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

• Label: 439569bb
• Number of curves: $2$
• Conductor: $439569$
• CM: no
• Rank: $1$

Elliptic curves in class 439569bb

LMFDB label	Cremona label	Weierstrass coefficients	Torsion structure	Modular degree	Optimality
439569.bb2	439569bb1	[1, -1, 1, -539, 139026]	[2]	688128	\(\Gamma_0(N)\)-optimal^*
439569.bb1	439569bb2	[1, -1, 1, -43634, 3483198]	[2]	1376256	\(\Gamma_0(N)\)-optimal^*

^*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 439569bb1.

Rank

The elliptic curves in class 439569bb have rank \(1\).

Complex multiplication

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

Modular form 439569.2.a.bb

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.

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

Isogeny graph

The vertices are labelled with Cremona labels.