Properties

Label 20160be
Number of curves $4$
Conductor $20160$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("20160.bj1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 20160be

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
20160.bj4 20160be1 [0, 0, 0, 1332, 29808] [2] 24576 \(\Gamma_0(N)\)-optimal
20160.bj3 20160be2 [0, 0, 0, -10188, 320112] [2, 2] 49152  
20160.bj2 20160be3 [0, 0, 0, -50508, -4082832] [2] 98304  
20160.bj1 20160be4 [0, 0, 0, -154188, 23302512] [2] 98304  

Rank

sage: E.rank()
 

The elliptic curves in class 20160be have rank \(0\).

Modular form 20160.2.a.bj

sage: E.q_eigenform(10)
 
\( q - q^{5} - q^{7} + 4q^{11} + 6q^{13} - 2q^{17} + O(q^{20}) \)

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.