Elliptic curve isogeny class with LMFDB label 12240.bj (Cremona label 12240cg)

• Label: 12240.bj
• Number of curves: $2$
• Conductor: $12240$
• CM: no
• Rank: $1$

Elliptic curves in class 12240.bj

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
12240.bj1	12240cg2	\([0, 0, 0, -956307, -371557294]\)	\(-32391289681150609/1228250000000\)	\(-3667534848000000000\)	\([]\)	\(181440\)	\(2.3322\)
12240.bj2	12240cg1	\([0, 0, 0, 57453, -1645486]\)	\(7023836099951/4456448000\)	\(-13306882424832000\)	\([]\)	\(60480\)	\(1.7829\)	\(\Gamma_0(N)\)-optimal

Rank

The elliptic curves in class 12240.bj have rank \(1\).

Complex multiplication

The elliptic curves in class 12240.bj do not have complex multiplication.

Modular form 12240.2.a.bj

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 LMFDB numbering.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with LMFDB labels.