Elliptic curve isogeny class with Cremona label 38850bj (LMFDB label 38850.bn)

• Label: 38850bj
• Number of curves: $4$
• Conductor: $38850$
• CM: no
• Rank: $1$

Elliptic curves in class 38850bj

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
38850.bn4	38850bj1	\([1, 0, 1, 1999, 28148]\)	\(56578878719/54390000\)	\(-849843750000\)	\([2]\)	\(61440\)	\(0.97612\)	\(\Gamma_0(N)\)-optimal
38850.bn3	38850bj2	\([1, 0, 1, -10501, 253148]\)	\(8194759433281/2958272100\)	\(46223001562500\)	\([2, 2]\)	\(122880\)	\(1.3227\)
38850.bn2	38850bj3	\([1, 0, 1, -71751, -7219352]\)	\(2614441086442081/74385450090\)	\(1162272657656250\)	\([2]\)	\(245760\)	\(1.6693\)
38850.bn1	38850bj4	\([1, 0, 1, -149251, 22175648]\)	\(23531588875176481/6398929110\)	\(99983267343750\)	\([2]\)	\(245760\)	\(1.6693\)

Rank

The elliptic curves in class 38850bj have rank \(1\).

Complex multiplication

The elliptic curves in class 38850bj do not have complex multiplication.

Modular form 38850.2.a.bj

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.