Elliptic curve isogeny class with Cremona label 9240r (LMFDB label 9240.e)

• Label: 9240r
• Number of curves: $4$
• Conductor: $9240$
• CM: no
• Rank: $1$

Elliptic curves in class 9240r

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
9240.e4	9240r1	\([0, -1, 0, 15609, 3615480]\)	\(26284586405881856/369163298455875\)	\(-5906612775294000\)	\([2]\)	\(46080\)	\(1.7070\)	\(\Gamma_0(N)\)-optimal
9240.e3	9240r2	\([0, -1, 0, -279636, 53452836]\)	\(9446361110552374864/661910688140625\)	\(169449136164000000\)	\([2, 2]\)	\(92160\)	\(2.0535\)
9240.e2	9240r3	\([0, -1, 0, -887136, -257344164]\)	\(75404081626158563716/15633273575910375\)	\(16008472141732224000\)	\([2]\)	\(184320\)	\(2.4001\)
9240.e1	9240r4	\([0, -1, 0, -4396056, 3549116700]\)	\(9175156963749600923236/50249267578125\)	\(51455250000000000\)	\([2]\)	\(184320\)	\(2.4001\)

Rank

The elliptic curves in class 9240r have rank \(1\).

Complex multiplication

The elliptic curves in class 9240r do not have complex multiplication.

Modular form 9240.2.a.r

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.