Elliptic curve isogeny class with Cremona label 406560ea (LMFDB label 406560.ea)

• Label: 406560ea
• Number of curves: $4$
• Conductor: $406560$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 406560ea have rank \(1\).

Complex multiplication

The elliptic curves in class 406560ea do not have complex multiplication.

Modular form 406560.2.a.ea

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.

\(\left(\begin{array}{rrrr} 1 & 2 & 2 & 2 \\ 2 & 1 & 4 & 4 \\ 2 & 4 & 1 & 4 \\ 2 & 4 & 4 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 406560ea

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
406560.ea3	406560ea1	\([0, 1, 0, -523486, 118462760]\)	\(139927692143296/27348890625\)	\(3100814593569000000\)	\([2, 2]\)	\(5898240\)	\(2.2649\)	\(\Gamma_0(N)\)-optimal^*
406560.ea1	406560ea2	\([0, 1, 0, -7934736, 8599897260]\)	\(60910917333827912/3255076125\)	\(2952481748521536000\)	\([2]\)	\(11796480\)	\(2.6115\)	\(\Gamma_0(N)\)-optimal^*
406560.ea4	406560ea3	\([0, 1, 0, 1077344, 702445544]\)	\(152461584507448/322998046875\)	\(-292971900375000000000\)	\([2]\)	\(11796480\)	\(2.6115\)
406560.ea2	406560ea4	\([0, 1, 0, -2565361, -1475424865]\)	\(257307998572864/19456203375\)	\(141180318135166464000\)	\([2]\)	\(11796480\)	\(2.6115\)

^*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 406560ea1.