Elliptic curve isogeny class with Cremona label 404586i (LMFDB label 404586.i)

• Label: 404586i
• Number of curves: $4$
• Conductor: $404586$
• CM: no
• Rank: $1$

Elliptic curves in class 404586i

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
404586.i3	404586i1	\([1, -1, 0, -245673, 27484029]\)	\(466025146777/177366672\)	\(624107870509333392\)	\([2]\)	\(5898240\)	\(2.1139\)	\(\Gamma_0(N)\)-optimal
404586.i2	404586i2	\([1, -1, 0, -1736253, -860603535]\)	\(164503536215257/4178071044\)	\(14701561419089756484\)	\([2, 2]\)	\(11796480\)	\(2.4605\)
404586.i4	404586i3	\([1, -1, 0, 286677, -2747997225]\)	\(740480746823/927484650666\)	\(-3263580827954251994826\)	\([2]\)	\(23592960\)	\(2.8071\)
404586.i1	404586i4	\([1, -1, 0, -27608463, -55828700901]\)	\(661397832743623417/443352042\)	\(1560042231714109962\)	\([2]\)	\(23592960\)	\(2.8071\)

Rank

The elliptic curves in class 404586i have rank \(1\).

Complex multiplication

The elliptic curves in class 404586i do not have complex multiplication.

Modular form 404586.2.a.i

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.

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

Isogeny graph

The vertices are labelled with Cremona labels.