Elliptic curve isogeny class with Cremona label 40080r (LMFDB label 40080.j)

• Label: 40080r
• Number of curves: $2$
• Conductor: $40080$
• CM: no
• Rank: $0$

Elliptic curves in class 40080r

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
40080.j2	40080r1	\([0, -1, 0, 11464, -4329360]\)	\(40675641638471/1996889557500\)	\(-8179259627520000\)	\([2]\)	\(258048\)	\(1.7331\)	\(\Gamma_0(N)\)-optimal
40080.j1	40080r2	\([0, -1, 0, -338456, -72633744]\)	\(1046819248735488409/47650971093750\)	\(195178377600000000\)	\([2]\)	\(516096\)	\(2.0797\)

Rank

The elliptic curves in class 40080r have rank \(0\).

Complex multiplication

The elliptic curves in class 40080r do not have complex multiplication.

Modular form 40080.2.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.

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

Isogeny graph

The vertices are labelled with Cremona labels.