Elliptic curve isogeny class with LMFDB label 78400.by (Cremona label 78400fk)

• Label: 78400.by
• Number of curves: $2$
• Conductor: $78400$
• CM: no
• Rank: $1$

Elliptic curves in class 78400.by

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
78400.by1	78400fk2	\([0, 1, 0, -292833, 60846463]\)	\(553463785/512\)	\(2569011200000000\)	\([]\)	\(622080\)	\(1.8800\)
78400.by2	78400fk1	\([0, 1, 0, -12833, -473537]\)	\(46585/8\)	\(40140800000000\)	\([]\)	\(207360\)	\(1.3307\)	\(\Gamma_0(N)\)-optimal

Rank

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

Complex multiplication

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

Modular form 78400.2.a.by

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.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with LMFDB labels.