Elliptic curve isogeny class with LMFDB label 60840.o (Cremona label 60840f)

• Label: 60840.o
• Number of curves: $4$
• Conductor: $60840$
• CM: no
• Rank: $0$

Elliptic curves in class 60840.o

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
60840.o1	60840f4	\([0, 0, 0, -15052323, 10700985022]\)	\(52337949619538/23423590125\)	\(168799460582533038336000\)	\([2]\)	\(4128768\)	\(3.1523\)
60840.o2	60840f2	\([0, 0, 0, -7447323, -7707677978]\)	\(12677589459076/213890625\)	\(770689333509264000000\)	\([2, 2]\)	\(2064384\)	\(2.8058\)
60840.o3	60840f1	\([0, 0, 0, -7416903, -7774668902]\)	\(50091484483024/14625\)	\(13174176641184000\)	\([2]\)	\(1032192\)	\(2.4592\)	\(\Gamma_0(N)\)-optimal
60840.o4	60840f3	\([0, 0, 0, -329043, -21828921842]\)	\(-546718898/28564453125\)	\(-205846510018500000000000\)	\([2]\)	\(4128768\)	\(3.1523\)

Rank

The elliptic curves in class 60840.o have rank \(0\).

Complex multiplication

The elliptic curves in class 60840.o do not have complex multiplication.

Modular form 60840.2.a.o

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.

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with LMFDB labels.