Elliptic curve isogeny class with Cremona label 68400ee (LMFDB label 68400.cd)

• Label: 68400ee
• Number of curves: $3$
• Conductor: $68400$
• CM: no
• Rank: $1$

Elliptic curves in class 68400ee

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
68400.cd2	68400ee1	$[0, 0, 0, -55875, 5085250]$	$-413493625/152$	$-7091712000000$	$[]$	$207360$	$1.4337$	$\Gamma_0(N)$-optimal
68400.cd3	68400ee2	$[0, 0, 0, 34125, 19323250]$	$94196375/3511808$	$-163846914048000000$	$[]$	$622080$	$1.9830$
68400.cd1	68400ee3	$[0, 0, 0, -307875, -528902750]$	$-69173457625/2550136832$	$-118979184033792000000$	$[]$	$1866240$	$2.5323$

Rank

The elliptic curves in class 68400ee have rank $1$.

Complex multiplication

The elliptic curves in class 68400ee do not have complex multiplication.

Modular form 68400.2.a.ee

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.

$\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)$

Isogeny graph

The vertices are labelled with Cremona labels.