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Properties

Label 5610.bk
Number of curves $2$
Conductor $5610$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("bk1")
 
E.isogeny_class()
 

Elliptic curves in class 5610.bk

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
5610.bk1 5610bl2 \([1, 0, 0, -9285, 236097]\) \(88526309511756241/26991954000000\) \(26991954000000\) \([2]\) \(21504\) \(1.2821\)  
5610.bk2 5610bl1 \([1, 0, 0, 1595, 25025]\) \(448733772344879/527357952000\) \(-527357952000\) \([2]\) \(10752\) \(0.93554\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 5610.bk have rank \(1\).

Complex multiplication

The elliptic curves in class 5610.bk do not have complex multiplication.

Modular form 5610.2.a.bk

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{3} + q^{4} + q^{5} + q^{6} - 4 q^{7} + q^{8} + q^{9} + q^{10} + q^{11} + q^{12} - 2 q^{13} - 4 q^{14} + q^{15} + q^{16} - q^{17} + q^{18} - 2 q^{19} + O(q^{20})\) 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.