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Properties

Label 2166f
Number of curves $2$
Conductor $2166$
CM no
Rank $0$
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Show commands: SageMath
E = EllipticCurve("f1")
 
E.isogeny_class()
 

Elliptic curves in class 2166f

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
2166.g2 2166f1 \([1, 1, 1, -967, -11587]\) \(14580432307/559872\) \(3840162048\) \([2]\) \(2240\) \(0.60690\) \(\Gamma_0(N)\)-optimal
2166.g1 2166f2 \([1, 1, 1, -2487, 31581]\) \(248028267187/76527504\) \(524902149936\) \([2]\) \(4480\) \(0.95347\)  

Rank

sage: E.rank()
 

The elliptic curves in class 2166f have rank \(0\).

Complex multiplication

The elliptic curves in class 2166f do not have complex multiplication.

Modular form 2166.2.a.f

sage: E.q_eigenform(10)
 
\(q + q^{2} - q^{3} + q^{4} + 2 q^{5} - q^{6} + 4 q^{7} + q^{8} + q^{9} + 2 q^{10} - 2 q^{11} - q^{12} + 4 q^{13} + 4 q^{14} - 2 q^{15} + q^{16} + 6 q^{17} + q^{18} + O(q^{20})\) Copy content Toggle raw display

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.

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.