Elliptic curve isogeny class with LMFDB label 479808.dw (Cremona label 479808dw)

• Label: 479808.dw
• Number of curves: $4$
• Conductor: $479808$
• CM: no
• Rank: $1$

Elliptic curves in class 479808.dw

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
479808.dw1	479808dw3	\([0, 0, 0, -2244396, 1294163696]\)	\(444893916104/9639\)	\(27089293813972992\)	\([2]\)	\(5505024\)	\(2.2696\)	\(\Gamma_0(N)\)-optimal^*
479808.dw2	479808dw2	\([0, 0, 0, -145236, 18714080]\)	\(964430272/127449\)	\(44772582831427584\)	\([2, 2]\)	\(2752512\)	\(1.9230\)	\(\Gamma_0(N)\)-optimal^*
479808.dw3	479808dw1	\([0, 0, 0, -37191, -2462740]\)	\(1036433728/122451\)	\(672137426084544\)	\([2]\)	\(1376256\)	\(1.5764\)	\(\Gamma_0(N)\)-optimal^*
479808.dw4	479808dw4	\([0, 0, 0, 225204, 98580944]\)	\(449455096/1753941\)	\(-4929248166964789248\)	\([2]\)	\(5505024\)	\(2.2696\)

^*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 479808.dw1.

Rank

The elliptic curves in class 479808.dw have rank \(1\).

Complex multiplication

The elliptic curves in class 479808.dw do not have complex multiplication.

Modular form 479808.2.a.dw

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.