Elliptic curve isogeny class with LMFDB label 47040.dz (Cremona label 47040gk)

• Label: 47040.dz
• Number of curves: $4$
• Conductor: $47040$
• CM: no
• Rank: $0$

Elliptic curves in class 47040.dz

LMFDB label	Cremona label	Weierstrass coefficients	Torsion structure	Modular degree	Optimality
47040.dz1	47040gk4	[0, 1, 0, -1171361, 487569375]	[2]	589824
47040.dz2	47040gk2	[0, 1, 0, -73761, 7479135]	[2, 2]	294912
47040.dz3	47040gk1	[0, 1, 0, -11041, -285601]	[2]	147456	\(\Gamma_0(N)\)-optimal
47040.dz4	47040gk3	[0, 1, 0, 20319, 25335519]	[2]	589824

Rank

The elliptic curves in class 47040.dz have rank \(0\).

Complex multiplication

The elliptic curves in class 47040.dz do not have complex multiplication.

Modular form 47040.2.a.dz

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.