Elliptic curve isogeny class with Cremona label 7488bu (LMFDB label 7488.i)

• Label: 7488bu
• Number of curves: $4$
• Conductor: $7488$
• CM: no
• Rank: $1$

Elliptic curves in class 7488bu

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
7488.i3	7488bu1	\([0, 0, 0, -1416, 20504]\)	\(420616192/117\)	\(87340032\)	\([2]\)	\(4096\)	\(0.50557\)	\(\Gamma_0(N)\)-optimal
7488.i2	7488bu2	\([0, 0, 0, -1596, 14960]\)	\(37642192/13689\)	\(163500539904\)	\([2, 2]\)	\(8192\)	\(0.85214\)
7488.i1	7488bu3	\([0, 0, 0, -10956, -430576]\)	\(3044193988/85293\)	\(4074936532992\)	\([2]\)	\(16384\)	\(1.1987\)
7488.i4	7488bu4	\([0, 0, 0, 4884, 105680]\)	\(269676572/257049\)	\(-12280707219456\)	\([2]\)	\(16384\)	\(1.1987\)

Rank

The elliptic curves in class 7488bu have rank \(1\).

Complex multiplication

The elliptic curves in class 7488bu do not have complex multiplication.

Modular form 7488.2.a.bu

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.