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Properties

Label 2166.e
Number of curves $2$
Conductor $2166$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("e1")
 
E.isogeny_class()
 

Elliptic curves in class 2166.e

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
2166.e1 2166c2 \([1, 0, 1, -897815, -223797814]\) \(248028267187/76527504\) \(24694484082533213616\) \([2]\) \(85120\) \(2.4257\)  
2166.e2 2166c1 \([1, 0, 1, -349095, 76681258]\) \(14580432307/559872\) \(180663806730924288\) \([2]\) \(42560\) \(2.0791\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 2166.2.a.e

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 LMFDB 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 LMFDB labels.