Elliptic curve isogeny class with Cremona label 422331w (LMFDB label 422331.w)

• Label: 422331w
• Number of curves: $2$
• Conductor: $422331$
• CM: no
• Rank: $0$

Elliptic curves in class 422331w

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
422331.w2	422331w1	\([1, 0, 0, -764, 25479]\)	\(-29791/153\)	\(-253306109511\)	\([2]\)	\(552960\)	\(0.87245\)	\(\Gamma_0(N)\)-optimal^*
422331.w1	422331w2	\([1, 0, 0, -18509, 965964]\)	\(423564751/867\)	\(1435401287229\)	\([2]\)	\(1105920\)	\(1.2190\)	\(\Gamma_0(N)\)-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 422331w1.

Rank

The elliptic curves in class 422331w have rank \(0\).

Complex multiplication

The elliptic curves in class 422331w do not have complex multiplication.

Modular form 422331.2.a.w

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.