Elliptic curve isogeny class with Cremona label 242550nj (LMFDB label 242550.nj)

• Label: 242550nj
• Number of curves: $4$
• Conductor: $242550$
• CM: no
• Rank: $1$

Elliptic curves in class 242550nj

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
242550.nj4	242550nj1	\([1, -1, 1, 110020, 114771647]\)	\(109902239/4312000\)	\(-5778492402375000000\)	\([2]\)	\(5308416\)	\(2.2799\)	\(\Gamma_0(N)\)-optimal
242550.nj2	242550nj2	\([1, -1, 1, -2976980, 1892883647]\)	\(2177286259681/105875000\)	\(141882625951171875000\)	\([2]\)	\(10616832\)	\(2.6265\)
242550.nj3	242550nj3	\([1, -1, 1, -992480, -3139808353]\)	\(-80677568161/3131816380\)	\(-4196933478075968437500\)	\([2]\)	\(15925248\)	\(2.8292\)
242550.nj1	242550nj4	\([1, -1, 1, -38808230, -92536241353]\)	\(4823468134087681/30382271150\)	\(40715149120401705468750\)	\([2]\)	\(31850496\)	\(3.1758\)

Rank

The elliptic curves in class 242550nj have rank \(1\).

Complex multiplication

The elliptic curves in class 242550nj do not have complex multiplication.

Modular form 242550.2.a.nj

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.