Elliptic curve isogeny class with LMFDB label 468468.bs (Cremona label 468468bs)

• Label: 468468.bs
• Number of curves: $2$
• Conductor: $468468$
• CM: no
• Rank: $1$

Elliptic curves in class 468468.bs

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
468468.bs1	468468bs2	\([0, 0, 0, -1008423, -333965970]\)	\(4662947952/717409\)	\(17448503796877241088\)	\([2]\)	\(13271040\)	\(2.4157\)	\(\Gamma_0(N)\)-optimal^*
468468.bs2	468468bs1	\([0, 0, 0, 109512, -28769715]\)	\(95551488/290521\)	\(-441620189073855792\)	\([2]\)	\(6635520\)	\(2.0691\)	\(\Gamma_0(N)\)-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 468468.bs1.

Rank

The elliptic curves in class 468468.bs have rank \(1\).

Complex multiplication

The elliptic curves in class 468468.bs do not have complex multiplication.

Modular form 468468.2.a.bs

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.