000\)	\([2]\)	\(512\)	\(0.53391\)		\(-16\)
1600.n2	1600o4	\([0, 0, 0, -1100, 14000]\)	\(287496\)	\(512000000\)	\([2]\)	\(512\)	\(0.53391\)		\(-16\)
1600.n3	1600o2	\([0, 0, 0, -100, 0]\)	\(1728\)	\(64000000\)	\([2, 2]\)	\(256\)	\(0.18733\)		\(-4\)
1600.n4	1600o1	\([0, 0, 0, 25, 0]\)	\(1728\)	\(-1000000\)	\([2]\)	\(128\)	\(-0.15924\)	\(\Gamma_0(N)\)-optimal	\(-4\)

Rank

The elliptic curves in class 1600.n have rank \(0\).

Complex multiplication

Each elliptic curve in class 1600.n has complex multiplication by an order in the imaginary quadratic field \(\Q(\sqrt{-1}) \).

Modular form 1600.2.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.

\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with LMFDB labels.