Elliptic curve isogeny class with LMFDB label 414736.by (Cremona label 414736by)

• Label: 414736.by
• Number of curves: $2$
• Conductor: $414736$
• CM: no
• Rank: $1$

Elliptic curves in class 414736.by

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
414736.by1	414736by2	\([0, -1, 0, -12658088, -17328498592]\)	\(12576878500/1127\)	\(20099216529091632128\)	\([2]\)	\(16220160\)	\(2.7439\)	\(\Gamma_0(N)\)-optimal^*
414736.by2	414736by1	\([0, -1, 0, -734428, -311051040]\)	\(-9826000/3703\)	\(-16510070720325269248\)	\([2]\)	\(8110080\)	\(2.3974\)	\(\Gamma_0(N)\)-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 414736.by1.

Rank

The elliptic curves in class 414736.by have rank \(1\).

Complex multiplication

The elliptic curves in class 414736.by do not have complex multiplication.

Modular form 414736.2.a.by

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.