Elliptic curve isogeny class with LMFDB label 423864.bu (Cremona label 423864bu)

• Label: 423864.bu
• Number of curves: $2$
• Conductor: $423864$
• CM: no
• Rank: $1$

Elliptic curves in class 423864.bu

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
423864.bu1	423864bu2	\([0, 0, 0, -840159, -296326350]\)	\(21882096/7\)	\(20980570109619456\)	\([2]\)	\(4838400\)	\(2.1067\)	\(\Gamma_0(N)\)-optimal^*
423864.bu2	423864bu1	\([0, 0, 0, -45414, -5926527]\)	\(-55296/49\)	\(-9178999422958512\)	\([2]\)	\(2419200\)	\(1.7601\)	\(\Gamma_0(N)\)-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 423864.bu1.

Rank

The elliptic curves in class 423864.bu have rank \(1\).

Complex multiplication

The elliptic curves in class 423864.bu do not have complex multiplication.

Modular form 423864.2.a.bu

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.

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

Isogeny graph

The vertices are labelled with LMFDB labels.