Elliptic curve isogeny class with Cremona label 5610a (LMFDB label 5610.c)

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

Elliptic curves in class 5610a

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
5610.c4	5610a1	\([1, 1, 0, -28, 208]\)	\(-2565726409/19388160\)	\(-19388160\)	\([2]\)	\(2048\)	\(0.081343\)	\(\Gamma_0(N)\)-optimal
5610.c3	5610a2	\([1, 1, 0, -748, 7552]\)	\(46380496070089/125888400\)	\(125888400\)	\([2, 2]\)	\(4096\)	\(0.42792\)
5610.c2	5610a3	\([1, 1, 0, -1048, 532]\)	\(127483771761289/73369857660\)	\(73369857660\)	\([2]\)	\(8192\)	\(0.77449\)
5610.c1	5610a4	\([1, 1, 0, -11968, 498988]\)	\(189602977175292169/1402500\)	\(1402500\)	\([2]\)	\(8192\)	\(0.77449\)

Rank

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

Complex multiplication

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

Modular form 5610.2.a.a

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.