Elliptic curve isogeny class with Cremona label 6720bi (LMFDB label 6720.c)

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

Elliptic curves in class 6720bi

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
6720.c4	6720bi1	$[0, -1, 0, -1600156, -768989294]$	$7079962908642659949376/100085966990454375$	$6405501887389080000$	$[2]$	$215040$	$2.4134$	$\Gamma_0(N)$-optimal
6720.c2	6720bi2	$[0, -1, 0, -25515001, -49598319815]$	$448487713888272974160064/91549016015625$	$374984769600000000$	$[2, 2]$	$430080$	$2.7600$
6720.c1	6720bi3	$[0, -1, 0, -408240001, -3174701034815]$	$229625675762164624948320008/9568125$	$313528320000$	$[2]$	$860160$	$3.1066$
6720.c3	6720bi4	$[0, -1, 0, -25427521, -49955395679]$	$-55486311952875723077768/801237030029296875$	$-26254935000000000000000$	$[2]$	$860160$	$3.1066$

Rank

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

Complex multiplication

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

Modular form 6720.2.a.bi

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.