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.