Properties

Label 16560.n
Number of curves $6$
Conductor $16560$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("16560.n1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 16560.n

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
16560.n1 16560bi4 [0, 0, 0, -15897603, 24397514498] [2] 294912  
16560.n2 16560bi5 [0, 0, 0, -3719523, -2365109278] [2] 589824  
16560.n3 16560bi3 [0, 0, 0, -1019523, 360270722] [2, 2] 294912  
16560.n4 16560bi2 [0, 0, 0, -993603, 381208898] [2, 2] 147456  
16560.n5 16560bi1 [0, 0, 0, -60483, 6281282] [2] 73728 \(\Gamma_0(N)\)-optimal
16560.n6 16560bi6 [0, 0, 0, 1265757, 1745607458] [2] 589824  

Rank

sage: E.rank()
 

The elliptic curves in class 16560.n have rank \(1\).

Modular form 16560.2.a.n

sage: E.q_eigenform(10)
 
\( q - q^{5} + 4q^{11} - 2q^{13} + 6q^{17} - 4q^{19} + O(q^{20}) \)

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 LMFDB numbering.

\(\left(\begin{array}{rrrrrr} 1 & 8 & 4 & 2 & 4 & 8 \\ 8 & 1 & 2 & 4 & 8 & 4 \\ 4 & 2 & 1 & 2 & 4 & 2 \\ 2 & 4 & 2 & 1 & 2 & 4 \\ 4 & 8 & 4 & 2 & 1 & 8 \\ 8 & 4 & 2 & 4 & 8 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.