Elliptic curve isogeny class with LMFDB label 491568.fv (Cremona label 491568fv)

• Label: 491568.fv
• Number of curves: $2$
• Conductor: $491568$
• CM: no
• Rank: $1$

Elliptic curves in class 491568.fv

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
491568.fv1	491568fv2	\([0, 1, 0, -23569653, -44050959261]\)	\(-3004935183806464000/2037123\)	\(-981669821755392\)	\([]\)	\(13996800\)	\(2.6263\)
491568.fv2	491568fv1	\([0, 1, 0, -284853, -63177885]\)	\(-5304438784000/497763387\)	\(-239867349881499648\)	\([]\)	\(4665600\)	\(2.0770\)	\(\Gamma_0(N)\)-optimal^*

^*optimality has not been determined rigorously for conductors over 400000. In this case the optimal curve is certainly one of the 0 curves highlighted, and conditionally curve 491568.fv1.

Rank

The elliptic curves in class 491568.fv have rank \(1\).

Complex multiplication

The elliptic curves in class 491568.fv do not have complex multiplication.

Modular form 491568.2.a.fv

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.

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

Isogeny graph

The vertices are labelled with LMFDB labels.