Elliptic curve isogeny class with Cremona label 400064br (LMFDB label 400064.br)

• Label: 400064br
• Number of curves: $2$
• Conductor: $400064$
• CM: no
• Rank: $0$

Elliptic curves in class 400064br

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
400064.br2	400064br1	\([0, -1, 0, -968989, -366845091]\)	\(-98260901558505084928/10035449471299\)	\(-10276300258610176\)	\([2]\)	\(4672512\)	\(2.1056\)	\(\Gamma_0(N)\)-optimal^*
400064.br1	400064br2	\([0, -1, 0, -15504209, -23492380111]\)	\(25156640481643577374288/262360721\)	\(4298518052864\)	\([2]\)	\(9345024\)	\(2.4521\)	\(\Gamma_0(N)\)-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 400064br1.

Rank

The elliptic curves in class 400064br have rank \(0\).

Complex multiplication

The elliptic curves in class 400064br do not have complex multiplication.

Modular form 400064.2.a.br

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.