Elliptic curve isogeny class with Cremona label 15680f (LMFDB label 15680.bv)

• Label: 15680f
• Number of curves: $4$
• Conductor: $15680$
• CM: no
• Rank: $2$

Elliptic curves in class 15680f

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
15680.bv4	15680f1	$[0, 0, 0, 7252, 378672]$	$1367631/2800$	$-86354742476800$	$[2]$	$36864$	$1.3585$	$\Gamma_0(N)$-optimal
15680.bv3	15680f2	$[0, 0, 0, -55468, 4066608]$	$611960049/122500$	$3778019983360000$	$[2, 2]$	$73728$	$1.7051$
15680.bv2	15680f3	$[0, 0, 0, -274988, -51867088]$	$74565301329/5468750$	$168661606400000000$	$[2]$	$147456$	$2.0517$
15680.bv1	15680f4	$[0, 0, 0, -839468, 296028208]$	$2121328796049/120050$	$3702459583692800$	$[2]$	$147456$	$2.0517$

Rank

The elliptic curves in class 15680f have rank $2$.

Complex multiplication

The elliptic curves in class 15680f do not have complex multiplication.

Modular form 15680.2.a.f

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.