Elliptic curve isogeny class with Cremona label 457776be (LMFDB label 457776.be)

• Label: 457776be
• Number of curves: $2$
• Conductor: $457776$
• CM: no
• Rank: $0$

Elliptic curves in class 457776be

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
457776.be2	457776be1	\([0, 0, 0, 235824, -92290705]\)	\(1048576/3267\)	\(-4518943775103113136\)	\([2]\)	\(8146944\)	\(2.2628\)	\(\Gamma_0(N)\)-optimal^*
457776.be1	457776be2	\([0, 0, 0, -2196111, -1076251606]\)	\(52927184/8019\)	\(177471246440413170432\)	\([2]\)	\(16293888\)	\(2.6094\)	\(\Gamma_0(N)\)-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 457776be1.

Rank

The elliptic curves in class 457776be have rank \(0\).

Complex multiplication

The elliptic curves in class 457776be do not have complex multiplication.

Modular form 457776.2.a.be

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.