Elliptic curve isogeny class with LMFDB label 441090.bw (Cremona label 441090bw)

• Label: 441090.bw
• Number of curves: $4$
• Conductor: $441090$
• CM: no
• Rank: $1$

Elliptic curves in class 441090.bw

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
441090.bw1	441090bw3	\([1, -1, 0, -12704184, 15960215740]\)	\(64443098670429961/6032611833300\)	\(21227215250959147041300\)	\([2]\)	\(66060288\)	\(3.0225\)	\(\Gamma_0(N)\)-optimal^*
441090.bw2	441090bw2	\([1, -1, 0, -2817684, -1540866560]\)	\(703093388853961/115124490000\)	\(405093580925806890000\)	\([2, 2]\)	\(33030144\)	\(2.6759\)	\(\Gamma_0(N)\)-optimal^*
441090.bw3	441090bw1	\([1, -1, 0, -2696004, -1703114672]\)	\(615882348586441/21715200\)	\(76410224518867200\)	\([2]\)	\(16515072\)	\(2.3294\)	\(\Gamma_0(N)\)-optimal^*
441090.bw4	441090bw4	\([1, -1, 0, 5121936, -8659529852]\)	\(4223169036960119/11647532812500\)	\(-40984683415027157812500\)	\([2]\)	\(66060288\)	\(3.0225\)

^*optimality has not been determined rigorously for conductors over 400000. In this case the optimal curve is certainly one of the 3 curves highlighted, and conditionally curve 441090.bw1.

Rank

The elliptic curves in class 441090.bw have rank \(1\).

Complex multiplication

The elliptic curves in class 441090.bw do not have complex multiplication.

Modular form 441090.2.a.bw

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.

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with LMFDB labels.