Elliptic curve isogeny class with LMFDB label 5610.o (Cremona label 5610n)

• Label: 5610.o
• Number of curves: $4$
• Conductor: $5610$
• CM: no
• Rank: $1$

Elliptic curves in class 5610.o

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
5610.o1	5610n4	\([1, 0, 1, -220364, -39529438]\)	\(1183430669265454849849/10449720703125000\)	\(10449720703125000\)	\([2]\)	\(69120\)	\(1.8973\)
5610.o2	5610n3	\([1, 0, 1, -23844, 403426]\)	\(1499114720492202169/796539777000000\)	\(796539777000000\)	\([2]\)	\(34560\)	\(1.5507\)
5610.o3	5610n2	\([1, 0, 1, -18899, 966116]\)	\(746461053445307689/27443694341250\)	\(27443694341250\)	\([6]\)	\(23040\)	\(1.3480\)
5610.o4	5610n1	\([1, 0, 1, -18729, 984952]\)	\(726497538898787209/1038579300\)	\(1038579300\)	\([6]\)	\(11520\)	\(1.0014\)	\(\Gamma_0(N)\)-optimal

Rank

The elliptic curves in class 5610.o have rank \(1\).

Complex multiplication

The elliptic curves in class 5610.o do not have complex multiplication.

Modular form 5610.2.a.o

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.

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with LMFDB labels.