Elliptic curve isogeny class with LMFDB label 62400.f (Cremona label 62400bi)

• Label: 62400.f
• Number of curves: $4$
• Conductor: $62400$
• CM: no
• Rank: $2$

Elliptic curves in class 62400.f

LMFDB label	Cremona label	Weierstrass coefficients	Torsion structure	Modular degree	Optimality
62400.f1	62400bi4	[0, -1, 0, -832033, 292395937]	[4]	589824
62400.f2	62400bi3	[0, -1, 0, -72033, 755937]	[2]	589824
62400.f3	62400bi2	[0, -1, 0, -52033, 4575937]	[2, 2]	294912
62400.f4	62400bi1	[0, -1, 0, -2033, 125937]	[2]	147456	\(\Gamma_0(N)\)-optimal

Rank

The elliptic curves in class 62400.f have rank \(2\).

Complex multiplication

The elliptic curves in class 62400.f do not have complex multiplication.

Modular form 62400.2.a.f

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.