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Properties

Label 204490.bg
Number of curves $2$
Conductor $204490$
CM no
Rank $1$
Graph

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

Elliptic curves in class 204490.bg

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
204490.bg1 204490cx1 \([1, 0, 1, -1810163, -946500722]\) \(-76711450249/851840\) \(-7284072407326732160\) \([]\) \(7741440\) \(2.4342\) \(\Gamma_0(N)\)-optimal
204490.bg2 204490cx2 \([1, 0, 1, 6062702, -4904977244]\) \(2882081488391/2883584000\) \(-24657488082983714816000\) \([]\) \(23224320\) \(2.9835\)  

Rank

sage: E.rank()
 

The elliptic curves in class 204490.bg have rank \(1\).

Complex multiplication

The elliptic curves in class 204490.bg do not have complex multiplication.

Modular form 204490.2.a.bg

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