Properties

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

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Show commands for: SageMath
sage: E = EllipticCurve("20160.br1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 20160.br

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
20160.br1 20160ei3 [0, 0, 0, -154188, -23302512] [2] 98304  
20160.br2 20160ei4 [0, 0, 0, -50508, 4082832] [2] 98304  
20160.br3 20160ei2 [0, 0, 0, -10188, -320112] [2, 2] 49152  
20160.br4 20160ei1 [0, 0, 0, 1332, -29808] [2] 24576 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Modular form 20160.2.a.br

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 LMFDB numbering.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.