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

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

Elliptic curves in class 486720.qa

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
486720.qa1	486720qa3	\([0, 0, 0, -10077132, 12266184944]\)	\(490757540836/2142075\)	\(493971901110293299200\)	\([2]\)	\(33030144\)	\(2.8237\)	\(\Gamma_0(N)\)-optimal^*
486720.qa2	486720qa2	\([0, 0, 0, -951132, -24711856]\)	\(1650587344/950625\)	\(54804574827325440000\)	\([2, 2]\)	\(16515072\)	\(2.4771\)	\(\Gamma_0(N)\)-optimal^*
486720.qa3	486720qa1	\([0, 0, 0, -677352, -214058104]\)	\(9538484224/26325\)	\(94854071816524800\)	\([2]\)	\(8257536\)	\(2.1305\)	\(\Gamma_0(N)\)-optimal^*
486720.qa4	486720qa4	\([0, 0, 0, 3794388, -197448784]\)	\(26198797244/15234375\)	\(-3513113770982400000000\)	\([2]\)	\(33030144\)	\(2.8237\)

^*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 486720.qa1.

Rank

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

Complex multiplication

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

Modular form 486720.2.a.qa

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 LMFDB 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 LMFDB labels.