Elliptic curve isogeny class with Cremona label 6630e (LMFDB label 6630.e)

• Label: 6630e
• Number of curves: $4$
• Conductor: $6630$
• CM: no
• Rank: $2$

Elliptic curves in class 6630e

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
6630.e3	6630e1	\([1, 1, 0, -587, 5229]\)	\(22428153804601/35802000\)	\(35802000\)	\([2]\)	\(5376\)	\(0.34711\)	\(\Gamma_0(N)\)-optimal
6630.e2	6630e2	\([1, 1, 0, -767, 1521]\)	\(50002789171321/27473062500\)	\(27473062500\)	\([2, 2]\)	\(10752\)	\(0.69369\)
6630.e1	6630e3	\([1, 1, 0, -7397, -246441]\)	\(44769506062996441/323730468750\)	\(323730468750\)	\([2]\)	\(21504\)	\(1.0403\)
6630.e4	6630e4	\([1, 1, 0, 2983, 15771]\)	\(2933972022568679/1789082460750\)	\(-1789082460750\)	\([2]\)	\(21504\)	\(1.0403\)

Rank

The elliptic curves in class 6630e have rank \(2\).

Complex multiplication

The elliptic curves in class 6630e do not have complex multiplication.

Modular form 6630.2.a.e

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.