Properties

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

Related objects

Downloads

Learn more about

Show commands for: SageMath
sage: E = EllipticCurve("ba1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 4080.ba

sage: E.isogeny_class().curves
 
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

sage: E.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

sage: E.q_eigenform(10)
 
\( q + q^{3} + q^{5} + q^{9} - 4q^{11} - 2q^{13} + q^{15} + q^{17} - 4q^{19} + O(q^{20}) \)

Isogeny matrix

sage: E.isogeny_class().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

sage: E.isogeny_graph().plot(edge_labels=True)
 

The vertices are labelled with LMFDB labels.