Elliptic curve isogeny class with LMFDB label 287490.b (Cremona label 287490b)

• Label: 287490.b
• Number of curves: $4$
• Conductor: $287490$
• CM: no
• Rank: $1$

Elliptic curves in class 287490.b

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
287490.b1	287490b3	\([1, 1, 0, -8172958, 8987739478]\)	\(23531588875176481/6398929110\)	\(16417901406845865990\)	\([2]\)	\(14008320\)	\(2.6700\)
287490.b2	287490b4	\([1, 1, 0, -3929058, -2924668782]\)	\(2614441086442081/74385450090\)	\(190852713741264426810\)	\([2]\)	\(14008320\)	\(2.6700\)
287490.b3	287490b2	\([1, 1, 0, -575008, 102696748]\)	\(8194759433281/2958272100\)	\(7590116851977888900\)	\([2, 2]\)	\(7004160\)	\(2.3234\)
287490.b4	287490b1	\([1, 1, 0, 109492, 11384448]\)	\(56578878719/54390000\)	\(-139549859385510000\)	\([2]\)	\(3502080\)	\(1.9769\)	\(\Gamma_0(N)\)-optimal

Rank

The elliptic curves in class 287490.b have rank \(1\).

Complex multiplication

The elliptic curves in class 287490.b do not have complex multiplication.

Modular form 287490.2.a.b

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.

\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with LMFDB labels.