Elliptic curve isogeny class with LMFDB label 6840.g (Cremona label 6840r)

• Label: 6840.g
• Number of curves: $4$
• Conductor: $6840$
• CM: no
• Rank: $0$

Elliptic curves in class 6840.g

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
6840.g1	6840r3	\([0, 0, 0, -273603, -55084498]\)	\(3034301922374404/1425\)	\(1063756800\)	\([2]\)	\(16384\)	\(1.5058\)
6840.g2	6840r4	\([0, 0, 0, -20523, -491722]\)	\(1280615525284/601171875\)	\(448772400000000\)	\([2]\)	\(16384\)	\(1.5058\)
6840.g3	6840r2	\([0, 0, 0, -17103, -860398]\)	\(2964647793616/2030625\)	\(378963360000\)	\([2, 2]\)	\(8192\)	\(1.1592\)
6840.g4	6840r1	\([0, 0, 0, -858, -18907]\)	\(-5988775936/9774075\)	\(-114004810800\)	\([4]\)	\(4096\)	\(0.81261\)	\(\Gamma_0(N)\)-optimal

Rank

The elliptic curves in class 6840.g have rank \(0\).

Complex multiplication

The elliptic curves in class 6840.g do not have complex multiplication.

Modular form 6840.2.a.g

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.

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

Isogeny graph

The vertices are labelled with LMFDB labels.