Properties

Label 16562bo
Number of curves 6
Conductor 16562
CM no
Rank 1
Graph

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Show commands for: SageMath

sage: E = EllipticCurve("16562.bv1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 16562bo

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
16562.bv5 16562bo1 [1, 1, 1, -4313, -222461] [2] 34560 \(\Gamma_0(N)\)-optimal
16562.bv4 16562bo2 [1, 1, 1, -87123, -9927793] [2] 69120  
16562.bv6 16562bo3 [1, 1, 1, 37092, 4630205] [2] 103680  
16562.bv3 16562bo4 [1, 1, 1, -294148, 50208829] [2] 207360  
16562.bv2 16562bo5 [1, 1, 1, -1412083, 647136433] [2] 311040  
16562.bv1 16562bo6 [1, 1, 1, -22611443, 41375346865] [2] 622080  

Rank

sage: E.rank()
 

The elliptic curves in class 16562bo have rank \(1\).

Modular form 16562.2.a.bv

sage: E.q_eigenform(10)
 
\( q + q^{2} + 2q^{3} + q^{4} + 2q^{6} + q^{8} + q^{9} + 2q^{12} + q^{16} - 6q^{17} + q^{18} + 2q^{19} + O(q^{20}) \)

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.

\(\left(\begin{array}{rrrrrr} 1 & 2 & 3 & 6 & 9 & 18 \\ 2 & 1 & 6 & 3 & 18 & 9 \\ 3 & 6 & 1 & 2 & 3 & 6 \\ 6 & 3 & 2 & 1 & 6 & 3 \\ 9 & 18 & 3 & 6 & 1 & 2 \\ 18 & 9 & 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.