Properties

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

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Show commands: SageMath
E = EllipticCurve("v1")
 
E.isogeny_class()
 

Elliptic curves in class 5586v

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
5586.w2 5586v1 \([1, 1, 1, 3723, -5314149]\) \(141420761/302579712\) \(-12210182784221184\) \([2]\) \(35840\) \(1.7657\) \(\Gamma_0(N)\)-optimal
5586.w1 5586v2 \([1, 1, 1, -435317, -108400741]\) \(226077997131559/5457072384\) \(220212554354489088\) \([2]\) \(71680\) \(2.1123\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 5586.2.a.v

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