Elliptic curve isogeny class with Cremona label 458640nl (LMFDB label 458640.nl)

• Label: 458640nl
• Number of curves: $4$
• Conductor: $458640$
• CM: no
• Rank: $0$

Elliptic curves in class 458640nl

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
458640.nl4	458640nl1	\([0, 0, 0, -8967, -1160026]\)	\(-3631696/24375\)	\(-535180595040000\)	\([2]\)	\(1769472\)	\(1.5095\)	\(\Gamma_0(N)\)-optimal^*
458640.nl3	458640nl2	\([0, 0, 0, -229467, -42217126]\)	\(15214885924/38025\)	\(3339526913049600\)	\([2, 2]\)	\(3538944\)	\(1.8561\)	\(\Gamma_0(N)\)-optimal^*
458640.nl2	458640nl3	\([0, 0, 0, -317667, -6778366]\)	\(20183398562/11567205\)	\(2031768173899376640\)	\([2]\)	\(7077888\)	\(2.2026\)	\(\Gamma_0(N)\)-optimal^*
458640.nl1	458640nl4	\([0, 0, 0, -3669267, -2705310286]\)	\(31103978031362/195\)	\(34251558082560\)	\([2]\)	\(7077888\)	\(2.2026\)

^*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 458640nl1.

Rank

The elliptic curves in class 458640nl have rank \(0\).

Complex multiplication

The elliptic curves in class 458640nl do not have complex multiplication.

Modular form 458640.2.a.nl

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.