Elliptic curve isogeny class with LMFDB label 435344.bd (Cremona label 435344bd)

• Label: 435344.bd
• Number of curves: $4$
• Conductor: $435344$
• CM: no
• Rank: $1$

Elliptic curves in class 435344.bd

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
435344.bd1	435344bd4	\([0, 0, 0, -7546019, -7978568078]\)	\(9614292367656708/2093\)	\(10344971506688\)	\([2]\)	\(5505024\)	\(2.3217\)
435344.bd2	435344bd3	\([0, 0, 0, -549419, -80774902]\)	\(3710860803108/1577224103\)	\(7795670523266382848\)	\([2]\)	\(5505024\)	\(2.3217\)	\(\Gamma_0(N)\)-optimal^*
435344.bd3	435344bd2	\([0, 0, 0, -471679, -124635810]\)	\(9392111857872/4380649\)	\(5413006340874496\)	\([2, 2]\)	\(2752512\)	\(1.9751\)	\(\Gamma_0(N)\)-optimal^*
435344.bd4	435344bd1	\([0, 0, 0, -24674, -2603445]\)	\(-21511084032/25465531\)	\(-1966676067529264\)	\([2]\)	\(1376256\)	\(1.6285\)	\(\Gamma_0(N)\)-optimal^*

^*optimality has not been determined rigorously for conductors over 400000. In this case the optimal curve is certainly one of the 0 curves highlighted, and conditionally curve 435344.bd1.

Rank

The elliptic curves in class 435344.bd have rank \(1\).

Complex multiplication

The elliptic curves in class 435344.bd do not have complex multiplication.

Modular form 435344.2.a.bd

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.

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

Isogeny graph

The vertices are labelled with LMFDB labels.