Elliptic curve isogeny class with LMFDB label 464232.r (Cremona label 464232r)

• Label: 464232.r
• Number of curves: $4$
• Conductor: $464232$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 464232.r have rank \(1\).

Complex multiplication

The elliptic curves in class 464232.r do not have complex multiplication.

Modular form 464232.2.a.r

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.

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with LMFDB labels.

Elliptic curves in class 464232.r

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
464232.r1	464232r3	\([0, 1, 0, -632712, 163713888]\)	\(45989074372/7555707\)	\(4602174187768777728\)	\([2]\)	\(9633792\)	\(2.3027\)	\(\Gamma_0(N)\)-optimal^*
464232.r2	464232r2	\([0, 1, 0, -178572, -26661600]\)	\(4135597648/385641\)	\(58723394645442816\)	\([2, 2]\)	\(4816896\)	\(1.9561\)	\(\Gamma_0(N)\)-optimal^*
464232.r3	464232r1	\([0, 1, 0, -174367, -28082890]\)	\(61604313088/621\)	\(5910164517456\)	\([2]\)	\(2408448\)	\(1.6096\)	\(\Gamma_0(N)\)-optimal^*
464232.r4	464232r4	\([0, 1, 0, 208288, -126007248]\)	\(1640689628/12223143\)	\(-7445105164613532672\)	\([2]\)	\(9633792\)	\(2.3027\)

^*optimality has not been determined rigorously for conductors over 400000. In this case the optimal curve is certainly one of the 3 curves highlighted, and conditionally curve 464232.r1.