Elliptic curve isogeny class with Cremona label 123840ey (LMFDB label 123840.i)

• Label: 123840ey
• Number of curves: $4$
• Conductor: $123840$
• CM: no
• Rank: $1$

Elliptic curves in class 123840ey

LMFDB label	Cremona label	Weierstrass coefficients	Torsion structure	Modular degree	Optimality
123840.i3	123840ey1	[0, 0, 0, -39468, -3014192]	[2]	294912	\(\Gamma_0(N)\)-optimal
123840.i2	123840ey2	[0, 0, 0, -50988, -1111088]	[2, 2]	589824
123840.i4	123840ey3	[0, 0, 0, 196692, -8739632]	[2]	1179648
123840.i1	123840ey4	[0, 0, 0, -482988, 128316112]	[2]	1179648

Rank

The elliptic curves in class 123840ey have rank \(1\).

Complex multiplication

The elliptic curves in class 123840ey do not have complex multiplication.

Modular form 123840.2.a.ey

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.