Properties

Label 9680.bb
Number of curves 4
Conductor 9680
CM no
Rank 0
Graph

Related objects

Downloads

Learn more about

Show commands for: SageMath
sage: E = EllipticCurve("9680.bb1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 9680.bb

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
9680.bb1 9680bc4 [0, -1, 0, -859140, -306223300] [2] 103680  
9680.bb2 9680bc3 [0, -1, 0, -53885, -4735828] [2] 51840  
9680.bb3 9680bc2 [0, -1, 0, -12140, -286900] [2] 34560  
9680.bb4 9680bc1 [0, -1, 0, -5485, 154992] [2] 17280 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 9680.bb have rank \(0\).

Modular form 9680.2.a.bb

sage: E.q_eigenform(10)
 
\( q + 2q^{3} + q^{5} - 4q^{7} + q^{9} + 4q^{13} + 2q^{15} - 4q^{19} + O(q^{20}) \)

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.

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.