Elliptic curve isogeny class with Cremona label 6288l (LMFDB label 6288.n)

• Label: 6288l
• Number of curves: $4$
• Conductor: $6288$
• CM: no
• Rank: $1$

Elliptic curves in class 6288l

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
6288.n4	6288l1	\([0, 1, 0, -472, -748]\)	\(2845178713/1609728\)	\(6593445888\)	\([2]\)	\(3456\)	\(0.57409\)	\(\Gamma_0(N)\)-optimal
6288.n2	6288l2	\([0, 1, 0, -5592, -162540]\)	\(4722184089433/9884736\)	\(40487878656\)	\([2, 2]\)	\(6912\)	\(0.92066\)
6288.n1	6288l3	\([0, 1, 0, -89432, -10323948]\)	\(19312898130234073/84888\)	\(347701248\)	\([2]\)	\(13824\)	\(1.2672\)
6288.n3	6288l4	\([0, 1, 0, -3672, -273900]\)	\(-1337180541913/7067998104\)	\(-28950520233984\)	\([2]\)	\(13824\)	\(1.2672\)

Rank

The elliptic curves in class 6288l have rank \(1\).

Complex multiplication

The elliptic curves in class 6288l do not have complex multiplication.

Modular form 6288.2.a.l

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.