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 \(1\).

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.