Elliptic curve isogeny class with Cremona label 486720nf (LMFDB label 486720.nf)

• Label: 486720nf
• Number of curves: $4$
• Conductor: $486720$
• CM: no
• Rank: $0$

Elliptic curves in class 486720nf

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
486720.nf4	486720nf1	$[0, 0, 0, 509028, 98671664]$	$253012016/219375$	$-12647209575536640000$	$[2]$	$8257536$	$2.3529$	$\Gamma_0(N)$-optimal^*
486720.nf3	486720nf2	$[0, 0, 0, -2532972, 873773264]$	$7793764996/3080025$	$710267289762137702400$	$[2, 2]$	$16515072$	$2.6994$	$\Gamma_0(N)$-optimal^*
486720.nf1	486720nf3	$[0, 0, 0, -35386572, 80997132944]$	$10625310339698/3855735$	$1778298843997055877120$	$[2]$	$33030144$	$3.0460$	$\Gamma_0(N)$-optimal^*
486720.nf2	486720nf4	$[0, 0, 0, -18351372, -29643084016]$	$1481943889298/34543665$	$15931841668818411847680$	$[2]$	$33030144$	$3.0460$

^*optimality has not been determined rigorously for conductors over 400000. In this case the optimal curve is certainly one of the 3 curves highlighted, and conditionally curve 486720nf1.

Rank

The elliptic curves in class 486720nf have rank $0$.

Complex multiplication

The elliptic curves in class 486720nf do not have complex multiplication.

Modular form 486720.2.a.nf

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.