Elliptic curve isogeny class with LMFDB label 720.f (Cremona label 720e)

• Label: 720.f
• Number of curves: $4$
• Conductor: $720$
• CM: no
• Rank: $1$

Elliptic curves in class 720.f

LMFDB label	Cremona label	Weierstrass coefficients	Torsion structure	Modular degree	Optimality
720.f1	720e3	[0, 0, 0, -1947, -33046]	[2]	512
720.f2	720e4	[0, 0, 0, -1227, 16346]	[4]	512
720.f3	720e2	[0, 0, 0, -147, -286]	[2, 2]	256
720.f4	720e1	[0, 0, 0, 33, -34]	[2]	128	\(\Gamma_0(N)\)-optimal

Rank

The elliptic curves in class 720.f have rank \(1\).

Complex multiplication

The elliptic curves in class 720.f do not have complex multiplication.

Modular form 720.2.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.

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

Isogeny graph

The vertices are labelled with LMFDB labels.