Elliptic curve isogeny class with LMFDB label 416955.be (Cremona label 416955be)

• Label: 416955.be
• Number of curves: $2$
• Conductor: $416955$
• CM: no
• Rank: $1$

Elliptic curves in class 416955.be

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
416955.be1	416955be2	\([0, -1, 1, -303721, 64530177]\)	\(-65860951343104/3493875\)	\(-164372427478875\)	\([]\)	\(3102624\)	\(1.7956\)	\(\Gamma_0(N)\)-optimal^*
416955.be2	416955be1	\([0, -1, 1, -481, 235716]\)	\(-262144/509355\)	\(-23963054716755\)	\([]\)	\(1034208\)	\(1.2463\)	\(\Gamma_0(N)\)-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 416955.be1.

Rank

The elliptic curves in class 416955.be have rank \(1\).

Complex multiplication

The elliptic curves in class 416955.be do not have complex multiplication.

Modular form 416955.2.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 LMFDB numbering.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with LMFDB labels.