Properties

Label 2550.bf
Number of curves $2$
Conductor $2550$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("bf1")
 
E.isogeny_class()
 

Elliptic curves in class 2550.bf

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
2550.bf1 2550be2 \([1, 0, 0, -690638, -220971858]\) \(3730569358698025/102\) \(996093750\) \([]\) \(18000\) \(1.6895\)  
2550.bf2 2550be1 \([1, 0, 0, -1628, 432]\) \(19088138515945/11040808032\) \(276020200800\) \([5]\) \(3600\) \(0.88479\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 2550.bf have rank \(0\).

Complex multiplication

The elliptic curves in class 2550.bf do not have complex multiplication.

Modular form 2550.2.a.bf

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{3} + q^{4} + q^{6} + 3 q^{7} + q^{8} + q^{9} - 3 q^{11} + q^{12} + 4 q^{13} + 3 q^{14} + q^{16} + q^{17} + q^{18} - 5 q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.