Elliptic curve isogeny class with Cremona label 67760cj (LMFDB label 67760.r)

• Label: 67760cj
• Number of curves: $2$
• Conductor: $67760$
• CM: no
• Rank: $1$

Elliptic curves in class 67760cj

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
67760.r1	67760cj1	\([0, -1, 0, -2240, 118912]\)	\(-2509090441/10718750\)	\(-5312384000000\)	\([]\)	\(124416\)	\(1.1268\)	\(\Gamma_0(N)\)-optimal
67760.r2	67760cj2	\([0, -1, 0, 19760, -2855488]\)	\(1721540467559/8070721400\)	\(-3999978657382400\)	\([]\)	\(373248\)	\(1.6761\)

Rank

The elliptic curves in class 67760cj have rank \(1\).

Complex multiplication

The elliptic curves in class 67760cj do not have complex multiplication.

Modular form 67760.2.a.cj

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.

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

Isogeny graph

The vertices are labelled with Cremona labels.