Elliptic curve isogeny class with Cremona label 414050z (LMFDB label 414050.z)

• Label: 414050z
• Number of curves: $2$
• Conductor: $414050$
• CM: no
• Rank: $1$

Elliptic curves in class 414050z

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
414050.z2	414050z1	\([1, 1, 0, 927300, -287981000]\)	\(397535/392\)	\(-86954979218778125000\)	\([]\)	\(13271040\)	\(2.5130\)	\(\Gamma_0(N)\)-optimal^*
414050.z1	414050z2	\([1, 1, 0, -9423950, 15642592750]\)	\(-417267265/235298\)	\(-52194726276071569531250\)	\([]\)	\(39813120\)	\(3.0623\)	\(\Gamma_0(N)\)-optimal^*

^*optimality has not been determined rigorously for conductors over 400000. In this case the optimal curve is certainly one of the 2 curves highlighted, and conditionally curve 414050z1.

Rank

The elliptic curves in class 414050z have rank \(1\).

Complex multiplication

The elliptic curves in class 414050z do not have complex multiplication.

Modular form 414050.2.a.z

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.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.