Properties

Label 5586e
Number of curves $2$
Conductor $5586$
CM no
Rank $0$
Graph

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

Elliptic curves in class 5586e

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
5586.k2 5586e1 \([1, 1, 0, 94, -1182]\) \(1843623047/14211126\) \(-696345174\) \([]\) \(3456\) \(0.37827\) \(\Gamma_0(N)\)-optimal
5586.k1 5586e2 \([1, 1, 0, -851, 34917]\) \(-1393520833033/10161910296\) \(-497933604504\) \([]\) \(10368\) \(0.92758\)  

Rank

sage: E.rank()
 

The elliptic curves in class 5586e have rank \(0\).

Complex multiplication

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

Modular form 5586.2.a.e

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{3} + q^{4} + 3 q^{5} + q^{6} - q^{8} + q^{9} - 3 q^{10} + 3 q^{11} - q^{12} + 4 q^{13} - 3 q^{15} + q^{16} - 6 q^{17} - q^{18} - q^{19} + O(q^{20})\) 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 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.