Properties

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

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Show commands for: SageMath
sage: E = EllipticCurve("9680.q1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 9680h

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
9680.q3 9680h1 [0, 0, 0, -242, 1331] [2] 2560 \(\Gamma_0(N)\)-optimal
9680.q2 9680h2 [0, 0, 0, -847, -7986] [2, 2] 5120  
9680.q1 9680h3 [0, 0, 0, -12947, -567006] [2] 10240  
9680.q4 9680h4 [0, 0, 0, 1573, -45254] [2] 10240  

Rank

sage: E.rank()
 

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

Modular form 9680.2.a.q

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

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.

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.