Elliptic curve isogeny class with LMFDB label 405600.bf (Cremona label 405600bf)

• Label: 405600.bf
• Number of curves: $2$
• Conductor: $405600$
• CM: no
• Rank: $1$

Elliptic curves in class 405600.bf

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
405600.bf1	405600bf2	\([0, -1, 0, -170408, -7246188]\)	\(14172488/7605\)	\(293663059560000000\)	\([2]\)	\(3096576\)	\(2.0430\)	\(\Gamma_0(N)\)-optimal^*
405600.bf2	405600bf1	\([0, -1, 0, 40842, -908688]\)	\(1560896/975\)	\(-4706138775000000\)	\([2]\)	\(1548288\)	\(1.6964\)	\(\Gamma_0(N)\)-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 405600.bf1.

Rank

The elliptic curves in class 405600.bf have rank \(1\).

Complex multiplication

The elliptic curves in class 405600.bf do not have complex multiplication.

Modular form 405600.2.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 LMFDB numbering.

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

Isogeny graph

The vertices are labelled with LMFDB labels.