Elliptic curve isogeny class with Cremona label 78400ko (LMFDB label 78400.df)

• Label: 78400ko
• Number of curves: $2$
• Conductor: $78400$
• CM: no
• Rank: $2$

Elliptic curves in class 78400ko

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
78400.df2	78400ko1	$[0, -1, 0, 8167, -399713]$	$4096/7$	$-102942875000000$	$[]$	$153600$	$1.3737$	$\Gamma_0(N)$-optimal
78400.df1	78400ko2	$[0, -1, 0, -726833, 239945287]$	$-2887553024/16807$	$-247165842875000000$	$[]$	$768000$	$2.1784$

Rank

The elliptic curves in class 78400ko have rank $2$.

Complex multiplication

The elliptic curves in class 78400ko do not have complex multiplication.

Modular form 78400.2.a.ko

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.

$\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)$

Isogeny graph

The vertices are labelled with Cremona labels.