Elliptic curve isogeny class with Cremona label 262080f (LMFDB label 262080.f)

• Label: 262080f
• Number of curves: $2$
• Conductor: $262080$
• CM: no
• Rank: $2$

Elliptic curves in class 262080f

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
262080.f2	262080f1	\([0, 0, 0, -20088, 6481512]\)	\(-44477724672/874680625\)	\(-17629530871680000\)	\([2]\)	\(2162688\)	\(1.7983\)	\(\Gamma_0(N)\)-optimal
262080.f1	262080f2	\([0, 0, 0, -658908, 205026768]\)	\(98104024066032/462109375\)	\(149023929600000000\)	\([2]\)	\(4325376\)	\(2.1449\)

Rank

The elliptic curves in class 262080f have rank \(2\).

Complex multiplication

The elliptic curves in class 262080f do not have complex multiplication.

Modular form 262080.2.a.f

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.

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.