Properties

Label 164080.n
Number of curves 2
Conductor 164080
CM no
Rank 1
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("164080.n1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 164080.n

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
164080.n1 164080j2 [0, 0, 0, -88735387, 321922512074] [] 66382848  
164080.n2 164080j1 [0, 0, 0, 153413, -149478166] [] 9483264 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 164080.n have rank \(1\).

Modular form 164080.2.a.n

sage: E.q_eigenform(10)
 
\( q + 3q^{3} + q^{5} - q^{7} + 6q^{9} - 5q^{11} + 7q^{13} + 3q^{15} - 3q^{17} + 8q^{19} + O(q^{20}) \)

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.

\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.