Elliptic curve isogeny class with LMFDB label 436800.kn (Cremona label 436800kn)

• Label: 436800.kn
• Number of curves: $4$
• Conductor: $436800$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 436800.kn have rank \(1\).

Complex multiplication

The elliptic curves in class 436800.kn do not have complex multiplication.

Modular form 436800.2.a.kn

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.

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with LMFDB labels.

Elliptic curves in class 436800.kn

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
436800.kn1	436800kn3	\([0, 1, 0, -82357633, -287703503137]\)	\(15082569606665230489/7751016000\)	\(31748161536000000000\)	\([2]\)	\(47775744\)	\(3.0741\)
436800.kn2	436800kn4	\([0, 1, 0, -81909633, -290987791137]\)	\(-14837772556740428569/342100087875000\)	\(-1401241959936000000000000\)	\([2]\)	\(95551488\)	\(3.4206\)
436800.kn3	436800kn1	\([0, 1, 0, -1213633, -231479137]\)	\(48264326765929/22299191460\)	\(91337488220160000000\)	\([2]\)	\(15925248\)	\(2.5248\)	\(\Gamma_0(N)\)-optimal^*
436800.kn4	436800kn2	\([0, 1, 0, 4274367, -1740679137]\)	\(2108526614950391/1540302022350\)	\(-6309077083545600000000\)	\([2]\)	\(31850496\)	\(2.8713\)

^*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 436800.kn1.