Properties

Label 32490bv
Number of curves $4$
Conductor $32490$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("32490.bu1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 32490bv

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
32490.bu3 32490bv1 [1, -1, 1, -100787, 12267011] [4] 184320 \(\Gamma_0(N)\)-optimal
32490.bu2 32490bv2 [1, -1, 1, -165767, -5433541] [2, 2] 368640  
32490.bu4 32490bv3 [1, -1, 1, 646483, -43446841] [2] 737280  
32490.bu1 32490bv4 [1, -1, 1, -2017697, -1101035329] [2] 737280  

Rank

sage: E.rank()
 

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

Modular form 32490.2.a.bu

sage: E.q_eigenform(10)
 
\( q + q^{2} + q^{4} + q^{5} + q^{8} + q^{10} - 4q^{11} - 2q^{13} + q^{16} - 2q^{17} + O(q^{20}) \)

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 Cremona numbering.

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)
 

The vertices are labelled with Cremona labels.