Elliptic curve isogeny class with Cremona label 12240v (LMFDB label 12240.bo)

• Label: 12240v
• Number of curves: $4$
• Conductor: $12240$
• CM: no
• Rank: $0$

Elliptic curves in class 12240v

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
12240.bo3	12240v1	$[0, 0, 0, -8562, 249991]$	$5951163357184/1129312125$	$13172296626000$	$[2]$	$27648$	$1.2350$	$\Gamma_0(N)$-optimal
12240.bo2	12240v2	$[0, 0, 0, -41367, -3010826]$	$41948679809104/3291890625$	$614345796000000$	$[2, 2]$	$55296$	$1.5816$
12240.bo1	12240v3	$[0, 0, 0, -648867, -201177326]$	$40472803590982276/281883375$	$210424811904000$	$[2]$	$110592$	$1.9281$
12240.bo4	12240v4	$[0, 0, 0, 41253, -13536614]$	$10400706415004/112060546875$	$-83652750000000000$	$[4]$	$110592$	$1.9281$

Rank

The elliptic curves in class 12240v have rank $0$.

Complex multiplication

The elliptic curves in class 12240v do not have complex multiplication.

Modular form 12240.2.a.v

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.