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

• Label: 486720hz
• Number of curves: $4$
• Conductor: $486720$
• CM: no
• Rank: $1$

Elliptic curves in class 486720hz

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
486720.hz4	486720hz1	\([0, 0, 0, -123708, 59442032]\)	\(-3631696/24375\)	\(-1405245508392960000\)	\([2]\)	\(8257536\)	\(2.1656\)	\(\Gamma_0(N)\)-optimal^*
486720.hz3	486720hz2	\([0, 0, 0, -3165708, 2163289232]\)	\(15214885924/38025\)	\(8768731972372070400\)	\([2, 2]\)	\(16515072\)	\(2.5122\)	\(\Gamma_0(N)\)-optimal^*
486720.hz1	486720hz3	\([0, 0, 0, -50620908, 138625462352]\)	\(31103978031362/195\)	\(89935712537149440\)	\([2]\)	\(33030144\)	\(2.8587\)	\(\Gamma_0(N)\)-optimal^*
486720.hz2	486720hz4	\([0, 0, 0, -4382508, 347336912]\)	\(20183398562/11567205\)	\(5334896531991167631360\)	\([2]\)	\(33030144\)	\(2.8587\)

^*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 486720hz1.

Rank

The elliptic curves in class 486720hz have rank \(1\).

Complex multiplication

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

Modular form 486720.2.a.hz

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.