Elliptic curve isogeny class with LMFDB label 4080.ba (Cremona label 4080be)

• Label: 4080.ba
• Number of curves: $8$
• Conductor: $4080$
• CM: no
• Rank: $1$

Elliptic curves in class 4080.ba

LMFDB label	Cremona label	Weierstrass coefficients	Torsion structure	Modular degree	Optimality
4080.ba1	4080be7	[0, 1, 0, -1815520, 940954100]	[8]	49152
4080.ba2	4080be3	[0, 1, 0, -348160, -79187020]	[2]	12288
4080.ba3	4080be5	[0, 1, 0, -115520, 14114100]	[2, 4]	24576
4080.ba4	4080be4	[0, 1, 0, -23040, -1089612]	[2, 4]	12288
4080.ba5	4080be2	[0, 1, 0, -21760, -1242700]	[2, 2]	6144
4080.ba6	4080be1	[0, 1, 0, -1280, -22092]	[2]	3072	\(\Gamma_0(N)\)-optimal
4080.ba7	4080be6	[0, 1, 0, 48960, -6475212]	[4]	24576
4080.ba8	4080be8	[0, 1, 0, 104800, 61791348]	[4]	49152

Rank

The elliptic curves in class 4080.ba have rank \(1\).

Complex multiplication

The elliptic curves in class 4080.ba do not have complex multiplication.

Modular form 4080.2.a.ba

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.

\(\left(\begin{array}{rrrrrrrr} 1 & 16 & 2 & 4 & 8 & 16 & 8 & 4 \\ 16 & 1 & 8 & 4 & 2 & 4 & 8 & 16 \\ 2 & 8 & 1 & 2 & 4 & 8 & 4 & 2 \\ 4 & 4 & 2 & 1 & 2 & 4 & 2 & 4 \\ 8 & 2 & 4 & 2 & 1 & 2 & 4 & 8 \\ 16 & 4 & 8 & 4 & 2 & 1 & 8 & 16 \\ 8 & 8 & 4 & 2 & 4 & 8 & 1 & 8 \\ 4 & 16 & 2 & 4 & 8 & 16 & 8 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with LMFDB labels.