Elliptic curve isogeny class with Cremona label 78400gw (LMFDB label 78400.go)

• Label: 78400gw
• Number of curves: $4$
• Conductor: $78400$
• CM: \(\Q(\sqrt{-7}) \)
• Rank: $1$

Elliptic curves in class 78400gw

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality	CM discriminant
78400.go4	78400gw1	\([0, 0, 0, -3500, 98000]\)	\(-3375\)	\(-1404928000000\)	\([2]\)	\(73728\)	\(1.0453\)	\(\Gamma_0(N)\)-optimal	\(-7\)
78400.go3	78400gw2	\([0, 0, 0, -59500, 5586000]\)	\(16581375\)	\(1404928000000\)	\([2]\)	\(147456\)	\(1.3919\)		\(-28\)
78400.go2	78400gw3	\([0, 0, 0, -171500, -33614000]\)	\(-3375\)	\(-165288374272000000\)	\([2]\)	\(516096\)	\(2.0183\)		\(-7\)
78400.go1	78400gw4	\([0, 0, 0, -2915500, -1915998000]\)	\(16581375\)	\(165288374272000000\)	\([2]\)	\(1032192\)	\(2.3648\)		\(-28\)

Rank

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

Complex multiplication

Each elliptic curve in class 78400gw has complex multiplication by an order in the imaginary quadratic field \(\Q(\sqrt{-7}) \).

Modular form 78400.2.a.gw

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.

\(\left(\begin{array}{rrrr} 1 & 2 & 7 & 14 \\ 2 & 1 & 14 & 7 \\ 7 & 14 & 1 & 2 \\ 14 & 7 & 2 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.