Elliptic curve isogeny class with LMFDB label 424536.dj (Cremona label 424536dj)

• Label: 424536.dj
• Number of curves: $2$
• Conductor: $424536$
• CM: no
• Rank: $0$

Elliptic curves in class 424536.dj

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
424536.dj1	424536dj2	\([0, 1, 0, -46328, -3426144]\)	\(665500/81\)	\(1338445528906752\)	\([2]\)	\(1769472\)	\(1.6329\)	\(\Gamma_0(N)\)-optimal^*
424536.dj2	424536dj1	\([0, 1, 0, 4212, -272448]\)	\(2000/9\)	\(-37179042469632\)	\([2]\)	\(884736\)	\(1.2863\)	\(\Gamma_0(N)\)-optimal^*

^*optimality has not been determined rigorously for conductors over 400000. In this case the optimal curve is certainly one of the 2 curves highlighted, and conditionally curve 424536.dj1.

Rank

The elliptic curves in class 424536.dj have rank \(0\).

Complex multiplication

The elliptic curves in class 424536.dj do not have complex multiplication.

Modular form 424536.2.a.dj

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.

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with LMFDB labels.