Elliptic curve isogeny class with LMFDB label 444752.cf (Cremona label 444752cf)

• Label: 444752.cf
• Number of curves: $2$
• Conductor: $444752$
• CM: no
• Rank: $1$

Elliptic curves in class 444752.cf

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
444752.cf1	444752cf2	\([0, -1, 0, -8228032, 6374359920]\)	\(1278763167594532/375974556419\)	\(18112567542083645582336\)	\([2]\)	\(26542080\)	\(2.9767\)	\(\Gamma_0(N)\)-optimal^*
444752.cf2	444752cf1	\([0, -1, 0, 1381788, 662282912]\)	\(24226243449392/29774625727\)	\(-358598015685627004672\)	\([2]\)	\(13271040\)	\(2.6302\)	\(\Gamma_0(N)\)-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 444752.cf1.

Rank

The elliptic curves in class 444752.cf have rank \(1\).

Complex multiplication

The elliptic curves in class 444752.cf do not have complex multiplication.

Modular form 444752.2.a.cf

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.