Elliptic curve isogeny class with Cremona label 5586j (LMFDB label 5586.i)

• Label: 5586j
• Number of curves: $4$
• Conductor: $5586$
• CM: no
• Rank: $1$

Elliptic curves in class 5586j

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
5586.i3	5586j1	\([1, 1, 0, -7914, 155268]\)	\(466025146777/177366672\)	\(20867011594128\)	\([2]\)	\(15360\)	\(1.2551\)	\(\Gamma_0(N)\)-optimal
5586.i2	5586j2	\([1, 1, 0, -55934, -5002080]\)	\(164503536215257/4178071044\)	\(491545880255556\)	\([2, 2]\)	\(30720\)	\(1.6017\)
5586.i1	5586j3	\([1, 1, 0, -889424, -323228562]\)	\(661397832743623417/443352042\)	\(52159924389258\)	\([2]\)	\(61440\)	\(1.9483\)
5586.i4	5586j4	\([1, 1, 0, 9236, -15885470]\)	\(740480746823/927484650666\)	\(-109117641666204234\)	\([2]\)	\(61440\)	\(1.9483\)

Rank

The elliptic curves in class 5586j have rank \(1\).

Complex multiplication

The elliptic curves in class 5586j do not have complex multiplication.

Modular form 5586.2.a.j

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.