Elliptic curve isogeny class with Cremona label 504c (LMFDB label 504.c)

• Label: 504c
• Number of curves: $4$
• Conductor: $504$
• CM: no
• Rank: $0$

Elliptic curves in class 504c

LMFDB label	Cremona label	Weierstrass coefficients	Torsion structure	Modular degree	Optimality
504.c4	504c1	[0, 0, 0, 9, -54]	[2]	64	\(\Gamma_0(N)\)-optimal
504.c3	504c2	[0, 0, 0, -171, -810]	[2, 2]	128
504.c1	504c3	[0, 0, 0, -2691, -53730]	[2]	256
504.c2	504c4	[0, 0, 0, -531, 3726]	[2]	256

Rank

The elliptic curves in class 504c have rank \(0\).

Complex multiplication

The elliptic curves in class 504c do not have complex multiplication.

Modular form 504.2.a.c

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.