Properties

Label 32490.p
Number of curves $2$
Conductor $32490$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("32490.p1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 32490.p

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
32490.p1 32490r2 [1, -1, 0, -232029, -42955515] [2] 163840  
32490.p2 32490r1 [1, -1, 0, -13149, -799227] [2] 81920 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 32490.p have rank \(1\).

Modular form 32490.2.a.p

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

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.