Elliptic curve isogeny class with Cremona label 286650ej (LMFDB label 286650.ej)

• Label: 286650ej
• Number of curves: $4$
• Conductor: $286650$
• CM: no
• Rank: $2$

Elliptic curves in class 286650ej

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
286650.ej4	286650ej1	\([1, -1, 0, -2574567, 1588568841]\)	\(1408317602329/2153060\)	\(2885306320004062500\)	\([2]\)	\(7962624\)	\(2.4418\)	\(\Gamma_0(N)\)-optimal
286650.ej3	286650ej2	\([1, -1, 0, -3346317, 558282591]\)	\(3092354182009/1689383150\)	\(2263934994660330468750\)	\([2]\)	\(15925248\)	\(2.7884\)
286650.ej2	286650ej3	\([1, -1, 0, -10457442, -11463322284]\)	\(94376601570889/12235496000\)	\(16396734850484625000000\)	\([2]\)	\(23887872\)	\(2.9911\)
286650.ej1	286650ej4	\([1, -1, 0, -161720442, -791526613284]\)	\(349046010201856969/7245875000\)	\(9710165500013671875000\)	\([2]\)	\(47775744\)	\(3.3377\)

Rank

The elliptic curves in class 286650ej have rank \(2\).

Complex multiplication

The elliptic curves in class 286650ej do not have complex multiplication.

Modular form 286650.2.a.ej

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.

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

Isogeny graph

The vertices are labelled with Cremona labels.