Elliptic curve isogeny class with LMFDB label 490050.iz (Cremona label 490050iz)

• Label: 490050.iz
• Number of curves: $2$
• Conductor: $490050$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 490050.iz have rank \(0\).

Complex multiplication

The elliptic curves in class 490050.iz do not have complex multiplication.

Modular form 490050.2.a.iz

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.

Elliptic curves in class 490050.iz

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
490050.iz1	490050iz1	\([1, -1, 1, -150305, -22397053]\)	\(-6699465/2\)	\(-112106594531250\)	\([]\)	\(3645000\)	\(1.6741\)	\(\Gamma_0(N)\)-optimal^*
490050.iz2	490050iz2	\([1, -1, 1, 76570, -82140803]\)	\(135/8\)	\(-2942125466878125000\)	\([]\)	\(10935000\)	\(2.2234\)	\(\Gamma_0(N)\)-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 490050.iz1.