Elliptic curve isogeny class with Cremona label 477950bx (LMFDB label 477950.bx)

• Label: 477950bx
• Number of curves: $2$
• Conductor: $477950$
• CM: no
• Rank: $0$

Elliptic curves in class 477950bx

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
477950.bx2	477950bx1	\([1, 0, 0, 2962, -127808]\)	\(103823/316\)	\(-8747082437500\)	\([2]\)	\(983040\)	\(1.1666\)	\(\Gamma_0(N)\)-optimal^*
477950.bx1	477950bx2	\([1, 0, 0, -27288, -1489058]\)	\(81182737/12482\)	\(345509756281250\)	\([2]\)	\(1966080\)	\(1.5132\)	\(\Gamma_0(N)\)-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 477950bx1.

Rank

The elliptic curves in class 477950bx have rank \(0\).

Complex multiplication

The elliptic curves in class 477950bx do not have complex multiplication.

Modular form 477950.2.a.bx

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.