Properties

Label 5166.o
Number of curves $2$
Conductor $5166$
CM no
Rank $0$
Graph

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

Elliptic curves in class 5166.o

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
5166.o1 5166r2 \([1, -1, 0, -86501814, 309682215836]\) \(98191033604529537629349729/10906239337336\) \(7950648476917944\) \([]\) \(345744\) \(2.9200\)  
5166.o2 5166r1 \([1, -1, 0, -174174, -25711084]\) \(801581275315909089/70810888830976\) \(51621137957781504\) \([]\) \(49392\) \(1.9471\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 5166.o have rank \(0\).

Complex multiplication

The elliptic curves in class 5166.o do not have complex multiplication.

Modular form 5166.2.a.o

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{4} + q^{5} + q^{7} - q^{8} - q^{10} + 2 q^{11} - q^{14} + q^{16} + 3 q^{17} - 8 q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)

Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)
 

The vertices are labelled with LMFDB labels.