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

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

Elliptic curves in class 486720md

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
486720.md4	486720md1	\([0, 0, 0, 509028, -98671664]\)	\(253012016/219375\)	\(-12647209575536640000\)	\([2]\)	\(8257536\)	\(2.3529\)	\(\Gamma_0(N)\)-optimal^*
486720.md3	486720md2	\([0, 0, 0, -2532972, -873773264]\)	\(7793764996/3080025\)	\(710267289762137702400\)	\([2, 2]\)	\(16515072\)	\(2.6994\)	\(\Gamma_0(N)\)-optimal^*
486720.md2	486720md3	\([0, 0, 0, -18351372, 29643084016]\)	\(1481943889298/34543665\)	\(15931841668818411847680\)	\([2]\)	\(33030144\)	\(3.0460\)	\(\Gamma_0(N)\)-optimal^*
486720.md1	486720md4	\([0, 0, 0, -35386572, -80997132944]\)	\(10625310339698/3855735\)	\(1778298843997055877120\)	\([2]\)	\(33030144\)	\(3.0460\)

^*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 486720md1.

Rank

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

Complex multiplication

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

Modular form 486720.2.a.md

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.