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Properties

Label 32490.bg
Number of curves $2$
Conductor $32490$
CM no
Rank $0$
Graph

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

Elliptic curves in class 32490.bg

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
32490.bg1 32490bm2 \([1, -1, 1, -97538, -11515669]\) \(2992209121/54150\) \(1857152618533350\) \([2]\) \(276480\) \(1.7251\)  
32490.bg2 32490bm1 \([1, -1, 1, -68, -521053]\) \(-1/3420\) \(-117293849591580\) \([2]\) \(138240\) \(1.3785\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 32490.bg have rank \(0\).

Complex multiplication

The elliptic curves in class 32490.bg do not have complex multiplication.

Modular form 32490.2.a.bg

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{4} - q^{5} - 2 q^{7} + q^{8} - q^{10} - 6 q^{13} - 2 q^{14} + q^{16} - 8 q^{17} + O(q^{20})\) 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.