Elliptic curve isogeny class with Cremona label 439569be (LMFDB label 439569.be)

• Label: 439569be
• Number of curves: $4$
• Conductor: $439569$
• CM: no
• Rank: $0$

Elliptic curves in class 439569be

LMFDB label	Cremona label	Weierstrass coefficients	Torsion structure	Modular degree	Optimality
439569.be3	439569be1	[1, -1, 1, -302204, -27246410]	[2]	5308416	\(\Gamma_0(N)\)-optimal^*
439569.be2	439569be2	[1, -1, 1, -2500049, 1503332848]	[2, 2]	10616832	\(\Gamma_0(N)\)-optimal^*
439569.be1	439569be3	[1, -1, 1, -39863414, 96884531020]	[2]	21233664	\(\Gamma_0(N)\)-optimal^*
439569.be4	439569be4	[1, -1, 1, -302204, 4052833048]	[2]	21233664

^*optimality has not been determined rigorously for conductors over 400000. In this case the optimal curve is certainly one of the 3 curves highlighted, and conditionally curve 439569be1.

Rank

The elliptic curves in class 439569be have rank \(0\).

Complex multiplication

The elliptic curves in class 439569be do not have complex multiplication.

Modular form 439569.2.a.be

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.