Elliptic curve isogeny class with Cremona label 257600x (LMFDB label 257600.x)

• Label: 257600x
• Number of curves: $2$
• Conductor: $257600$
• CM: no
• Rank: $0$

Elliptic curves in class 257600x

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
257600.x2	257600x1	\([0, 1, 0, -35033, 2569063]\)	\(-74299881664/1958887\)	\(-125368768000000\)	\([2]\)	\(1146880\)	\(1.4878\)	\(\Gamma_0(N)\)-optimal
257600.x1	257600x2	\([0, 1, 0, -564033, 162856063]\)	\(38758598383688/25921\)	\(13271552000000\)	\([2]\)	\(2293760\)	\(1.8343\)

Rank

The elliptic curves in class 257600x have rank \(0\).

Complex multiplication

The elliptic curves in class 257600x do not have complex multiplication.

Modular form 257600.2.a.x

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.

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

Isogeny graph

The vertices are labelled with Cremona labels.