Elliptic curve isogeny class with LMFDB label 1680.f (Cremona label 1680n)

• Label: 1680.f
• Number of curves: $4$
• Conductor: $1680$
• CM: no
• Rank: $1$

Elliptic curves in class 1680.f

LMFDB label	Cremona label	Weierstrass coefficients	Torsion structure	Modular degree	Optimality
1680.f1	1680n3	[0, -1, 0, -1800, 30000]	[4]	1024
1680.f2	1680n2	[0, -1, 0, -120, 432]	[2, 2]	512
1680.f3	1680n1	[0, -1, 0, -40, -80]	[2]	256	\(\Gamma_0(N)\)-optimal
1680.f4	1680n4	[0, -1, 0, 280, 2352]	[2]	1024

Rank

The elliptic curves in class 1680.f have rank \(1\).

Complex multiplication

The elliptic curves in class 1680.f do not have complex multiplication.

Modular form 1680.2.a.f

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.

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

Isogeny graph

The vertices are labelled with LMFDB labels.