Elliptic curve isogeny class with LMFDB label 439824.cs (Cremona label 439824cs)

• Label: 439824.cs
• Number of curves: $4$
• Conductor: $439824$
• CM: no
• Rank: $1$

Elliptic curves in class 439824.cs

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
439824.cs1	439824cs3	\([0, -1, 0, -53740472, 151653218928]\)	\(35618855581745079337/188166132\)	\(90675434551984128\)	\([4]\)	\(21233664\)	\(2.8704\)	\(\Gamma_0(N)\)-optimal^*
439824.cs2	439824cs2	\([0, -1, 0, -3360632, 2367677040]\)	\(8710408612492777/19986042384\)	\(9631080040182644736\)	\([2, 2]\)	\(10616832\)	\(2.5238\)	\(\Gamma_0(N)\)-optimal^*
439824.cs3	439824cs4	\([0, -1, 0, -2153272, 4090821232]\)	\(-2291249615386537/13671036998388\)	\(-6587940175148440829952\)	\([2]\)	\(21233664\)	\(2.8704\)
439824.cs4	439824cs1	\([0, -1, 0, -287352, 7398000]\)	\(5445273626857/3103398144\)	\(1495497475045195776\)	\([2]\)	\(5308416\)	\(2.1772\)	\(\Gamma_0(N)\)-optimal^*

^*optimality has not been determined rigorously for conductors over 400000. In this case the optimal curve is certainly one of the 3 curves highlighted, and conditionally curve 439824.cs1.

Rank

The elliptic curves in class 439824.cs have rank \(1\).

Complex multiplication

The elliptic curves in class 439824.cs do not have complex multiplication.

Modular form 439824.2.a.cs

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.