Properties

Label 116928.br
Number of curves $6$
Conductor $116928$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("116928.br1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 116928.br

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
116928.br1 116928ck4 [0, 0, 0, -117863436, -492511936016] [2] 6291456  
116928.br2 116928ck6 [0, 0, 0, -24462156, 37856255344] [2] 12582912  
116928.br3 116928ck3 [0, 0, 0, -7507596, -7385292560] [2, 2] 6291456  
116928.br4 116928ck2 [0, 0, 0, -7366476, -7695474320] [2, 2] 3145728  
116928.br5 116928ck1 [0, 0, 0, -451596, -125063696] [2] 1572864 \(\Gamma_0(N)\)-optimal
116928.br6 116928ck5 [0, 0, 0, 7189044, -32775207824] [2] 12582912  

Rank

sage: E.rank()
 

The elliptic curves in class 116928.br have rank \(0\).

Modular form 116928.2.a.br

sage: E.q_eigenform(10)
 
\( q - 2q^{5} + q^{7} + 4q^{11} + 2q^{13} - 2q^{17} + 4q^{19} + O(q^{20}) \)

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.