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Properties

Label 204490bg
Number of curves $2$
Conductor $204490$
CM no
Rank $0$
Graph

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

Elliptic curves in class 204490bg

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
204490.cx1 204490bg1 \([1, 0, 0, -20875, -3173015]\) \(-117649/440\) \(-3762434094693560\) \([]\) \(1105920\) \(1.6743\) \(\Gamma_0(N)\)-optimal
204490.cx2 204490bg2 \([1, 0, 0, 183615, 75310247]\) \(80062991/332750\) \(-2845340784112004750\) \([]\) \(3317760\) \(2.2236\)  

Rank

sage: E.rank()
 

The elliptic curves in class 204490bg have rank \(0\).

Complex multiplication

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

Modular form 204490.2.a.bg

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