Elliptic curve isogeny class with LMFDB label 123840.dk (Cremona label 123840cd)

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

Elliptic curves in class 123840.dk

LMFDB label	Cremona label	Weierstrass coefficients	Torsion structure	Modular degree	Optimality
123840.dk1	123840cd4	[0, 0, 0, -482988, -128316112]	[2]	1179648
123840.dk2	123840cd2	[0, 0, 0, -50988, 1111088]	[2, 2]	589824
123840.dk3	123840cd1	[0, 0, 0, -39468, 3014192]	[2]	294912	\(\Gamma_0(N)\)-optimal
123840.dk4	123840cd3	[0, 0, 0, 196692, 8739632]	[2]	1179648

Rank

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

Complex multiplication

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

Modular form 123840.2.a.dk

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.