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Properties

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

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Show commands: SageMath
E = EllipticCurve("o1")
 
E.isogeny_class()
 

Elliptic curves in class 5586.o

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
5586.o1 5586s2 \([1, 0, 1, -7376, -244366]\) \(377149515625/90972\) \(10702764828\) \([2]\) \(6144\) \(0.91345\)  
5586.o2 5586s1 \([1, 0, 1, -516, -2894]\) \(128787625/44688\) \(5257498512\) \([2]\) \(3072\) \(0.56688\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 5586.2.a.o

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