Elliptic curve isogeny class with Cremona label 53816c (LMFDB label 53816.d)

• Label: 53816c
• Number of curves: $4$
• Conductor: $53816$
• CM: no
• Rank: $1$

Elliptic curves in class 53816c

LMFDB label	Cremona label	Weierstrass coefficients	Torsion structure	Modular degree	Optimality
53816.d4	53816c1	[0, 0, 0, 961, -59582]	[2]	57600	\(\Gamma_0(N)\)-optimal
53816.d3	53816c2	[0, 0, 0, -18259, -893730]	[2, 2]	115200
53816.d2	53816c3	[0, 0, 0, -56699, 4111158]	[2]	230400
53816.d1	53816c4	[0, 0, 0, -287339, -59284090]	[2]	230400

Rank

The elliptic curves in class 53816c have rank \(1\).

Complex multiplication

The elliptic curves in class 53816c do not have complex multiplication.

Modular form 53816.2.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.