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

• Label: 441090.cx
• Number of curves: $4$
• Conductor: $441090$
• CM: no
• Rank: $0$

Elliptic curves in class 441090.cx

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
441090.cx1	441090cx3	\([1, -1, 1, -98440673, 375913784081]\)	\(29981943972267024529/4007065140000\)	\(14099835461295591540000\)	\([2]\)	\(51609600\)	\(3.2692\)	\(\Gamma_0(N)\)-optimal^*
441090.cx2	441090cx4	\([1, -1, 1, -39547553, -91927904623]\)	\(1943993954077461649/87266819409120\)	\(307069576338154706500320\)	\([2]\)	\(51609600\)	\(3.2692\)
441090.cx3	441090cx2	\([1, -1, 1, -6693953, 4779952337]\)	\(9427227449071249/2652468249600\)	\(9333356104530590745600\)	\([2, 2]\)	\(25804800\)	\(2.9226\)	\(\Gamma_0(N)\)-optimal^*
441090.cx4	441090cx1	\([1, -1, 1, 1093567, 490586321]\)	\(41102915774831/53367275520\)	\(-187785767777568030720\)	\([2]\)	\(12902400\)	\(2.5761\)	\(\Gamma_0(N)\)-optimal^*

^*optimality has not been determined rigorously for conductors over 400000. In this case the optimal curve is certainly one of the 3 curves highlighted, and conditionally curve 441090.cx1.

Rank

The elliptic curves in class 441090.cx have rank \(0\).

Complex multiplication

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

Modular form 441090.2.a.cx

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.

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

Isogeny graph

The vertices are labelled with LMFDB labels.