Properties

Label 64009c
Number of curves $2$
Conductor $64009$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("c1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 64009c

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
64009.a2 64009c1 [1, 1, 1, -15881, 763720] [] 75504 \(\Gamma_0(N)\)-optimal
64009.a1 64009c2 [1, 1, 1, -161356, -97589018] [] 830544  

Rank

sage: E.rank()
 

The elliptic curves in class 64009c have rank \(1\).

Complex multiplication

The elliptic curves in class 64009c do not have complex multiplication.

Modular form 64009.2.a.c

sage: E.q_eigenform(10)
 
\( q - q^{2} + 2q^{3} - q^{4} - q^{5} - 2q^{6} - 2q^{7} + 3q^{8} + q^{9} + q^{10} - 2q^{12} - q^{13} + 2q^{14} - 2q^{15} - q^{16} - 5q^{17} - q^{18} + 6q^{19} + O(q^{20}) \)

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.

\(\left(\begin{array}{rr} 1 & 11 \\ 11 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.