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

• Label: 458640du
• Number of curves: $4$
• Conductor: $458640$
• CM: no
• Rank: $1$

Elliptic curves in class 458640du

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
458640.du4	458640du1	\([0, 0, 0, -2035803, -1847039222]\)	\(-2656166199049/2658140160\)	\(-933799405967439298560\)	\([2]\)	\(17694720\)	\(2.7195\)	\(\Gamma_0(N)\)-optimal^*
458640.du3	458640du2	\([0, 0, 0, -38162523, -90711545078]\)	\(17496824387403529/6580454400\)	\(2311700677858846310400\)	\([2, 2]\)	\(35389440\)	\(3.0661\)	\(\Gamma_0(N)\)-optimal^*
458640.du2	458640du3	\([0, 0, 0, -43807323, -62111601398]\)	\(26465989780414729/10571870144160\)	\(3713877172143366157762560\)	\([2]\)	\(70778880\)	\(3.4127\)	\(\Gamma_0(N)\)-optimal^*
458640.du1	458640du4	\([0, 0, 0, -610545243, -5806639863542]\)	\(71647584155243142409/10140000\)	\(3562162040586240000\)	\([2]\)	\(70778880\)	\(3.4127\)

^*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 458640du1.

Rank

The elliptic curves in class 458640du have rank \(1\).

Complex multiplication

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

Modular form 458640.2.a.du

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.