Properties

Label 166635n
Number of curves 4
Conductor 166635
CM no
Rank 0
Graph

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Show commands for: SageMath

sage: E = EllipticCurve("166635.n1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 166635n

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
166635.n3 166635n1 [1, -1, 1, -12002, 482456] [2] 360448 \(\Gamma_0(N)\)-optimal
166635.n2 166635n2 [1, -1, 1, -35807, -2002786] [2, 2] 720896  
166635.n4 166635n3 [1, -1, 1, 83218, -12572206] [2] 1441792  
166635.n1 166635n4 [1, -1, 1, -535712, -150774514] [2] 1441792  

Rank

sage: E.rank()
 

The elliptic curves in class 166635n have rank \(0\).

Modular form 166635.2.a.n

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

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 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.