Elliptic curve isogeny class with Cremona label 449106bm (LMFDB label 449106.bm)

• Label: 449106bm
• Number of curves: $2$
• Conductor: $449106$
• CM: no
• Rank: $1$

Elliptic curves in class 449106bm

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
449106.bm2	449106bm1	\([1, 1, 1, -42489, -3568569]\)	\(-351447414193/22278144\)	\(-537740237991936\)	\([2]\)	\(2457600\)	\(1.5801\)	\(\Gamma_0(N)\)-optimal^*
449106.bm1	449106bm2	\([1, 1, 1, -689849, -220822585]\)	\(1504154129818033/5519808\)	\(133234746466752\)	\([2]\)	\(4915200\)	\(1.9267\)	\(\Gamma_0(N)\)-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 449106bm1.

Rank

The elliptic curves in class 449106bm have rank \(1\).

Complex multiplication

The elliptic curves in class 449106bm do not have complex multiplication.

Modular form 449106.2.a.bm

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.