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

• Label: 418950lu
• Number of curves: $4$
• Conductor: $418950$
• CM: no
• Rank: $1$

Elliptic curves in class 418950lu

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
418950.lu4	418950lu1	\([1, -1, 1, 102918145, -854539259353]\)	\(89962967236397039/287450726400000\)	\(-385211465343129600000000000\)	\([2]\)	\(165888000\)	\(3.7845\)	\(\Gamma_0(N)\)-optimal^*
418950.lu3	418950lu2	\([1, -1, 1, -969593855, -10011646715353]\)	\(75224183150104868881/11219310000000000\)	\(15034948421820468750000000000\)	\([2]\)	\(331776000\)	\(4.1311\)	\(\Gamma_0(N)\)-optimal^*
418950.lu2	418950lu3	\([1, -1, 1, -36398651855, -2672850827759353]\)	\(-3979640234041473454886161/1471455901872240\)	\(-1971891639470916599703750000\)	\([2]\)	\(829440000\)	\(4.5892\)
418950.lu1	418950lu4	\([1, -1, 1, -582378481355, -171062857882490353]\)	\(16300610738133468173382620881/2228489100\)	\(2986388528090329687500\)	\([2]\)	\(1658880000\)	\(4.9358\)

^*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 418950lu1.

Rank

The elliptic curves in class 418950lu have rank \(1\).

Complex multiplication

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

Modular form 418950.2.a.lu

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.

\(\left(\begin{array}{rrrr} 1 & 2 & 5 & 10 \\ 2 & 1 & 10 & 5 \\ 5 & 10 & 1 & 2 \\ 10 & 5 & 2 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.