Properties

Label 2166.a
Number of curves $4$
Conductor $2166$
CM no
Rank $0$
Graph

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

Elliptic curves in class 2166.a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
2166.a1 2166b3 \([1, 1, 0, -154515, 23313369]\) \(8671983378625/82308\) \(3872252373348\) \([2]\) \(12960\) \(1.5777\)  
2166.a2 2166b4 \([1, 1, 0, -150905, 24459183]\) \(-8078253774625/846825858\) \(-39839668543190898\) \([2]\) \(25920\) \(1.9243\)  
2166.a3 2166b1 \([1, 1, 0, -2895, -5787]\) \(57066625/32832\) \(1544610364992\) \([2]\) \(4320\) \(1.0284\) \(\Gamma_0(N)\)-optimal
2166.a4 2166b2 \([1, 1, 0, 11545, -31779]\) \(3616805375/2105352\) \(-99048139655112\) \([2]\) \(8640\) \(1.3750\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 2166.2.a.a

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{3} + q^{4} + q^{6} - 4q^{7} - q^{8} + q^{9} - q^{12} + 4q^{13} + 4q^{14} + q^{16} + 6q^{17} - q^{18} + O(q^{20})\)  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.

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.