Elliptic curve isogeny class with Cremona label 6720j (LMFDB label 6720.w)

• Label: 6720j
• Number of curves: $4$
• Conductor: $6720$
• CM: no
• Rank: $0$

Elliptic curves in class 6720j

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
6720.w3	6720j1	$[0, -1, 0, -285, -1683]$	$2508888064/118125$	$120960000$	$[2]$	$3072$	$0.31171$	$\Gamma_0(N)$-optimal
6720.w2	6720j2	$[0, -1, 0, -785, 6417]$	$3269383504/893025$	$14631321600$	$[2, 2]$	$6144$	$0.65828$
6720.w1	6720j3	$[0, -1, 0, -11585, 483777]$	$2624033547076/324135$	$21242511360$	$[2]$	$12288$	$1.0049$
6720.w4	6720j4	$[0, -1, 0, 2015, 39457]$	$13799183324/18600435$	$-1218998108160$	$[2]$	$12288$	$1.0049$

Rank

The elliptic curves in class 6720j have rank $0$.

Complex multiplication

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

Modular form 6720.2.a.j

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.