Properties

Label 86640cy
Number of curves $2$
Conductor $86640$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("86640.ch1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 86640cy

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
86640.ch2 86640cy1 [0, 1, 0, -3616, 84980] [2] 92160 \(\Gamma_0(N)\)-optimal
86640.ch1 86640cy2 [0, 1, 0, -58336, 5403764] [2] 184320  

Rank

sage: E.rank()
 

The elliptic curves in class 86640cy have rank \(1\).

Modular form 86640.2.a.ch

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

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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.