Elliptic curve isogeny class with Cremona label 418950je (LMFDB label 418950.je)

• Label: 418950je
• Number of curves: $4$
• Conductor: $418950$
• CM: no
• Rank: $2$

Elliptic curves in class 418950je

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
418950.je3	418950je1	\([1, -1, 1, -285228005, 1871206483997]\)	\(-1914980734749238129/20440940544000\)	\(-27392815313289216000000000\)	\([2]\)	\(199065600\)	\(3.6975\)	\(\Gamma_0(N)\)-optimal^*
418950.je2	418950je2	\([1, -1, 1, -4575276005, 119118218323997]\)	\(7903870428425797297009/886464000000\)	\(1187946541971000000000000\)	\([2]\)	\(398131200\)	\(4.0440\)	\(\Gamma_0(N)\)-optimal^*
418950.je4	418950je3	\([1, -1, 1, 942515995, 9739860115997]\)	\(69096190760262356111/70568821500000000\)	\(-94568970056193773437500000000\)	\([2]\)	\(597196800\)	\(4.2468\)
418950.je1	418950je4	\([1, -1, 1, -5107122005, 89703975199997]\)	\(10993009831928446009969/3767761230468750000\)	\(5049160399867057800292968750000\)	\([2]\)	\(1194393600\)	\(4.5933\)

^*optimality has not been determined rigorously for conductors over 400000. In this case the optimal curve is certainly one of the 2 curves highlighted, and conditionally curve 418950je1.

Rank

The elliptic curves in class 418950je have rank \(2\).

Complex multiplication

The elliptic curves in class 418950je do not have complex multiplication.

Modular form 418950.2.a.je

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.

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.