Elliptic curve isogeny class with Cremona label 8400e (LMFDB label 8400.z)

• Label: 8400e
• Number of curves: $4$
• Conductor: $8400$
• CM: no
• Rank: $0$

Elliptic curves in class 8400e

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
8400.z4	8400e1	\([0, -1, 0, 217, 10062]\)	\(4499456/180075\)	\(-45018750000\)	\([2]\)	\(6144\)	\(0.72405\)	\(\Gamma_0(N)\)-optimal
8400.z3	8400e2	\([0, -1, 0, -5908, 169312]\)	\(5702413264/275625\)	\(1102500000000\)	\([2, 2]\)	\(12288\)	\(1.0706\)
8400.z2	8400e3	\([0, -1, 0, -16408, -586688]\)	\(30534944836/8203125\)	\(131250000000000\)	\([2]\)	\(24576\)	\(1.4172\)
8400.z1	8400e4	\([0, -1, 0, -93408, 11019312]\)	\(5633270409316/14175\)	\(226800000000\)	\([2]\)	\(24576\)	\(1.4172\)

Rank

The elliptic curves in class 8400e have rank \(0\).

Complex multiplication

The elliptic curves in class 8400e do not have complex multiplication.

Modular form 8400.2.a.e

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.

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

Isogeny graph

The vertices are labelled with Cremona labels.