Elliptic curve isogeny class with LMFDB label 1989.e (Cremona label 1989e)

• Label: 1989.e
• Number of curves: $6$
• Conductor: $1989$
• CM: no
• Rank: $1$

Elliptic curves in class 1989.e

LMFDB label	Cremona label	Weierstrass coefficients	Torsion structure	Modular degree	Optimality
1989.e1	1989e5	[1, -1, 0, -181566, 29819155]	[2]	8192
1989.e2	1989e3	[1, -1, 0, -12501, 368032]	[2, 2]	4096
1989.e3	1989e2	[1, -1, 0, -4896, -126293]	[2, 2]	2048
1989.e4	1989e1	[1, -1, 0, -4851, -128840]	[2]	1024	\(\Gamma_0(N)\)-optimal
1989.e5	1989e4	[1, -1, 0, 1989, -458150]	[2]	4096
1989.e6	1989e6	[1, -1, 0, 34884, 2462449]	[2]	8192

Rank

The elliptic curves in class 1989.e have rank \(1\).

Modular form 1989.2.a.e

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.

\(\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 8 & 8 & 4 \\ 2 & 1 & 2 & 4 & 4 & 2 \\ 4 & 2 & 1 & 2 & 2 & 4 \\ 8 & 4 & 2 & 1 & 4 & 8 \\ 8 & 4 & 2 & 4 & 1 & 8 \\ 4 & 2 & 4 & 8 & 8 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with LMFDB labels.