Properties

Label 166410.a
Number of curves $4$
Conductor $166410$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("a1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 166410.a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
166410.a1 166410by3 [1, -1, 0, -13953825, 19929326575] [2] 11354112  
166410.a2 166410by2 [1, -1, 0, -1473075, -172169375] [2, 2] 5677056  
166410.a3 166410by1 [1, -1, 0, -1140255, -467780099] [2] 2838528 \(\Gamma_0(N)\)-optimal
166410.a4 166410by4 [1, -1, 0, 5682555, -1358572829] [2] 11354112  

Rank

sage: E.rank()
 

The elliptic curves in class 166410.a have rank \(1\).

Complex multiplication

The elliptic curves in class 166410.a do not have complex multiplication.

Modular form 166410.2.a.a

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

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 LMFDB 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 LMFDB labels.