Elliptic curve isogeny class with LMFDB label 490960.bi (Cremona label 490960bi)

• Label: 490960.bi
• Number of curves: $4$
• Conductor: $490960$
• CM: no
• Rank: $1$

Elliptic curves in class 490960.bi

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
490960.bi1	490960bi4	\([0, 0, 0, -419843, -102459742]\)	\(84944038338/2088025\)	\(201181134182451200\)	\([2]\)	\(3538944\)	\(2.1041\)
490960.bi2	490960bi2	\([0, 0, 0, -58843, 3168858]\)	\(467720676/180625\)	\(8701606149760000\)	\([2, 2]\)	\(1769472\)	\(1.7575\)
490960.bi3	490960bi1	\([0, 0, 0, -51623, 4513222]\)	\(1263257424/425\)	\(5118591852800\)	\([2]\)	\(884736\)	\(1.4109\)	\(\Gamma_0(N)\)-optimal^*
490960.bi4	490960bi3	\([0, 0, 0, 186637, 22758162]\)	\(7462174302/6640625\)	\(-639823981600000000\)	\([2]\)	\(3538944\)	\(2.1041\)

^*optimality has not been determined rigorously for conductors over 400000. In this case the optimal curve is certainly one of the 0 curves highlighted, and conditionally curve 490960.bi1.

Rank

The elliptic curves in class 490960.bi have rank \(1\).

Complex multiplication

The elliptic curves in class 490960.bi do not have complex multiplication.

Modular form 490960.2.a.bi

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.