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Properties

Label 5586d
Number of curves $2$
Conductor $5586$
CM no
Rank $0$
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Show commands: SageMath
E = EllipticCurve("d1")
 
E.isogeny_class()
 

Elliptic curves in class 5586d

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
5586.j1 5586d1 \([1, 1, 0, -4484, -116388]\) \(84778086457/904932\) \(106464344868\) \([2]\) \(7680\) \(0.93177\) \(\Gamma_0(N)\)-optimal
5586.j2 5586d2 \([1, 1, 0, -1054, -285830]\) \(-1102302937/298433646\) \(-35110420018254\) \([2]\) \(15360\) \(1.2783\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 5586.2.a.d

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