Elliptic curve isogeny class with Cremona label 1290d (LMFDB label 1290.e)

• Label: 1290d
• Number of curves: $4$
• Conductor: $1290$
• CM: no
• Rank: $0$

Elliptic curves in class 1290d

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
1290.e3	1290d1	\([1, 0, 1, -69, -224]\)	\(35578826569/51600\)	\(51600\)	\([2]\)	\(192\)	\(-0.19366\)	\(\Gamma_0(N)\)-optimal
1290.e2	1290d2	\([1, 0, 1, -89, -88]\)	\(76711450249/41602500\)	\(41602500\)	\([2, 2]\)	\(384\)	\(0.15292\)
1290.e1	1290d3	\([1, 0, 1, -839, 9212]\)	\(65202655558249/512820150\)	\(512820150\)	\([2]\)	\(768\)	\(0.49949\)
1290.e4	1290d4	\([1, 0, 1, 341, -604]\)	\(4403686064471/2721093750\)	\(-2721093750\)	\([2]\)	\(768\)	\(0.49949\)

Rank

The elliptic curves in class 1290d have rank \(0\).

Complex multiplication

The elliptic curves in class 1290d do not have complex multiplication.

Modular form 1290.2.a.d

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.