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

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

Elliptic curves in class 439569.be

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
439569.be1	439569be3	\([1, -1, 1, -39863414, 96884531020]\)	\(82483294977/17\)	\(1443876645515769153\)	\([2]\)	\(21233664\)	\(2.8717\)	\(\Gamma_0(N)\)-optimal^*
439569.be2	439569be2	\([1, -1, 1, -2500049, 1503332848]\)	\(20346417/289\)	\(24545902973768075601\)	\([2, 2]\)	\(10616832\)	\(2.5252\)	\(\Gamma_0(N)\)-optimal^*
439569.be3	439569be1	\([1, -1, 1, -302204, -27246410]\)	\(35937/17\)	\(1443876645515769153\)	\([2]\)	\(5308416\)	\(2.1786\)	\(\Gamma_0(N)\)-optimal^*
439569.be4	439569be4	\([1, -1, 1, -302204, 4052833048]\)	\(-35937/83521\)	\(-7093765959418973848689\)	\([2]\)	\(21233664\)	\(2.8717\)

^*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 439569.be1.

Rank

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

Complex multiplication

The elliptic curves in class 439569.be 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 LMFDB 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 LMFDB labels.