Properties

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

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Show commands for: SageMath
sage: E = EllipticCurve("32490.by1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 32490.by

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
32490.by1 32490br2 [1, -1, 1, -11845922, -15689857579] [2] 1167360  
32490.by2 32490br1 [1, -1, 1, -734342, -249206011] [2] 583680 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Modular form 32490.2.a.by

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

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.