Elliptic curve isogeny class with LMFDB label 466578.eq (Cremona label 466578eq)

• Label: 466578.eq
• Number of curves: $2$
• Conductor: $466578$
• CM: no
• Rank: $1$

Elliptic curves in class 466578.eq

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
466578.eq1	466578eq2	\([1, -1, 1, -84105545, -292300223295]\)	\(5182207647625/91449288\)	\(1161082590020204793652872\)	\([2]\)	\(77856768\)	\(3.4139\)	\(\Gamma_0(N)\)-optimal^*
466578.eq2	466578eq1	\([1, -1, 1, -121505, -13103680719]\)	\(-15625/5842368\)	\(-74177414801645736595392\)	\([2]\)	\(38928384\)	\(3.0673\)	\(\Gamma_0(N)\)-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 466578.eq1.

Rank

The elliptic curves in class 466578.eq have rank \(1\).

Complex multiplication

The elliptic curves in class 466578.eq do not have complex multiplication.

Modular form 466578.2.a.eq

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.

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with LMFDB labels.