Elliptic curve isogeny class with LMFDB label 493680.eg (Cremona label 493680eg)

• Label: 493680.eg
• Number of curves: $2$
• Conductor: $493680$
• CM: no
• Rank: $2$

Elliptic curves in class 493680.eg

LMFDB label	Cremona label	Weierstrass coefficients	Torsion structure	Modular degree	Optimality
493680.eg1	493680eg2	[0, 1, 0, -277856, 35917044]	[2]	5898240	\(\Gamma_0(N)\)-optimal^*
493680.eg2	493680eg1	[0, 1, 0, 51264, 3926580]	[2]	2949120	\(\Gamma_0(N)\)-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 493680.eg1.

Rank

The elliptic curves in class 493680.eg have rank \(2\).

Complex multiplication

The elliptic curves in class 493680.eg do not have complex multiplication.

Modular form 493680.2.a.eg

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.