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Properties

Label 5610.bg
Number of curves $2$
Conductor $5610$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("bg1")
 
E.isogeny_class()
 

Elliptic curves in class 5610.bg

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
5610.bg1 5610bf2 \([1, 0, 0, -11764986, -15533261340]\) \(-180093466903641160790448289/4344384000\) \(-4344384000\) \([]\) \(136080\) \(2.2968\)  
5610.bg2 5610bf1 \([1, 0, 0, -145146, -21349404]\) \(-338173143620095981729/979226371031040\) \(-979226371031040\) \([3]\) \(45360\) \(1.7475\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 5610.bg have rank \(0\).

Complex multiplication

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

Modular form 5610.2.a.bg

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

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.