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

• Label: 479808nz
• Number of curves: $4$
• Conductor: $479808$
• CM: no
• Rank: $0$

Elliptic curves in class 479808nz

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
479808.nz4	479808nz1	\([0, 0, 0, 27636, 477812720]\)	\(103823/4386816\)	\(-98629108855140777984\)	\([2]\)	\(14155776\)	\(2.5154\)	\(\Gamma_0(N)\)-optimal^*
479808.nz3	479808nz2	\([0, 0, 0, -9004044, 10213963760]\)	\(3590714269297/73410624\)	\(1650496493497746456576\)	\([2, 2]\)	\(28311552\)	\(2.8620\)	\(\Gamma_0(N)\)-optimal^*
479808.nz1	479808nz3	\([0, 0, 0, -143350284, 660610980848]\)	\(14489843500598257/6246072\)	\(140430899131635990528\)	\([2]\)	\(56623104\)	\(3.2085\)	\(\Gamma_0(N)\)-optimal^*
479808.nz2	479808nz4	\([0, 0, 0, -19164684, -17069386768]\)	\(34623662831857/14438442312\)	\(324620567283633160716288\)	\([2]\)	\(56623104\)	\(3.2085\)

^*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 479808nz1.

Rank

The elliptic curves in class 479808nz have rank \(0\).

Complex multiplication

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

Modular form 479808.2.a.nz

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.

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

Isogeny graph

The vertices are labelled with Cremona labels.