Properties

Label 5586.n
Number of curves $2$
Conductor $5586$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("n1")
 
E.isogeny_class()
 

Elliptic curves in class 5586.n

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
5586.n1 5586q2 \([1, 0, 1, -93861, 7699024]\) \(2266158235375/675584064\) \(27262253814118848\) \([2]\) \(43008\) \(1.8592\)  
5586.n2 5586q1 \([1, 0, 1, 15899, 806096]\) \(11015140625/13307904\) \(-537021928009728\) \([2]\) \(21504\) \(1.5126\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 5586.n have rank \(1\).

Complex multiplication

The elliptic curves in class 5586.n do not have complex multiplication.

Modular form 5586.2.a.n

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{3} + q^{4} - q^{6} - q^{8} + q^{9} + q^{12} + q^{16} - 4 q^{17} - q^{18} - q^{19} + O(q^{20})\) 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.