Properties

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

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Show commands: SageMath
E = EllipticCurve("br1")
 
E.isogeny_class()
 

Elliptic curves in class 32490.br

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
32490.br1 32490bq1 \([1, -1, 1, -117032, -17714761]\) \(-14317849/2700\) \(-33428747133600300\) \([]\) \(393984\) \(1.8948\) \(\Gamma_0(N)\)-optimal
32490.br2 32490bq2 \([1, -1, 1, 808933, 86734091]\) \(4728305591/3000000\) \(-37143052370667000000\) \([3]\) \(1181952\) \(2.4441\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 32490.2.a.br

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{4} + q^{5} - q^{7} + q^{8} + q^{10} - 6 q^{11} + 5 q^{13} - q^{14} + q^{16} + O(q^{20})\) 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.