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Properties

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

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Show commands: SageMath
E = EllipticCurve("x1")
 
E.isogeny_class()
 

Elliptic curves in class 5586x

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
5586.x2 5586x1 \([1, 1, 1, -49736, -4015159]\) \(115650783909361/8339853312\) \(981175402303488\) \([2]\) \(64512\) \(1.6233\) \(\Gamma_0(N)\)-optimal
5586.x1 5586x2 \([1, 1, 1, -159496, 19693001]\) \(3814038123905521/773540010432\) \(91006208687314368\) \([2]\) \(129024\) \(1.9699\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 5586.2.a.x

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