Elliptic curve isogeny class with Cremona label 418968be (LMFDB label 418968.be)

• Label: 418968be
• Number of curves: $2$
• Conductor: $418968$
• CM: no
• Rank: $1$

Elliptic curves in class 418968be

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
418968.be2	418968be1	\([0, 0, 0, -7935, -219006]\)	\(54000/11\)	\(11255464712448\)	\([2]\)	\(720896\)	\(1.2199\)	\(\Gamma_0(N)\)-optimal^*
418968.be1	418968be2	\([0, 0, 0, -39675, 2847078]\)	\(1687500/121\)	\(495240447347712\)	\([2]\)	\(1441792\)	\(1.5665\)	\(\Gamma_0(N)\)-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 418968be1.

Rank

The elliptic curves in class 418968be have rank \(1\).

Complex multiplication

The elliptic curves in class 418968be do not have complex multiplication.

Modular form 418968.2.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.