Elliptic curve isogeny class with Cremona label 429429bf (LMFDB label 429429.bf)

• Label: 429429bf
• Number of curves: $2$
• Conductor: $429429$
• CM: no
• Rank: $1$

Elliptic curves in class 429429bf

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
429429.bf2	429429bf1	\([1, 0, 0, 32607, 392976]\)	\(985074875/586971\)	\(-2284561285013007\)	\([2]\)	\(1520640\)	\(1.6364\)	\(\Gamma_0(N)\)-optimal^*
429429.bf1	429429bf2	\([1, 0, 0, -132558, 3134715]\)	\(66184391125/37202781\)	\(144797670016776777\)	\([2]\)	\(3041280\)	\(1.9830\)	\(\Gamma_0(N)\)-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 429429bf1.

Rank

The elliptic curves in class 429429bf have rank \(1\).

Complex multiplication

The elliptic curves in class 429429bf do not have complex multiplication.

Modular form 429429.2.a.bf

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.