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Properties

Label 5390.bf
Number of curves $2$
Conductor $5390$
CM no
Rank $0$
Graph

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

Elliptic curves in class 5390.bf

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
5390.bf1 5390ba2 \([1, 0, 0, -291061, 60415711]\) \(-23178622194826561/1610510\) \(-189474890990\) \([]\) \(33000\) \(1.6180\)  
5390.bf2 5390ba1 \([1, 0, 0, 489, 16841]\) \(109902239/1100000\) \(-129413900000\) \([]\) \(6600\) \(0.81331\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 5390.bf have rank \(0\).

Complex multiplication

The elliptic curves in class 5390.bf do not have complex multiplication.

Modular form 5390.2.a.bf

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{3} + q^{4} - q^{5} + q^{6} + q^{8} - 2 q^{9} - q^{10} + q^{11} + q^{12} + 6 q^{13} - q^{15} + q^{16} + 7 q^{17} - 2 q^{18} - 5 q^{19} + O(q^{20})\) 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.