Elliptic curve isogeny class with Cremona label 5040bo (LMFDB label 5040.bg)

• Label: 5040bo
• Number of curves: $4$
• Conductor: $5040$
• CM: no
• Rank: $1$

Elliptic curves in class 5040bo

LMFDB label	Cremona label	Weierstrass coefficients	Torsion structure	Modular degree	Optimality
5040.bg3	5040bo1	[0, 0, 0, -507, -2774]	[2]	3072	\(\Gamma_0(N)\)-optimal
5040.bg2	5040bo2	[0, 0, 0, -3387, 73834]	[2, 2]	6144
5040.bg1	5040bo3	[0, 0, 0, -53787, 4801354]	[2]	12288
5040.bg4	5040bo4	[0, 0, 0, 933, 249226]	[4]	12288

Rank

The elliptic curves in class 5040bo have rank \(1\).

Complex multiplication

The elliptic curves in class 5040bo do not have complex multiplication.

Modular form 5040.2.a.bo

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.