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Properties

Label 166410f
Number of curves $2$
Conductor $166410$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("f1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 166410f

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
166410.ct2 166410f1 [1, -1, 1, 2579008, -578956309] [] 8322048 \(\Gamma_0(N)\)-optimal
166410.ct1 166410f2 [1, -1, 1, -29621327, 72605965079] [3] 24966144  

Rank

sage: E.rank()
 

The elliptic curves in class 166410f have rank \(0\).

Complex multiplication

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

Modular form 166410.2.a.f

sage: E.q_eigenform(10)
 
\( q + q^{2} + q^{4} + q^{5} + 2q^{7} + q^{8} + q^{10} + 3q^{11} - 4q^{13} + 2q^{14} + q^{16} + 3q^{17} - q^{19} + O(q^{20}) \)

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.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.