Properties

Label 9680t
Number of curves 4
Conductor 9680
CM no
Rank 1
Graph

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Show commands for: SageMath

sage: E = EllipticCurve("9680.ba1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 9680t

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
9680.ba3 9680t1 [0, -1, 0, -161, 596] [2] 2880 \(\Gamma_0(N)\)-optimal
9680.ba4 9680t2 [0, -1, 0, 444, 3500] [2] 5760  
9680.ba1 9680t3 [0, -1, 0, -5001, -134440] [2] 8640  
9680.ba2 9680t4 [0, -1, 0, -4396, -168804] [2] 17280  

Rank

sage: E.rank()
 

The elliptic curves in class 9680t have rank \(1\).

Modular form 9680.2.a.ba

sage: E.q_eigenform(10)
 
\( q + 2q^{3} - q^{5} + 2q^{7} + q^{9} - 2q^{13} - 2q^{15} + 6q^{17} - 4q^{19} + O(q^{20}) \)

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 Cremona 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 Cremona labels.