Elliptic curve isogeny class with Cremona label 6720bj (LMFDB label 6720.a)

• Label: 6720bj
• Number of curves: $4$
• Conductor: $6720$
• CM: no
• Rank: $2$

Elliptic curves in class 6720bj

LMFDB label	Cremona label	Weierstrass coefficients	Torsion structure	Modular degree	Optimality
6720.a3	6720bj1	[0, -1, 0, -36, -30]	[2]	1536	\(\Gamma_0(N)\)-optimal
6720.a2	6720bj2	[0, -1, 0, -281, 1881]	[2, 2]	3072
6720.a1	6720bj3	[0, -1, 0, -4481, 116961]	[2]	6144
6720.a4	6720bj4	[0, -1, 0, -1, 5185]	[2]	6144

Rank

The elliptic curves in class 6720bj have rank \(2\).

Complex multiplication

The elliptic curves in class 6720bj do not have complex multiplication.

Modular form 6720.2.a.bj

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.

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

Isogeny graph

The vertices are labelled with Cremona labels.