Elliptic curve isogeny class with Cremona label 1600u (LMFDB label 1600.l)

• Label: 1600u
• Number of curves: $2$
• Conductor: $1600$
• CM: \(\Q(\sqrt{-1}) \)
• Rank: $1$

Elliptic curves in class 1600u

LMFDB label	Cremona label	Weierstrass coefficients	Torsion structure	Modular degree	Optimality	CM discriminant
1600.l2	1600u1	[0, 0, 0, 125, 0]	[2]	320	\(\Gamma_0(N)\)-optimal	-4
1600.l1	1600u2	[0, 0, 0, -500, 0]	[2]	640		-4

Rank

The elliptic curves in class 1600u have rank \(1\).

Complex multiplication

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

Modular form 1600.2.a.u

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.

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

Isogeny graph

The vertices are labelled with Cremona labels.