Elliptic curve isogeny class with Cremona label 78400gz (LMFDB label 78400.ey)

• Label: 78400gz
• Number of curves: $4$
• Conductor: $78400$
• CM: no
• Rank: $1$

Elliptic curves in class 78400gz

LMFDB label	Cremona label	Weierstrass coefficients	Torsion structure	Modular degree	Optimality
78400.ey4	78400gz1	[0, 0, 0, 4900, 686000]	[2]	196608	\(\Gamma_0(N)\)-optimal
78400.ey3	78400gz2	[0, 0, 0, -93100, 10290000]	[2, 2]	393216
78400.ey2	78400gz3	[0, 0, 0, -289100, -47334000]	[2]	786432
78400.ey1	78400gz4	[0, 0, 0, -1465100, 682570000]	[2]	786432

Rank

The elliptic curves in class 78400gz have rank \(1\).

Complex multiplication

The elliptic curves in class 78400gz do not have complex multiplication.

Modular form 78400.2.a.gz

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.