Elliptic curve isogeny class with LMFDB label 422730.ey (Cremona label 422730ey)

• Label: 422730.ey
• Number of curves: $2$
• Conductor: $422730$
• CM: no
• Rank: $1$

Elliptic curves in class 422730.ey

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
422730.ey1	422730ey2	\([1, -1, 1, -44690252, 114960047951]\)	\(13540496380264015726564729/5864914552058284800\)	\(4275522708450489619200\)	\([2]\)	\(47185920\)	\(3.1104\)	\(\Gamma_0(N)\)-optimal^*
422730.ey2	422730ey1	\([1, -1, 1, -2354252, 2380156751]\)	\(-1979497032253723108729/2209921299210240000\)	\(-1611032627124264960000\)	\([2]\)	\(23592960\)	\(2.7638\)	\(\Gamma_0(N)\)-optimal^*

^*optimality has not been determined rigorously for conductors over 400000. In this case the optimal curve is certainly one of the 2 curves highlighted, and conditionally curve 422730.ey1.

Rank

The elliptic curves in class 422730.ey have rank \(1\).

Complex multiplication

The elliptic curves in class 422730.ey do not have complex multiplication.

Modular form 422730.2.a.ey

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.

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

Isogeny graph

The vertices are labelled with LMFDB labels.